MEASUREMENTS OF TURBULENCE PARAMETERS AND DISSIPATION
6.6
IN COMPLEX TERRAIN 1
1
1
2
R.Krishnamurthy* , R.Calhoun , H.J.S.Fernando , and G. S. Poulos 1 2
Arizona State University, Tempe, AZ
National Center for Atmospheric Research, Boulder, CO
1. Introduction:
evaluations can be made using either the inertial
The dissipation rate of turbulent kinetic
sub-range
of
spectra
measured
by
sonic
energy is one of the key intrinsic parameters
anemometers (by fitting Kolmogorov spectra) or
used
via empirical formulae combined with lidar data.
to
parameterize
turbulence
in
environmental and in engineering flows. It
In this paper, the efficacy of the current
represents the rate of energy transfer to smaller
generation of coherent Doppler lidar as a tool for
eddies in the inertial sub-range and the rate of
turbulence parameter retrieval is evaluated
conversion of kinetic energy of turbulence into
through an intercomparison of lidar and sonic-
heat in the viscous sub-range. This quantity
based approaches.
characterizes
the
energy
cascade
in
3D
atmospheric turbulence and is an important parameter characterizing the dynamical and dispersive state of the atmosphere.
2. Experimental setup: During March and April of 2006, a field
The
study, the Terrain-induced Rotors EXperiment
dissipation rate is difficult to measure directly
(TREX), was conducted in Owens Valley,
because of the required high spatial resolution,
California (www.eol.ucar.edu/projects/trex/), the
and thus may be inferred using measurements
purpose of the field experiment was to better
of quantities at scales larger than the dissipation
understand the dynamics of mountain lee waves
scales. The direct measurements are made
and rotors while simultaneously investigating the
using sub-millimeter scale hot-film and hot-wire
nocturnal boundary layer and thermally driven
anemometers (e.g. Poulos et al. 2006) with
valley flows during quiescent periods.
application of the Taylor hypothesis, and indirect
datasets allow comparisons between traditional
TREX
atmospheric measurement systems such as * Corresponding author address:
sonic and hot-film anemometers and remote
R. Krishnamurthy, Arizona State Univ.,
sensors.
Dept. of Mech. and Aerospace Eng.,
A large number of in situ and remote
Tempe, AZ 85281;
sensing instruments were positioned in the
e-mail:
[email protected]
valley to investigate the turbulent rotational motions and downslope wind storms over the
valley. Arizona State University (ASU) deployed
can be expressed for in-situ measurements as in
a sodar/RASS, a flux tower, and a coherent
Frehlich, Hannon and Henderson, (1998):
Doppler lidar. The ASU coherent Doppler lidar emits 500 infrared laser pulses per second into
[ v ' (r − s / 2) − v ' (r + s / 2) ]2
D v ( s, r ) =
.
(1)
the atmosphere. Aerosol particles present in the
For locally stationary turbulence, using the
atmosphere scatter laser light back to the lidar,
relationships between autocorrelation, structure
and the Doppler shift is measured, yielding
function, and the von Karman energy spectrum
radial velocities. Doppler lidar systems have
of energy containing eddies, the structure
been used in previous experiments to analyze
function can be written as
flows
in
complex
terrains.
Banta
(1999)
deployed Doppler lidar near the Grand Canyon
Dv ( s, r ) = 2σ v2' Λ[s / Lo (r )].
to observe various flow patterns.
where,
Data from ‘stare’ scans carried out on th
st
April 30 and May 1 during TREX have been used in this paper for estimating the spatial averaging effects of the lidar and assessing the performance of the lidar in measuring the turbulence parameters. The stare scans were
(2)
Lo (r ) is the measure of the outer scale
of turbulence, which is proportional to outer length scales such as the integral length scale Li ,
σ v2'
is the variance of turbulent velocity
fluctuations. For the von Karman’s model (Hinze 1959),
performed with 72m range gates using elevation angles of -1.39 and -0.53 degrees and azimuthal
Λ ( x) = 1.0 − 0.5925485 x1 / 3 K 1 / 3 ( x) .
(3)
angles of 71.40 degrees and 72.19 degrees, th
respectively, on April 30
st
and May 1 .
For
where K1/3(x) is the modified Bessel function of
these scans, the lidar was focused on two different meteorological towers where sonic anemometers were placed
order 1/3.
Li (or
1 ) is the integral length scale ki
and the relationship between
The sonic towers were placed at a distance of 1.5km from the lidar. The lidar
Li and Lo is given
by
performed a number of different scans, in
Li = 0.7468343Lo (r ) .
addition to the ‘stare’ scans on the towers where
If the outer scale is very large
the sonic anemometers were placed.
Kolmogorov model is valid, viz.
3. Theoretical Considerations
Dv ( s ) = C v ε 2 / 3 s 2 / 3
Classical
turbulence
theories
of
Kolmogorov and others provide a theoretical foundation for dissipation estimates through a well-known relationship between the structure function and dissipation. The structure function
where
ε
(4)
Lo
