Ocean Dynamics DOI 10.1007/s10236-006-0078-x
Harvey Seim . Jackson Blanton . Susan Elston
Tidal circulation and energy dissipation in a shallow, sinuous estuary
Received: 15 June 2005 / Accepted: 24 March 2006 # Springer-Verlag 2006
Abstract The tidal dynamics in a pristine, mesotidal (>2 m range), marsh-dominated estuary are examined using moored and moving vessel field observations. Analysis focuses on the structure of the M2 tide that accounts for approximately 80% of the observed tidal energy, and indicates a transition in character from a near standing wave on the continental shelf to a more progressive wave within the estuary. A slight maximum in water level (WL) occurs in the estuary 10–20 km from the mouth. M2 WL amplitude decreases at 0.015 m/km landward of this point, implying head of tide approximately 75 km from the mouth. In contrast, tidal currents in the main channel 25 km inland are twice those at the estuary mouth. Analysis suggests the tidal character is consistent with a strongly convergent estuarine geometry controlling the tidal response in the estuary. First harmonic (M4) current amplitude follows the M2 WL distribution, peaking at mid-estuary, whereas M4 WL is greatest farther inland. The major axis current amplitude is strongly influenced by local bathymetry and topography. On most bends a momentum core shifts from the inside to outside of the bend moving seaward, similar to that seen in unidirectional river flow but with point bars shifted seaward of the bends. Dissipation rate estimates, based on changes in energy flux, are 0.18–1.65 W m−2 or 40–175 μW kg–1. A strong (0.1 m/s), depth-averaged residual flow is produced at the bends, which resembles flow around headlands, forming counter-rotating eddies that Responsible editor: Paulo Salles H. Seim (*) Department of Marine Sciences, University of North Carolina, 12-7 Venable Hall, CB#3300, Chapel Hill, NC 27599, USA e-mail:
[email protected] J. Blanton . S. Elston Skidaway Institute of Oceanography, 10 Ocean Science Circle, Savannah, GA 31411, USA e-mail:
[email protected] e-mail:
[email protected]
meet at the apex of the bends. A large sub-basin in the estuary exhibits remarkably different tidal characteristics and may be resonant at a harmonic of the M2 tide. Keywords Tides . Estuaries . Dissipation . Convergent topography . Tidal propagation
1 Introduction Tides are often responsible for the bulk of the kinetic energy present in estuaries. They play a critical role in determining the strength of vertical mixing in an estuary, can produce significant residual (mean) circulation, and drive lateral circulations within the estuary (Geyer et al. 2000; Ianniello 1977, 1979; Li and O’Donnell 1997). In estuaries, tidal propagation has often been viewed as the superposition of incident and reflected waves under the influence of friction (e.g., Ippen 1966; Harleman 1966), and observations interpreted in terms of standing or progressive waves. It is now understood that strongly convergent topographies can dramatically alter the nature of tidal propagation and require markedly different interpretations of observed amplitude and phase patterns (Jay 1991; Friedrichs and Aubrey 1994; Lanzoni and Seminara 1998; Blanton et al. 2002; Prandle 2003). We in this study present detailed observations of the spatial structure of the surface tides and depth-averaged tidal currents in the Satilla River estuary, an essentially pristine salt-marsh estuary along the coastline of Georgia, USA. A principal finding of this study is that the tidal propagation suggests that the estuary exhibits strongly convergent geometry. We therefore make comparison of the observations against the solutions of Friedrichs and Aubrey (1994) to better understand the factors controlling the tidal response in the estuary. We also note that the Satilla River, which lies at the center of the South Atlantic Bight, experiences some of the largest tides in the southeast US. A recent study (Blanton et al. 2004) indicates that the presence of an extensive estuarine/tidal inlet complex (ETIC) along this coastline significantly modifies the semidiurnal tides across much of
Fig. 1 Bathymetric map of the Satilla River showing station locations. Elevations below mean low water (MLW) are positive; those above are negative. The –2 m boundary marks the limit of the intertidal area. The survey domains discussed in the text are bounded by the following stations: domain AB—station 3 to station 4; domain CD—station 4 to station 6 and station 7
the continental shelf and plays an important role in setting the tidal characteristics. Simulations of shelf tides with varying geometries indicate that inclusion of the ETIC increases tidal amplitude 5–10% well out onto the shelf. Hence, there is renewed interest in understanding the detailed nature of the tides in the estuaries to better understand the coupling between the shelf and inshore waters. Our hope is that by better understanding the nature of tidal propagation in the estuary, we can further our understanding of the tidal solutions within the entire Bight. The sinuous geometry of the Satilla River estuary is also characteristic of many of the estuaries along the South Atlantic Bight. Understanding the role that channel geometry plays in setting the tidal and residual circulation is largely unexplored, and we in this study take a first look at its influence. We find that the channel bends produce marked variability in the tidal current amplitude and phases similar to that observed in rivers and impart a tidal residual circulation within the estuary reminiscent of that around headlands. The reasonably dense observing array enables an estimate of the tidal energy flux into the system. We estimate the dissipation rate within the estuary as the divergence of this flux. This type of budget calculation to estimate dissipation rates complements recent intensive field programs to more directly measure dissipation rates (e.g., Peters 2003; Simpson et al. 2004). We find the dissipation rate to be enhanced in the region of a channel junction, suggesting that these types of features may play an important role in the energy budget of the estuary.
