D-R-A-F-T
Ultra-Shallow Water Waves
In broad shallow areas with depths less than about 2 m, wind-waves most often are
in the transition range where wave length Lw is greater than twice the local depth D
and wave bed friction affects wave growth and depth-limited wave conditions.
Atmospheric drag coefficients are also affected since they depend on wave
conditions, and since:
Equation 8
τ a = ρ a Cd U 2
a
where
=
air density
ρa
Cd
=
atmospheric drag coefficient
Ua
=
wind speed corrected to 10 m reference height
atmospheric shear stress is affected as well. It was found in Laguna Madre Texas that
atmospheric drag coefficients can be approximated by:
Equation 9
2
⎛
⎞
0.4
Cd = ⎜
⎟
⎜ 16.11 - 0.5 ln( D' ) - 2.48 ln(U
⎟
⎝
⎠
a
in water depths less than 2 m, where D' is an effective depth. Wave height and period
were found to be related to Cd and D' at this site, and D' was found to be the water
depth or depth to the vegetation canopy top.
A momentum balance approach is used to estimate wind-wave shear stress, since the
uncertainties in specifying widely varying wave friction factors makes it possible to
over estimate momentum transfer. Wind-waves are assumed to be fully-developed
with dissipation equal to momentum input from the atmosphere. Atmospheric shear
stress is partitioned between currents and waves. In deep water, dissipation by white
capping and wave-wave interaction leads to most atmospheric momentum eventually
going into the currents. In ultra-shallow water the shear stress going into bed by
wave action is a fraction of the input such that:
Equation 10
τ wb = 5.38 -0.5 , for U > 5 m/sec
Ua
a
τa
When RMA2 has used the marsh porosity option (DM cards) shear stresses should
be adjusted in the SED2D WES simulation for more accurate estimates of the bed
exchange. Therefore, the marsh porosity information must be provided (in
appropriate units) and the program will compute the needed adjustments. The
adjustment is made by computing a conveyance distribution within the marsh
porosity depth distribution based on Manning's equation. This is then extended to a
shear stress distribution that is averaged and a correction factor developed for the
conventionally derived shear stress from one of the options above
10
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