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Page Title:
COMBINED CURRENT/WAVE SHEAR STRESS (cont.) |
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 Technical Note DOER-N1
April 1998
As defined in the CJ model, bed shear stress due to combined current and wave action may be
calculated from:
1
τbm
= ρ f w uwbm m
2
2
(4)
where τbm is the maximum bed shear stress, and uwbm, the amplitude of the bottom orbital velocity
at the top of the wave boundary layer (or maximum bottom orbital velocity), is calculated from
linear wave theory by:
Hs gkTs
uwbm =
4π cosh(hHs )
(5)
period, and h is the total water depth.
m is calculated by:
m = ( + σ 2 + 2σ cos(δ - α ) )
0.5
1
(6)
2
f c U
τcb
σ=
=
τwbm f w uwbm
(7)
where σ is the ratio of τcb (bottom shear stress due to currents) and τwbm, the amplitude of τwb (i.e.,
τwbm is the maximum value of the oscillatory τwb, bed shear stress due to waves). δ is the angle of
the current direction and α is the angle of the wave direction. Note that if τcb >> τwbm, then:
2
f c U
m →
f w uwbm
(8)
and thus τbm → τcb. Similarly, if τcb << τwbm, then m → 1 and τbm → τwbm.
Ultimately, the prediction of the shear stress depends on the turbulence-related friction factors.
There are separate friction factors fc and fw for current and wave-related processes. It is beyond the
scope of this TN to describe the methods for estimating the friction factors. It will suffice to say
that the friction factor equations are experimentally determined. The procedure for computation of
bottom shear stress is as follows:
on the right-hand side of this equation is zero):
5
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