2 Background The Satilla River, a shallow coastal plain river near the Georgia/Florida border, is a partially mixed estuary which
experiences 1 to 2.5-m range semidiurnal tides. It has a drainage basin of 9,143 km2 and a length of about 362 km from its headwaters to the Atlantic Ocean (Dame et al. 2000; Blanton et al. 2001). The peak axial currents at spring tide are 1 to 1.5 m s1 while the peak axial currents at neap tide are weaker and vary between 0.3 and 0.65 m–1 (Seim et al. 2002; Blanton et al. 2002). The Satilla has an average discharge of less than 80 m3 s1 but can vary from 0 to 150 m3 s–1 over an annual cycle (Blanton et al. 2001; USGS 2004). The main channel of the Satilla is marked by nine channel bends and two short straight reaches that extend from its mouth between Jekyll and Cumberland Islands to 38 km upriver. The majority of these bends are broadly concave (bends to the north, radius of curvature 1,200 m) each followed by more sharp convex bends (to the south, radius of curvature 800 m). A triple junction near river Table 1 Location of moorings in the Satilla for the SAT1 and SAT2 experiments SAT1
SAT2
Station
Latitude
Longitude
1 2 LT1 3 4 4a 5 6 7 (WOC) LT2
30 59:9390 30 59:7500 30 58:4000 30 59:5900 30 58:5900
81 24:1300 81 27:5290 81 30:7800 81 31:5590 81 34:3700
30 59:7990 30 58:0390 31 00:8700
81 38:1800 81 39:4690 81 38:3990
Latitude
Longitude
30 59:7390 30 58:4000 30 59:5900 30 58:6260 30 58:2500 30 59:8020 30 58:0160 31 00:8700 30 58:4500
81 27:5810 81 30:7800 81 31:5540 81 34:4020 81 34:6500 81 38:1820 81 39:4740 81 38:3190 81 43:6100
Table 2 Stations of moored instrumentation for SAT1 and SAT2 Station
1
2
LT1
3
4
4a
5
6
7
LT2
Distance (km) Depth (m) HW width (m) LW width (m) Parameters (SAT1) Parameters (SAT2)
0 9.8 5,600 5,200 P, CB _
4 8.9 3,800 3,000 P, CP P, CB
10 3.4 5,400 1,500 P P
13 9.3 3,800 1,100 P, CB P, CB
18 7.9 6,000 900 P, CP P, CP
18 5.0 6,000 900 _ P, CB
25 9.6 6,000 500 P, CB P, CP
30 8.5 2,300 200 P, CB P, CP
WOC + 4 10.2 3,600 170 P, CB P, CP
39 4.3 1,400 300 _ P
Station 4a is separated from station 4 by a shoal which emerges at low water. Station 7 is in White Oak Creek (WOC). Distance is measured from the mouth of the estuary. Station depth was calculated from bottom pressure using UNESCO (1985) protocol. LW and HW widths calculated from regional GIS data by Alice Chalmers, University of Georgia P Subsurface pressure from SeaBird sensors, CB bottom current from InterOcean S-4, CP current profile from RDI workhorse
km 26 marks the mouth of White Oak Creek (WOC), a subbasin tidal creek that enters the Satilla River from the north (Fig. 1). Upriver, beyond the triple junction at river km 26, the Satilla is a nearly fresh river where mariculture (crawfish farms) and old rice plantations still thrive. The bathymetry of the system is complex because there is no maintained navigation channel on the Satilla. A significant challenge to the observational program is defining the bathymetry, which has not been fully surveyed since the late 1920s. At low tide, many of the reaches between channel bends seaward of the triple junction have midchannel sand bars that effectively divide the main estuarine channel in two, often referred to as flood (shallower) and ebb (deeper) tide channels (Sexton and Hayes 1996). The two channels are not always obvious on navigation charts. The flood and ebb tidal channels typically have widths between 200 and 500 m. Figure 1 shows most of these features clearly. Another geometric feature worth noting is the broad fringing marsh. The high water width of the estuary is typically 5–10 times that of the low water width and reflects the large intertidal area within the Satilla. However, swift tidal currents are restricted to the main channels, and below, we consider the low water widths to be more representative of the momentum carrying breadth of the estuary.
3 Observations In 1999, we undertook two, 2-month long field efforts in the Satilla River estuary, designed to sample high (winter/ spring, January 20 to March 20) and low (fall, September 9 to October 19) river discharge conditions. These were designated SAT1 and SAT2, respectively. In each case, two sampling schemes were employed: a series of alongchannel moorings (Table 1), deployed for the full 2-month period; and several intensive small-boat sampling exercises, designed to yield a picture of the three-dimensional variability of the circulation and density field over the tidal cycle for a limited reach of the estuary. Mooring locations are shown in Fig. 1. The mooring array used ADCPs and Interocean S4 current meters to measure currents, and SBE Seacats to measure pressure, temperature, and conductivity (Table 2).
Therefore, in some locations, full-depth velocity profiles were available, while in other locations, currents were observed at a single depth. For the intensive small-boat sampling exercises, we occupied four adjacent sections of the estuary designated as sections A through D (Fig. 1), once at spring tide and once at neap tides. Each sampling period lasted approximately 13 h, during which a small vessel towed a 600 kHz broadband ADCP suspended from a sled around a predefined track at 3 m/s. The vessel stopped at a number of predefined stations to collect CTD profiles on each circuit, and this limited the number of times the track was completed to 10–11 times over the 13-h period. We refer to these intensive sampling efforts as roving samples. The eight roving sampling periods were split between the high (reaches A and B) and low (reaches C and D) river discharge mooring programs. The field program was in general quite successful. Though some surface buoys with attached CTDs were lost, the other moored instrumentation was recovered. Some S4s failed to record for the designed lifetime. We were able to execute seven of the eight planned roving samples; one had to be canceled because of the forced coastal evacuation associated with Hurricane Floyd. Our focus in this paper is on the depth-averaged tidal and mean circulation in the estuary. We first examine the moored observations, which give a straightforward impression of the tidal propagation within the estuary. We then reexamine the tides using the roving sampling, which present a more complicated picture of the tidal current dynamics and the importance of local topography. This is followed by an estimation of the tidal energy flux into the estuary and the energy dissipation this implies.
