Distinct effects of processes and boundary conditions on fluvial and coastal morphodynamics and stratigraphy M.G. Kleinhans1, F. Schuurman1, W.M. van Dijk1, W.I. van de Lageweg1, B. Castelle2 and B.G. Ruessink1 1 2
Dept. of Geography, Fac. of Geosciences, Universiteit Utrecht, Utrecht, THE NETHERLANDS.
[email protected] CNRS, Université de Bordeaux, Talence, FRANCE
1. Introduction River and coastal morphodynamics are the result of sediment transport induced by flowing water and gravity on bed slopes. The depositional architecture, in turn, is caused by the dynamics of morphology, including sedimentary and erosional processes associated to channel migration and scouring (e.g. Van de Lageweg et al. 2013, this volume). This is true for overloaded systems forced to avulse, including Distributive Fluvial Systems, deltas and alluvial fans, but also for all non-aggrading systems, e.g. river channels on fluvial plains, channels and shoals in tidal basins and estuaries, sandbars and rip channels in surfzones of sandy coasts. We focus on non-aggrading conditions to exclude allogenic forcing. However, this does not entail steady boundary conditions: these can be dynamic to represent (external) time-varying processes usually not included in models, e.g. climate (discharge regime, wind-generated waves, tides and sediment fluxes). A fundamental question is to what extent morphodynamics and stratigraphy are results of internal processes and of dynamic boundary conditions (Oreskes et al. 1994, Kleinhans et al. 2005). The prevailing view is that minor perturbations within the system are sufficient to maintain natural dynamics of morphology and autogenic signals in stratigraphy under constant boundary conditions. Whilst some models support this view, e.g. meander simulators, the question cannot be answered by field data because boundary conditions in nature are always dynamic. Here we show, using theory, physics-based modelling and experimentation, that systems only stay dynamic when forced with sufficiently large perturbations, whereas dynamics of morphology disappears under entirely constant conditions. In addition to braided and meandering channels we involve rip channels in the coastal zone to emphasise that our reasoning is valid across environments. 2. Evidence for effects of dynamic boundaries In this section we discuss evidence from theoretical, numerical and experimental work on the effects of dynamic boundary conditions on morphodynamics. 2.1 Theory on dynamic meandering channels Many patterns of channels and bars in rivers, estuaries and coasts can be studied analytically by linearising the relevant equations of flow and sediment transport. These are perturbed with infinitesimal cosines of varying wavelengths which are studied to determine whether they dampen or grow, and which wavelength grows fastest. Theoretical Contents
Programme
understanding of the formation of meanders was obtained in the past with linear stability analyses, i.e. based on simplified analytical physics. Although linearised theory usually predicts initial pattern formation under steady conditions only, Lanzoni and Seminara (2006) were able to study dynamics. They found that bars and channel curvature usually convect in downstream direction. This implies that, to sustain meandering dynamics, the upstream boundary must continuously be perturbed in transverse direction, so that instabilities continue to propagate from the upstream boundary in downstream direction where they convect out of the system. In nature such perturbations can occur in the form of upstream meander or bar dynamics. 2.2 Theory on rip channels in the surfzone Rip channels are striking patterns in the sand along wave‐ dominated beaches. They are often part of an accreting coast sequence developing from an alongshore‐uniform barred‐beach state following a storm event and therefore have preservation potential. Linear stability analysis shows that rip channels are nearshore instabilities that emerge as a result of the positive feedback between hydrodynamics (waves and wave-driven circulation), sediment transport and the evolving morphology (Falqués et al. 2000, overview in Van Enckevort et al. 2004). Positive perturbations result in intensified wave breaking and onshore flows. The more intense breaking results in a larger waterlevel immediately shoreward of the positive perturbations, causing water to flow alongshore as so-called feeder currents. These currents meet landward of the negative perturbations, where they turn seaward as rip currents. When the sand concentration is maximum at the breaker zone, this flow pattern causes positive feedback: the positive perturbations become shallower and grow into shoals, while the negative perturbations become deeper and grow into rip channels (Falques et al., 2000). Using time-invariant wave forcing, a regular alongshore wavelength emerges of about 3 to 5 times the surf zone width, typically several hundreds of meters, depending on factors that control the strength of the surf zone circulation, including wave height, water depth above a pre-existing sandbar, distance between the bar and the shoreline, and the volume of the trough. Under obliquely incident waves rip channels migrate alongshore with constant spacing. This contrasts with common field observations of irregular and random alongshore rip spacings (van Enckevort et al. 2004)
39
2.3 Experiments with dynamic meandering Meandering occurs in a range of relatively small channel aspect ratios, which requires strengthened but erodible banks and self-forming, cohesive or vegetated floodplains. Given this interaction with self-formed floodplain, meandering is then hypothesized to originate from bar and bend instability, starting with small perturbations in flow and channel curvature that lead to erosion in outer bends, growing into larger bends that are limited in size by cutoffs. However, dynamic meandering was notoriously difficult to reproduce in laboratory experiments. Alternate bars may self-excite from small bed perturbations in an initially straight channel, but high-amplitude meanders did not self-excite in experiments. In fact, it has long been known that a significant static perturbation is required at the upstream boundary to initiate bends, e.g. an inflow duct with a fixed 30-45º angle with the valley gradient orientation.
