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Combined Wave-Current Bottom Stress

Compute combined wave-current bottom stress using the Madsen (1994) model. Wave-orbital velocities are computed from the input wave statistics using the Soulsby (2006) approximation that assumes a JONSWAP spectrum. That calculation uses the zero-crossing period Tz, and we assume 1.28*Tz = Td, where Td is the input dominant wave period. It returns the root-mean-square orbital velocity uRMS. The Madsen (1994) routine requires the representative orbital velocity ubr = sqrt(2)*uRMS and the representative period Tr, This program uses Td as input to the Madsen routine, which may slightly overestimate bottom stress. Current velocities are assumed to be measure 1 m above the bottom (1 mab). The wave direction and current directions are not used.


Input

Enter
Parameters:

 

Value

Units
Water depth h
Wave height Hs
Wave period Td
Wave direction
Current speed
at 1 mab
Current
direction
Grain size D50

Results

Wave-orbital
velocity ubr
Grain
roughness ks
Friction
factor fwc
Current shear
stress τ*c
Wave shear
stress τ*w
Apparent
bottom
roughness z0
Critical shear
stress τcr
Wave-current
combined
stress τ*cw

References

Madsen, O.S., 1994, Spectral wave-current bottom boundary layer flows: Coastal Engineering 1994. Proceedings, 24th International Conference Coastal Engineering Research Council, p. 384-398.

Soulsby, R.L., 1997, Dynamics of Marine Sands: London, Thomas Telford, 249 p.

Soulsby, R.L., 2006, Simplified calculation of wave orbital velocities: HR Wallingford Ltd TR-155, 12 pp. + figures p.


Disclaimer

Although this program has been used by the USGS, no warranty, expressed or implied, is made by the USGS or the United States Government as to the accuracy and functioning of the program and related program material nor shall the fact of distribution constitute any such warranty, and no responsibility is assumed by the USGS in connection therewith.


csherwood@usgs.gov
Last revised: 15 April 2015

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