4 Analysis 4.1 Moored observations The tidal characteristics were determined for all water level (WL) and current time series observations. For locations with ADCPs, the observations were masked to remove measurements contaminated by interference with the surface, then depth-averaged to produce a vector time
Table 3 “T_TIDE” (Pawlowicz et al. 2002) output for bottom pressure at station 4 Tide
amp
pha
snr
MM MSF O1 K1 N2 M2 S2 MN4 M4 MS4 2MN6 M6 M8
0.0270.012 0.0500.013 0.0780.014 0.1010.014 0.1800.027 0.9250.027 0.1530.024 0.0290.011 0.0650.010 0.0250.009 0.0180.006 0.0290.007 0.0040.003
12528 5615 22011 2237 368 481 7910 32119 3358.60 34924 22320 23913 6140
5.1 15 30 55 44 1,200 40 7.5 47 8.2 10 20 2.1
Tabulated are the tidal amplitude (amp) in meters, phase (pha) in degrees with the 95% confidence interval estimates, and signal to noise ratio (snr) Number of observations = 9,283, and record length was 38.68 days. Start time was 09-Sep-1999. Rayleigh criterion was set to 1.0. Greenwich phase computed with nodal corrections applied to amplitude and phase relative to center time. Mean pressure was 7.26 db and data trend = 0. Percent variance predicted/ variance original = 94.4%
series. These time series, along with those collected with pressure gauges and by the S4 current meters, were then subjected to a harmonic analysis (Pawlowicz et al. 2002) to estimate tidal constituent parameters. The tidal analysis
includes an estimate of errors (Tables 3 and 4); statistically significant constituent parameters were identified as those for which the sea level or current tidal analysis gave signal to noise values greater than 5. For the mooring locations in mid-estuary, we found that the tidal current amplitude measured 1 m above the bottom was 0.85 to 0.89 of the depth-averaged tidal current and therefore had applied a scaling of 1/0.87 to the S4 calculated tidal current amplitude estimates for comparison with the ADCP observations. 4.2 Moving vessel observations The processed, depth-averaged, 15-s averaged roving ADCP observations were analyzed on a 200-m grid. For each cell in the sampling grid, a simple least-squares fit was used to estimate the mean, tidal current ellipse parameters at semidiurnal and quatradiurnal frequencies, and an error term for the time series of current observations in the cell. The fit was performed for a grid cell if there were a minimum of seven clusters of observation times over the tidal cycle. Often there was more than one 15-s average in a grid cell from a circuit, in which case multiple current estimates were included. Typically, there were nine or ten sets of current observations per grid cell over the 13-h sampling period. The root-mean-square values of the errors average at 1.6 cm/s during spring tides and 1.3 cm/s during neap tides. There were some differences in the coverage between spring and neap tide surveys largely because during spring tides, some shallows became impassable at
Table 4 “T_TIDE” (Pawlowicz et al. 2002) output for tidal ellipse parameters of the vertically averaged velocity at station 4 Tide
major
inc
pha
snr
MM MSF O1 K1 N2 M2 S2 MN4 M4 MS4 2MN6 M6 M8
0.040.00 0.030.00 0.040.01 0.040.01 0.120.02 0.640.02 0.110.02 0.030.01 0.100.01 0.030.01 0.040.01 0.070.01 0.030.01
1280 1330 1318 1286 1308 1292 1318 13223 1307 13427 12917 1299 12812
1940 1940 1468 1496 3449 3512 2510 22328 2069 24827 16717 1849 4510
4.9e+04 3.1e+04 56 67 49 1.5e+03 30 5.2 44 6 13 32 24
Tabulated are the major axis amplitudes (major) in ms1 , inclination (inc) in degrees relative to east, and phase (pha) in degrees, each with the 95% confidence interval estimates given to the right of each parameter. Signal to noise ratio (snr) is given in the last column Number of observations = 4,642, and record length was 38.68 days. Start time was 09-Sep-1999. Rayleigh criterion was set to 1.0. Greenwich phase computed with nodal corrections applied to amplitude and phase relative to center time. Mean east and north velocities were 0.0749 and −0.0828 ms1 , respectively, and data trend for both components = 0. Percent variance predicted/variance for original for east and north components = 96.5 and 96.3%, respectively
low water. The most dramatic example was in domain A where we were unable to adequately sample the shallower channel to the west of the marsh island near mooring 3.
5 Results 5.1 Moored observations 5.1.1 M2 Tide Plots of the M2 tidal harmonics along the Satilla River reveal a steady change in the character of the tidal wave from the shelf to the headwaters of the estuary. The M2 WL amplitude peaks between the inlet and the triple junction (Fig. 2) in the lower 20 km of the estuary and then begins to decrease steadily upstream of the triple junction along the main trunk of the Satilla River. The one measurement point in WOC, the largest branch off the Satilla River in the estuary, shows increased amplitude and suggests that this sub-basin may be resonant in some sense. The trend in WL is in contrast to the steady increase in amplitude observed on the shelf where the WL increases from 0.6 m at the shelf break to 0.95 m at the inlet mouth, a distance of 120 km (Blanton et al. 2004). Extrapolating the offshore amplitude increase into the estuary would suggest that the WL amplitude should be 9 cm larger at the triple junction than is observed, and emphasizes the change in propagation behavior from the shelf to the estuarine setting. Phase of M2 WL increases nearly linearly within the estuary at close to 1.5°/km, nearly ten times the rate of
M2 Water Level Amplitude 1 SAT 1 SAT 2
0.95 Sta 7 Sta 4a
meter
0.9 0.85 0.8 0.75 1 0.7
2
0
LT1 5
3
10
5
6
15 20 25 Distance from ocean (km)
4
30
LT2 35
40
M2 Water Level Phase 80 SAT 1 SAT 2
70 60 degree