without length scale (Schuurman & Kleinhans, this volume). Despite the simplicity of these codes, the dynamics of the braiding generally reduce to nearly static even when the upstream boundary is continuously randomly perturbed (Murray 2007). 2.5 Modelling of dynamic fluvial channels Two-dimensional numerical model runs (Delft3D: Lesser et al. 2004, NAYS-2D: Jang & Shimizu 2010) demonstrate that a systematically changing boundary enhances dynamics and sinuosity in contrast to a random perturbation of upstream discharge distribution over the upstream boundary (Fig. 2). Despite the lack of cohesive floodplain formation and physics-based bank erosion, a linear transverse movement of discharge inflow produced a sinuous channel with slowly migrating bars whereas a fixed inflow resulted in a weakly braided river with mid-channel bars. On the other hand, 0.5% random noise on an equal discharge distribution in a wide initial channel without the raised floodplains produced a braided river due to the large channel aspect ratio. Also braiding models either require large perturbations or become static after development from plane bed (Schuurman and Kleinhans 2011). All these physics-based modelling studies support the hypothesis that sustained upstream perturbation is required for natural dynamic meandering and not just for short experiments where perturbations could not grow over limited length.
Figure 1: Static weakly sinuous experimental channel induced by static perturbation (top) and dynamic meandering (bottom) induced by dynamic inflow boundary perturbation. Van Dijk et al. (2012) demonstrated that sustained dynamic meandering not only requires floodplain formation and destruction, but also requires alternating transverse movement of the inflow boundary, mimicking perturbations migrating into the reach of interest in agreement with Lanzoni and Seminara (2006). Whilst a fixed inflow boundary causes nearly static incipient meandering, our dynamic experimental setup produced for the first time high-sinuosity migrating meanders with series of scroll bars and infrequent bend cutoffs (Fig. 1). 2.4 Dynamics in reduced complexity models of meandering and braiding Meandering and braided rivers were often studied in the past with simpler numerical models. Meander simulation models only require a minor initial perturbation to continue dynamic meandering. However, these codes are inherently so unstable that they require much smoothing (Crosato 2007), and we argue that the ‘autogenic’ dynamics are a model artefact rather than a representation of natural dynamics.
Figure 2: Fluvial bars modelled in Delft3D (a-c) and NAYS (d,e). Only when the inflow is dynamic (laterally migrating, c and e) the bends are sustained and dynamic. 2.5 Dynamics of modelled surfzone rip channels Linear models are restricted to the initial growth of rip channels and, by definition, produce alongshore regular and temporally constant alongshore lengths. Non-linear models on the other hand can be used to explore the finiteamplitude behaviour of rip channels as a function of boundary conditions (Fig. 3).
Braided rivers were often modelled with cellular automats that only route sediment as a function of slope (Murray 2007). Such models produce braiding patterns often
Contents
Programme
40
Figure 3: Rip channels in a nonlinear model with constant wave forcing (top) and time-varying wave direction (bottom). Note merging rips at 4.4 km. Such nonlinear modelling shows that three-dimensional pattern and dynamics of rip currents are very sensitive to variations in forcing. Time-varying wave direction at the seaward boundary caused a natural variability of rip spacing, migration rate and direction (Castelle and Ruessink 2011; Fig. 3) in agreement with observations (Van Enckevort et al. 2004). In contrast, when the wave forcing is constant, a steady state is reached. The morphological response depends on the frequency and amplitude of variation relative to the adaptation time of the rip channels. The most striking dynamics that emerge with varying forcing are commonly observed in nature: the merging and splitting of bars leading to a change of the number of rip currents. Neither these morphodynamics nor the resulting stratification would have been produced without continued perturbations enforced at one of the boundaries. Ashton and Murray (2006) and Kaergaard and Fredsoe (2012) present similar findings for a different shoreface systems and comparable physics-based model systems. 