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 *T _{z}*, and we assume 1.28*

Parameters:

**Value**

Water depth *h*

Wave height *H*_{s}

Wave period *T*_{d}

Wave direction

Current speed

at 1 mab

at 1 mab

Current

direction

direction

Grain size *D*_{50}

Wave-orbital

velocity*u*_{br}

velocity

Grain

roughness*k*_{s}

roughness

Friction

factor*f*_{wc}

factor

Current shear

stress*τ*_{*c}

stress

Wave shear

stress*τ*_{*w}

stress

Apparent

bottom

roughness*z*_{0}

bottom

roughness

Critical shear

stress*τ*_{cr}

stress

Wave-current

combined

stress*τ*_{*cw}

combined

stress

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.

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