Fig. 2 Change in M2 WL tidal amplitude (top panel) and M2 phase (bottom panel) along the main channel during SAT1 (red) and SAT2 (blue). The offset in values between the two deployments is associated with a seasonal cycle of the tide in the South Atlantic Bight. Station 4a, located in the secondary channel, and station 7, in WOC, are marked by asterisks. See Tables 1 and 2 for station information
phase change observed on the shelf. The Greenwich phase observed at the mouth of the Satilla merges smoothly with the values and cotidal charts in Blanton et al. (2004), indicating that a robust depiction of the regional tidal structure is emerging. The change in amplitude and phase of the M2 WL at the seaward boundary of the barrier islands suggests that the tide is increasingly progressive in nature within the estuary and more reflective seaward of this boundary. It is worth noting that SAT1 and SAT2 suggest significant differences in the WL amplitude and phase. The sense of the differences (amplitude greater in SAT1, phase angle greater in SAT2) is consistent with the analysis of 10 years of WL observations by Blanton et al. (2004). They found that amplitude peaked in spring and was minimum in fall, with a range of variability of about 5%, and that phase was greatest in fall and least in spring, varying by 4–5°. Our observations jibe with these earlier results but provide no explanation for the variability. The M2 velocity major axis amplitude increases significantly moving inland (Fig. 3). Exceptions are at station 4a (amplitude lower by 30%) and in WOC (station 7). The one station that was occupied with both types of current meters shows quite different values of current but the locations of the moorings were not identical (see Table 1). The repeated occupation at station 4 suggests that the seasonal variations seen in the WLs are also present in the currents. The growth in major axis amplitude along the main channel is likely related to the decreasing (low water) channel width (Table 2). Forming tidal transport as the product of the low water channel width, depth, and major
Sta 7
50
Sta 4a
40 30 1 20
0
2
LT1 5
10
3
4
5
6
15 20 25 Distance from ocean (km)
30
LT2 35
40
axis amplitude reveals a regular decrease in upstream mass transport carried by the tide, as one would anticipate. This assumes that the transport is carried entirely in the main channel and that the marsh fills laterally. Hence, the velocity increase is consistent with a response to convergent geometry in the estuary and is explored further in the discussion. The velocity phase increases at roughly 2°/km within the estuary, a somewhat greater rate than observed for the WLs. Extrapolating observed values to the mouth of the estuary suggests a current phase there of approximately 320° Greenwich. Though not obvious in the cotidal charts presented in Blanton et al. (2004), there is a rapid phase increase on the seaward side of the inlets such that phases in the inlet mouths along the Georgia coast are roughly 30° later than offshore of the barrier islands (B. Blanton, personal communication). Therefore, the observed tidal current phases mesh with existing offshore values. The rate of phase change in the estuary is more than 20 times that on the shelf and again suggests a major transition in character of the tide once it enters the inlets. The phase difference between velocity and WL (Fig. 4) is everywhere less than 90° and decreases appreciably moving inshore. The cause of the change in phase difference is difficult to determine in a frictional, convergent geometry (Jay 1991; Friedrichs and Aubrey 1994) but has important implications for the energy flux carried by the tide. Previous results suggested that the tide is increasingly progressive in nature as it enters the estuary and moves inshore and is consistent with the decreasing phase difference. Note, however, the sharp increase of the
5.1.2 Overtides Friction and channel convergence in the Satilla generate significant energy in the shallow-water constituents (Blanton et al. 2002). M4 is generated primarily through nonlinear terms in the equations of motion and continuity, but friction can also play a minor role (Parker 1991). In the Satilla, WL distortion (M4 =M2 ) is less than 0.1 except for station 7 in WOC (Fig. 5). The phase of M4 WL relative to that of M2 , expressed as (2M2 M4 ), is remarkably steady, slowly increasing in the landward direction from 110 to 140° in the main channel (Fig. 5—bottom panel). The value of 2M2 M4 increases to about 150° in WOC. Values of 2M2 M4 close to 90° indicate maximum distortion in favor of ebb-dominant currents (Friedrichs and Aubrey 1988), and the increase in WOC to a value approaching 180° suggests that the distortion becomes a little more symmetric. For velocity, M4 =M2 reaches a maximum of 0.16 near km 10. The along-channel distribution resembles that of the M2 WL amplitude. M4 =M2 is quite small up the main channel after passing the triple junction at the entrance to WOC but jumps to more than 0.20 inside WOC proper. Values of 2M2 M4 for velocity increase, moving inland from 100 to 170 in the main channel as far as station 5. This M2 Velocity Amplitude
1 SAT 1 SAT 2
0.9
ms
-1
0.8 0.7 0.6 Sta 7
0.5 Sta 4a 0.4 0.3
2 0
3 5
10
4 15 20 Distance from ocean (km)
5 25
6 30
35
M2 Velocity Phase 380 SAT 1 SAT 2
370 360 degree
Fig. 3 Change in M2 tidal current major axis amplitude (top panel) and phase (bottom panel) along the main channel during SAT1 (red) and SAT2 (blue). Station 4a, located in the secondary channel, and station 7, in WOC, are marked by asterisks
phase difference at station 7 (WOC). There is a consistent and significant shift in phase difference between the spring and fall cruises. We leave further interpretation on this topic to the discussion.