4. Discussion We presented converging and compelling evidence that morphological systems in equilibrium require sustained perturbations to maintain dynamics. Initial static perturbations are not sufficient because their effects migrate out of the domain of interest. This conclusion is supported by physics-based theory for river meanders and bars, by experiments with dynamic meandering rivers, by physics-based numerical modelling of rip currents, meandering rivers and braided rivers and by reducedcomplexity modelling of braided rivers. We must therefore conclude that a boundary with sustained dynamic conditions is a necessary condition to explain morphodynamics in nature, and is not an artefact of models or experiments. An inevitable consequence is that many modelling and experimental studies published until now have terminated model runs too soon to observe the decay of dynamics under constant boundary conditions, or have ignored such results. Another consequence is that sensible perturbations and dynamics must be chosen for morphodynamic models and experiments, and sensitivity to the perturbations must be assessed. Aggrading disequilibrium systems such as deltas, alluvial fans and other Distributive Fluvial Systems are inherently dynamic because their aggradation causes avulsion. It could be argued that these systems do not require
Contents
Programme
sustained dynamic perturbations at the upstream boundary. However, these systems are often studied with reduced complexity models that must invoke some stochastic component, such as triggers for avulsion. These could be seen as a simplistic representation of internal subgrid dynamics or as a dynamic forcing. It would be interesting to test what amplitude and frequency of a sustained dynamic perturbation at the upstream boundary would cause dynamic systems without hardwired stochastic subgrid processes. 3. Conclusions Morphology in state-of-the-art physics-based models becomes static after some time if boundary conditions are fixed, and require continuous perturbation to maintain dynamics in agreement with theory and experiments. This implies that sustained perturbation is a necessary condition for natural dynamics in fluvial and coastal systems and not merely a requirement for models or experiments. Future modelling and experiments must take this into account, and studies reported until now must be re-evaluated. Acknowledgments MGK, WMvD, FS and BGR are supported by the Netherlands Organisation for Scientific Research (NWO). WIvdL was supported by ExxonMobil Upstream Research. Deltares is acknowledged for support and open source Delft3D code and Shimizu is acknowledged for sharing his meandering code. References Ashton, A.D., and Murray, A.B. (2006) High-angle wave instability and emergent shoreline shapes: 2. Wave climate analysis and comparisons to nature, J. Geophys. Res., 111, F04012 Castelle, B. and Ruessink, B.G. (2011) Modeling formation and subsequent nonlinear evolution of rip channels: Time‐varying versus time‐invariant wave forcing, J. Geophys. Res., 116, F04008 Crosato, A. (2007) Effects of smoothing and regridding in numerical meander migration models, Water Resour. Res., 43, W01401 Falqués, A., Coco, G. and Huntley, D.A. (2000) A mechanism for the generation of wave-driven rhythmic patterns in the surf zone, J. Geophys. Res., 105, C10 Jang, C.L. and Shimizu, Y. (2005) Numerical simulation of relatively wide, shallow channels with erodible banks, J. Hydraul. Eng., 131(7), 565–575. Kaergaard, K. and Fredsoe, J. (2012) Numerical modeling of shoreline undulations part 2: Varying wave climate and comparison with observations, Coastal Engineering, http://dx.doi.org/10.1016/j.coastaleng.2012.11.003 Kleinhans, M.G. Buskes, C.J.J. and De Regt, H.W. (2005) Terra Incognita: Explanation and Reductionism in Earth Science. Int. Studies in the Philosophy of Science 19(3), 289-317 Lanzoni, S., and Seminara, G. (2006), On the nature of meander instability, J. Geophys. Res., 111, F04006
41
Lesser, G.R., Roelvink, J.A., van Kester, J.A.T.M. and Stelling, G. (2004) Development and validation of a three-dimensional morphological model. Journal of Coastal Engineering, 51(8-9), 883–915. Murray, A.B. (2007) Reducing model complexity for explanation and prediction. Geomorphology 90, 178– 191 Oreskes, N., Shrader-Frechette, K. and Belitz, K. (1994) Verification, validation and confirmation of numerical models in the earth sciences. Science 263, 641–42. Schuurman, F. and Kleinhans, M.G. (2011) Self-formed braided bar pattern in a numerical model. In: Proc. 7th IAHR Meeting RCEM, Beijing, China. Schuurman, F. and Kleinhans, M.G. (this volume) River planform modelling requires physics-based bar formation. Van de Lageweg, W.I., Schuurman, F., Shimizy, Y., van Dijk, W.M. and Kleinhans, M.G. (this volume) Preservation of dynamic meander stratigraphy during aggradational and non-aggradational conditions. Van de Lageweg, W.I., van Dijk, W.M. and Kleinhans, M.G. (2013) Channel belt architecture formed by a meandering river. Sedimentology, doi:10.1111/j.13653091.2012.01365.x Van Dijk, W.M., van de Lageweg, W.I. and Kleinhans, M.G. (2012) Experimental meandering river with chute cutoffs. J. Geophys. Res., 117, F03023. Van Enckevort, I.M.J., Ruessink, B.G., Coco, G., Suzuki, K., Turner, I.L., Plant, N.G. and Holman, R.A. (2004) Observations of nearshore crescentic sandbars. J. Geophys. Res., 109, C06028
Contents
Programme
42