350
Sta 7 Sta 4a
340 330 320
2 0
3 5
10
4 15 20 Distance from ocean (km)
5 25
6 30
35
Phase Difference between Water Level and Velocity
Fig. 4 Change in the M2 phase difference (elevation–current) along the main channel during SAT1 (red) and SAT2 (blue). Station 4a, located in the secondary channel, and station 7, in WOC, are marked by asterisks
75 SAT 1 SAT 2 Sta 7 70
65 Sta 2 Sta 4a degree
60
55
50
45
2 40
0
defines an increasingly ebb-dominant system (Friedrichs and Aubrey 1988). Farther upstream relative phase decreases to 60° as the system transitions to a more riverine structure, but in WOC, relative phase increases to 200°, a value also indicating ebb dominance. The general transition of the tide in the main channel is visualized in diagrams of velocity vs WL for the sum of the
3 5
10
4
15 20 Distance from ocean (km)
5
6
25
30
35
M2 , M4 , and M6 constituents (Fig. 6) which form a series of ellipses. The tilt of those in the main channel increases with distance from the ocean indicating increasing progressive character (Blanton et al. 2002). Note that M6 is almost equal to M4 at station 4 (Tables 3 and 4), indicating that M6 competes with the importance of M4 upstream of the triple junction. Moreover, maximum ebb occurs closer to low M4/M2 amplitude in Satilla River (SAT2)
Fig. 5 Change in M4 tidal amplitude (top panel) and the relative phase, 2M2 M4 , (bottom panel) along the channel. WL for station 4a, located off the main channel, is represented by black circles; station 4a velocity is represented by black triangles
0.25 Water level Velocity
0.2
Sta 7 0.15 0.1 Sta 4a
0.05 0
2 0
3 5
10
4
15 20 Distance from ocean (km)
5
6
25
30
35
2M2-M4 phase in Satilla River (SAT2) 250 Water level Velocity
o
Degrees ( )
200
Sta 7 150 100 Sta 4a 50 0
2 0
3 5
10
4
15 20 Distance from ocean (km)
5
6
25
30
35
water with distance from the ocean while maximum flood occurs closer to high water. Station 7 (WOC) deviates from this picture. Low water and slack water occur at the same time, while maximum flood occurs close to high water. These and other observations of tidal currents in estuaries along the SAB coast do not fit all aspects of the model of ebb and flood dominance associated with the presence or absence of tidal flats (Aubrey and Speer 2004; Speer and Aubrey 1985), particularly in relation to the duration of the ebb and flood phase. The theory put forward by Friedrichs and Aubrey (1988) is more applicable to systems with no freshwater discharge. Most of the estuarine and creek systems in the SAB have enough freshwater input to impose an ebbward pressure gradient that prolongs the duration of the ebb phase. This makes the ebb phase stronger and longer as opposed to the classical definition of shorter but stronger ebb flow in ebb dominant systems. 5.2 Moving vessel observations 5.2.1 Semidiurnal tide The semidiurnal tidal ellipses from all surveys reveal a strongly rectilinear tidal current aligned with the channel axis. Minor axis amplitudes are noticeable only near channel bends and are the only places that the tide departs from being purely rectilinear. For this reason, we will focus on the major axis amplitude and phase of the tidal ellipses. The least-squares fits of the semidiurnal major axis amplitudes reveal strong spatial gradients. These observations indicate more structure to the current field than revealed in the moored observations. Large changes occur where depth changes abruptly, near channel bends, and at the junctions of tributaries (Fig. 7).
Because the roving samples in one section were collected at different times in the spring–neap cycle at an adjacent one, semidiurnal current amplitude estimates by the least-squares fits at a given point will not be the same. These variations in estimated tidal amplitude between surveys complicate interpretation of the observations, as do nonlinear effects. We can account for the variation in tidal amplitude by defining an amplitude correction for each of the surveys such that the semidiurnal amplitude found from the short-term least squares fit is related to the M2 amplitude found from the 2-month moored deployments made simultaneously. We have chosen to use the depthaveraged current at station 4 as our reference because it lies in the center of the estuary. From the station 4 time series, we form a least-squares estimate of the semidiurnal amplitude applicable to each of the roving sampling times. This amounts to a linear correction and cannot account for nonlinear effects. We have implemented a correction for each of the sample domains by scaling the raw least-squares semidiurnal fits by the ratio of the long-term M2 amplitude to the short-term semidiurnal estimate. The correction works reasonably well—overlap regions (most notably between B and C at spring tide) agree well on amplitude, and spring vs neap versions are similar though not identical (not shown). We note that the spring tide fits with just semidiurnal and quatradiurnal tides are much poorer representations of the currents than at neap tides (Fig. 8). The fits still capture the majority (> 90% ) of the signal variance but something else is going on. Particularly at spring tides, maximum ebb flow is achieved rapidly after slack water and remains at a nearly constant value until decelerating rapidly toward the next slack water. Flood current is established early but is not sustained and slows nearly linearly. Neither behavior is captured well with only two tidal constituents. It is susWater level vs velocity (M2, M4, and M6 components)
Fig. 6 Correlations of velocity vs WL for the sum of the M2 , M4 , and M6 constituents during SAT2. Flood currents are positive. See Tables 1 and 2 for station information
1 Sta 2 Sta 3 Sta 4 Sta 4a Sta 5 Sta 6 Sta 7
Water level (m)
0.5
0
-0.5
-1
-1.5 -1
-0.8
-0.6
-0.4
-0.2
0 0.2 Velocity (m/s)
0.4
0.6
0.8
1
Fig. 7 M2 major axis amplitudes during the spring and neap tide surveys
pected that the abrupt accelerations are related to the estuary hypsometry and the flooding and emptying of the marshes. There is no obvious increase in the roving samples current amplitude moving inland as was implied by the mooring data. Possible explanations are that the alongchannel extent of the moving vessel observations (from west of mooring 3 to east of moorings 6/7) is too small to realize the trend, or it could be that the spatial variability associated with depth variations and with the bends overwhelms the along-channel variations visually. Considering the latter, the simplest possible explanation for spatial variability owing to depth variations is that the velocity is proportional to water depth. This is because in deeper water, the surface velocity is more likely to achieve a free-stream velocity. Assuming that the tidal current amplitude profile resembles a logarithmic layer, e.g., uðzÞ ¼
U1 logðz=z0 Þ κ
would expect the depth-averaged current U to vary as Rwe z logðzÞdz / logðz=z0 Þ 1 if spatial variations of the z0 depth-averaged tidal current amplitude were due only to depth of the boundary layer. Scaling the velocity in this way appears to account for depth dependence (i.e., it removes a minor trend in scatter plots of major axis
amplitude vs local depth) but this accounts for only 15% of the observed amplitude variability. There remains considerable scatter of the corrected, depth-normalized velocities for a given depth in the estuary; obviously, other factors are important. The scatter is not random in space and is observed to be associated with channel bends and channel junctions (Fig. 9). Considering the momentum balance, we presume that this is an indication of where local surface pressure gradients or nonlinearities are greatest in space. A repeatable pattern is apparent in the corrected, depthnormalized velocities associated with each of the channel bends east of the triple junction. Currents are greatest on the inside of the bend to the landward side and greatest on the outside of the bend to the seaward side. Minimum currents occur to the landward side on the outside of bends. Maximum values exceed minimum values by 25–50%. This pattern is reminiscent of that in riverine channel bends (e.g., Smith and McLean 1984) despite the differing channel geometry in the Satilla of midchannels bars and point bars shifted seaward. The point bars are large enough to prevent sampling of the current on the inside of bends seaward of the point. The strong spatial structure to the current field is consistent with the bends being where local surface pressure gradients and/or field accelerations are large. Previous work has associated bends with the generation of secondary circulation that can overturn the water column (Seim and Gregg 1997) and augmentation of
Fig. 8 Examples of least-squares semidiurnal fits (dotted) to mooring time series (solid) at station 4
bed friction through vertical advection of horizontal momentum (Seim et al. 2002). The phase of the current at the semidiurnal frequencies increases steadily moving upstream, changing by about 30° Fig. 9 Plots of corrected, depthnormalized semidiurnal major axis amplitudes show strong spatial structure
in the main channel between stations 3 and 6, similar to that observed in the moored observations (Fig. 10). We have not attempted to reference the phase to Greenwich, given that the phase is not specific to a semidiurnal constituent.
However, within a survey, the differences in phase are meaningful. Two features stand out: the smaller phase angle seen in the shallower of the two channels that characterize the reaches between bends where the phase is as much as 20° earlier (e.g., the easternmost portion of the neap survey and the N–S reach in the spring survey), and the remarkable phase changes associated with the triple junction. In the latter case, the phase change appears to be significantly different between spring and neap tides and suggests an amplitude dependence to this structure. The phase in WOC is notably earlier than in the main channel, and the phase changes over a single cell (< 200 m). This effect was visually obvious on the river. Near low water, for example, it was common to see the flow ebbing in the main channel but flooding in WOC, creating remarkable divergence within the triple junction, with the seaward-flowing water in the main channel flowing upstream into WOC. 5.2.2 Overtides The depiction of the quatradiurnal tides from the roving samples is difficult to interpret. As noted earlier, the leastsquares fit with a limited number of constituents captured the current variability much better at neap tides than at spring tides. However, the spring tide survey appears to Fig. 10 Phase of the current at the semidiurnal tidal frequency. Phase reference is arbitrary (i.e., not Greenwich). The spring and neap samplings are shown separately
reproduce the unusual trend seen in the moored observations, with M4 reaching a local maximum near station 3 and being much larger in WOC. The same is not true of the neap tide surveys, in particular in domain D where the magnitude of the quatradiurnal major axis amplitude is significantly greater than in the spring tide survey (Fig. 11). The magnitude of the M4 current in WOC is worthy of special note: values exceed 0.3 m/s near the entrance to the creek, consistent with it being near an M4 WL node for this sub-basin of the estuary. 5.2.3 Mean currents Mean flows for the seven roving ADCP surveys reveal a relatively strong (0.1 m/s) and consistent flow structure associated with the channel bends (Fig. 12). Flow is toward the apex of the bend from both sides on the inside of the bend, toward the outside at the point, and away from the point, in both directions, on the outside of the bend. The pattern is reminiscent of the tidally averaged flow around headlands (Geyer and Signell 1990; Geyer 1993). Consistency of the roving sampling estimates and mooring means suggests that the depth-averaged residual flow is largely driven by the interaction of the tide with the bend topography and that it is reasonably stable.
Fig. 11 Amplitude of the quatradiurnal major axis for the spring and neap surveys
East of −81.62° W, the mean flow is seaward in the deeper channel of the reaches between bends and landward in the shallower channel. This type of ebb/flood channel dominance is well known (e.g., Kjerfve 1978; Kjerfve and Proehl 1979) and is thought to result from stronger inertial influence in the deeper channel (Uncles and Kjerfve 1986). There is a noticeable modulation of the mean flow speeds between spring and neap tides, again consistent with the notion that the mean flow is dominated by the tidal residual. The only exception to this occurs in domain D where the neap survey captured a strong storage event (mean inflow throughout the section).
6 Energy flux and dissipation The tidally averaged energy flux P for a unit width of cross section is (Pugh 1987): 1 P ¼ ρghηu 2
½W m1
(1)
where η is the WL fluctuation, u is the water velocity over depth h, ρ is water density, and g is the acceleration
of gravity. Using Eq. 1, we calculated fluxes for each station along the channel (Table 5). Errors associated with the energy flux per unit channel width arise from uncertainty in the tidal constituents (less than 5%). There is a steady increase in upstream energy flux per unit width between stations 2 and 6. The increase is the result of increased current amplitudes and decreased phase differences upstream. This along-channel flux divergence requires an across-channel flux convergence. Assuming that the energy flux at the mooring locations is representative of that across the wetted (low-water) channel, we can estimate the total upstream energy flux Pt as shown in Table 5. In computing errors for the energy flux through a cross section, we assume an uncertainty of 10% in channel width. This estimate will likely overestimate the total energy flux, particularly in the more seaward reaches of the estuary where broad shoals exist between the low-water marks and where tidal velocities are smaller than in the main channel. A comparison of energy flux at stations 4 and 4a suggests that an additional uncertainty of 10–15% is to be expected, accounted for in the calculations. We find that the narrowing of the low-water channel more than compensates for the upstream increase in energy flux per unit width such that the total upstream energy flux decreases moving inland.
Fig. 12 The depth-averaged residual current estimated from the roving samples during spring (top) and neap (bottom) tides
We can ascribe the change in total upstream energy flux to dissipation D , formed as the difference in energy flux divided by the distance L separating the two stations, or D ¼ ½Ptnþ1 Ptn L ½W m1
(2)
where n is a station counter. This is the dissipation that occurs per meter of along-channel distance between station pairs, similar to a formulation used by Lavelle et al. (1988). How the dissipation is distributed in depth and across the estuary cannot be determined from the existing
observations, but we can form a bulk estimate of the dissipation per unit mass (Wkg1 ) by dividing Eq. 2 by h, b, and ρ . These two estimates for D are given in Table 6. Upstream of station 5 the channel splits; we should therefore compare the total energy flux Pt at station 5 with the sum of Pt at stations 6 and 7 (see Table 5). Doing so, we find a nearly tenfold increase in D; implying a much greater dissipation along this reach of the estuary. Apparently, the triple junction and large phase changes associated with WOC are effective mechanisms for dissipating tidal energy and are in important sink within the system.
Table 5 Flux of tidal energy between the main channel stations due to M2, M4, and M6 tidal constituents Station
Station 2
Station 3
Station 4
Station 5
Station 6
Station 7
Distance (m) Depth (m) Width (m) uðm2 s1 Þ P (kWm1 ) Pt (MW )
4,000 8.9 3000 0:0930:005 4:160:22 12:471:45
11,000 9.3 1100 0:1340:006 6:260:33 6:880:80
15,000 7.9 900 0:1570:004 6:230:20 5:610:65
21,000 9.6 500 0:2020:012 9:740:58 4:870:57
25,000 8.5 200 0:2560:014 10:930:64 2:190:25
26,000 10.2 170 0:0800:004 4:100:20 0:700:08
Depths are tidal averages at the moorings. Widths are LW values, assumed to be representative of the momentum-carrying channel
An alternative estimate of tidal energy dissipation at each station can be formed assuming a boundary layer (Taylor 1919): 3
D ¼ < ρCd ½U 2 2 >
(3)
where the bracket pair represents the average over the M2 cycle, Cd is the drag coefficient, and U is the tidal velocity. We use Cd ¼ 0:002 , a representative value for the Satilla (Seim et al. 2002). This results in values of 0:07 0:5 W =m2, comparable to the values estimated by energy flux divergence (Table 6). A bias toward a lower estimate is possible because the formulation does not account for all processes producing dissipation, specifically, form drag and drag in marsh grass. Dissipation of tidal energy in the Satilla is of the order of 1 W =m2 (Table 6). This compares favorably with another coastal plain estuary (Coos Bay, Oregon) with estimated dissipation rates between 2 and 4 W =m2 (Blanton 1969). It also is consistent with numerical estimates. Blanton et al. (2004) find that about 25% of the total energy dissipated in the SAB occurs in the estuaries. Numerical simulations in their paper indicate that the dissipation rate is of the order of 0.5 Wm2 inside the estuaries, a rate that compares favorably with the directly measured results in Table 6 and using Eq. 3. Thus, numerical simulations and the direct measurements are consistent.
7 Discussions It is clear that unlike some inlets which can effectively choke the tide (e.g., Kjerfve and Knoppers 1991), the entrance to the Satilla admits a strong tidal energy flux. The abrupt change from slow variations in phase on the shelf, reminiscent of a standing wave, to steady phase changes within the estuary implies that reflection of the tidal wave occurs on the seaward side of the barrier islands, not within the estuary. Interpreting the phase changes in Fig. 2 as wave speed indicates that the tide moves upstream at approximately 5 m/s, which for a shallow water wave requires an average depth of 2.5 m. Assessing the actual average depth of the Satilla is not straightforward, given the uncertainties in bathymetry and the large intertidal regions, but we note that Seim et al. (2002) find an effective depth in mid-estuary of 2.5–3.5 m. All indications are that the tide within the estuary is increasingly progressive in nature as it
propagates upstream, consistent with the observed changes in the phase difference between the currents and WLs. This leaves only geometric convergence within the estuary to explain the WL maximum 10–20 km shoreward of the coastline. As with depth, the dynamically relevant width of the estuarine system is difficult to assess but assuming the low-water widths are representative, rapid changes in width occur between stations 2 and 3 (roughly 10 km inshore) and again between stations 4 and 5 (roughly 20 km inshore). Fitting the lower water widths with an exponentially decaying function suggests a length scale of width variations Lb of 10.5 km. Friedrichs and Aubrey (1994) undertook an analytical representation of dissipative, strongly convergent estuaries. They define an estuary as strongly convergent if Lb λ, where λ is the tidal wavelength. They find that for this class of estuary, there is a remarkable change in character of the tide, and that to first order, a reflected wave is inconsistent with the solution. For shallow estuaries pffiffi (of order 10 m depth), the wave speed is similar to ðgHÞ, like a progressive wave, but the currents are nonetheless predicted to lead WL by approximately 90°, as in a standing wave. Using a wave speed of 5 m/s for the M2 tide in the Satilla implies that λ ¼ 224km and that Lb =λ ¼ 0:05; thus, the Satilla is consistent with the criteria in Friedrichs and Aubrey (1994), and its tidal character seems to closely match their predictions. Several other consistencies are worth noting. At second order, Friedrichs and Aubrey (1994) suggest that tidal phase will vary more linearly within the estuary than tidal amplitude, as we observe. They go on to suggest that tidal amplitude and phase difference between currents and WLs are controlled by the local geometry rather than by the wave interference patterns. This suggests that the peak in tidal amplitude reflects the more strongly convergent geometry in the lower estuary and that landward of this point friction dominates over inertia. The departure of the phase difference from quadrature reflects the finite convergence rate in the estuary. The distribution of the M4 current amplitude, which also is a maximum at mid-estuary, is also consistent with rapid convergence. Left unresolved is how the strongly convergent estuaries of the southeast US (as suggested by this study and by the similarity in character of the tide along the South Carolina and Georgia coastlines) interact with the shelf tide. Observations from WOC, the largest sub-basin within the estuary, indicate that it has tidal characteristics distinct
Table 6 Dissipation of tidal energy between the main channel stations due to M2, M4, and M6 tidal constituents Station interval
Stations 2-3
Stations 3-4
Stations 4-5
Stations 5–(6+7)
Distance interval (km) Mean depth (m) Width (m) Dissipation/along-channel distance (W m1 ) Dissipation/unit area (W m2 ) Dissipation/unit mass (W kg 1 )
7 9.1 2,050 798133 0:390:07 427
4 8.6 1,000 32053 0:320:05 366
6 8.8 700 12320 0:180:03 203
4.5 9.2 268 44274 1:650:28 17529
from the rest of the system. The amplitude of M2 is enhanced and the phase difference between currents and WL increases immediately upon entry to the sub-basin, both suggestive of some form of resonance. Given the remarkable amplitude increase (fourfold) of M4 in WOC, it may be that the basin is resonant at a higher harmonic of M2 ; the remarkable maximum in M4 current amplitude (0.3 m/s) at the entrance seen in the roving samples reinforces this idea. Most surprising to us is to find resonance-like behavior in a physical system which is presumably highly damped. What role the sub-basin may play in maintaining the inshore amplitude of the tide is open to investigation. All of the above issues play a critical role in determining the energy flux distribution within the estuary. The increasing tidal currents and decreasing phase difference between the currents and WL lead to a threefold increase in upstream energy flux per unit width. Accounting for the change in width of the estuary using the low-water width results in reasonable estimates of energy flux in the estuary and estimates of bulk dissipation rates via flux divergence, which are consistent with other estimates. We have attempted to estimate the errors associated with this method and suggest that it may be a reasonable representation (within 25%) of the magnitude and spatial structure of the dissipation in the estuary. Concerns include cross-channel variability in the current and the dynamically relevant depths and widths of the estuary. The shift in phase difference between SAT1 and SAT2 implies a seasonal variation in energy dissipation; the implications of this seasonal change locally and globally are unexplored. Overtide generation is of moderate amplitude in the main channel of Satilla but provides important clues to the dynamics in the estuary. Maximum values reach 10% of the amplitude of the primary tide. First harmonic (M4 ) amplitudes increase linearly; this is consistent with the development in Friedrichs and Aubrey (1994) and suggests that we can estimate the tidal distortion parameter γ, defined as the difference between the finite amplitude parameter (ratio of tidal amplitude to average water depth) and the intertidal parameter (1—low water width/mean water width), based on the distribution. Friedrichs and 2π Aubrey (1994) suggest that M4 =M2 ¼ jγj 2 λ x; for an amplitude ratio of 0.1 at x ¼ 25 km, we find that γ ¼ 0:28. The finite amplitude parameter for the Satilla is 0.28–0.4 (for a mean depth of 3.5 and 2.5 m); together with the estimate of γ , this suggests that an effective low water width nearly equals to the mean water width. The M4 currents mimic the distribution of the primary tide, peaking roughly 15 km inshore of the coastline, suggesting the prominence of channel convergence in generating the M4 component. In contrast, the M6 WL and current amplitudes increase steadily moving inshore, consistent with a regular distortion of the tidal wave by friction. Though we have provided only a cursory review of the dataset, the roving samples have the potential to shed light
on some of these issues. They reveal strong spatial variability in the velocity field, which raises some questions about the representativeness of the moored observations with regard to total transport and phase of the currents. An earlier study suggested that the momentum balance was approximately linear near station 3 (Seim et al. 2002). In this study, we find that a simple depth scaling accounts for only a small fraction of the observed tidal amplitude variability. This indicates the importance of local pressure gradients and/or nonlinearities in determining the magnitude of the currents. An obvious next step would be to better understand the spatial structure of the local pressure field and to quantify the role of the nonlinearities in determining the current amplitudes. The mean depth-averaged circulation is remarkably strong, regularly exceeding 10 cm/s, and the structure is obviously related to the channel geometry. A classic headlands circulation is realized at the point of every bend but with a well-defined return flow on the outside of the bends. The implications of the mean flow field on the mass field distribution, sediment transportation and deposition patterns, and passive particle retention and dispersion within the estuary are largely unexplored but worthy of further study.
8 Conclusions An intensive observational program in a shallow, pristine salt-marsh estuary has been used to describe the tidal character in detail. Analysis of moored times series indicates a transition in the character of the tidal wave as it enters the estuary, changing from a near standing wave on the continental shelf to a more progressive wave within the estuary. The M2 WL amplitude reaches a maximum of 10– 20 km landward of the estuary mouth, whereas tidal current amplitudes in the main channel continue to increase up to 30 km inland. This tidal character is consistent with the depiction of a strongly convergent estuary in Friedrichs and Aubrey (1994) and suggests care in interpreting estuarine tidal dynamics in the SAB in terms of simple standing or progressive waves. Roving samples reveal considerable spatial structure to the tidal currents, of which only a small fraction can be accounted for by depth variations. Channel bends strongly impact the tidal currents and impart a structure similar to that seen in rivers. Overtides are generally moderate in size along the main channel, typically of amplitude < 20 % of the driving component, the exception being a sub-basin which may be resonant at some harmonic of M2 . Depthaveraged mean currents are strong and obviously related to the topography of the channel bends. The pattern is reminiscent of that generated around headlands by bidirectional flow. The modulation of tidal-averaged current on the spring–neap cycle suggests that it is largely driven by the tides.
Energy dissipation rates within the estuary are estimated from the divergence of the energy flux. Accuracy of the estimate is limited by representation of the geometry. Three separate estimates are reasonably consistent and suggest a bulk dissipation rate of 0:5 1:5 W m2 or about 104 W kg 1 . A notable and typical characteristic of the Satilla is the slight maximum in WL amplitude landward of the connection to the sea. An explanation of the cross-shore structure of the tide remains uncertain but the Satilla observations may help advance our understanding. Acknowledgements We wish to thank several people who made indispensable contributions to this study. Julie Amft, Cheryl Burden Ross, Trent Moore, and Guoqing Lin played critical roles in the design, planning, and execution of the field program; it could not have happened without them. Anna Boyette at Skidaway Institute of Oceanography contributed to the preparation of the figures. The crew of the R/V BLUE FIN (Captain Jay Fripp, Raymond Sweatte, and Mike Richter) of the Skidaway Institute of Oceanography gave us dedicated enthusiasm and support in carrying out the field experiments. We also thank two anonymous reviewers for their thoughtful comments. We gratefully acknowledge the following agencies who supported the work described in this paper: the Georgia Coastal Zone Management Program (Grant No. RR100-279/9262764), National Science Foundation (LMER Grant No. DEB-9412089 and LTER Grant No. OCE-9982133), NOAA Coastal Ocean Program (Grant to South Carolina Sea Grant Consortium entitled “Tidal Circulation and Salt Transport in a Tidal Creek–Salt Marsh Complex”), and the Office of Naval Research (the SEACOOS program, N00014-02-1-0972).
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