### Abstract

A set of depth-integrated equations describing combined wave-current flows is derived and validated. To account for the effect of turbulence induced by interactions between waves and currents with arbitrary horizontal vorticity, new additional stress terms are introduced. These stresses are functions of a parameter b that relates the relative importance of wave radiation stress and bottom friction stress to the wave-current interaction. To solve the equations, a fourth-order MUSCL-TVD scheme with an approximate Riemann solver is adopted. As a first-order check of the model, the Doppler shift effect and wave dispersion over linearly sheared currents are analytically shown to be retained appropriately in the equation set. The model results are then validated through comparisons with three experimental data sets. First, based on the experiments of Kemp and Simons (1982, 1983), a reasonable functional form of b is estimated. Second, simulations examining the propagation of a weakly dispersive wave over a depth-uniform or linearly sheared current are performed. Finally, the model is applied to a more complex configuration where bichromatic waves interact with spatially varying currents. Simulated results indicate that the model is capable of predicting nearshore interactions of waves with currents of arbitrary vertical structure. One of the unique properties of the developed model is its ability to assimilate an external current field from any source, be it from a circulation model or an observation, and predict the interaction of a nonlinear and dispersive wave field with that current. •Examine nonlinear waves interacting with a current of arbitrary vertical structure•Employ depth-integrated, Boussinesq-type approach•The model accurately predicts the combined wave-current velocity structure.•The approach can assimilate external current field from any source.

Original language | English |
---|---|

Pages (from-to) | 64-84 |

Number of pages | 21 |

Journal | Coastal Engineering |

Volume | 90 |

DOIs | |

Publication status | Published - 2014 Jan 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Following currents
- Opposing currents
- Radiation stress
- Sheared currents
- Turbulence mixing
- Wave-current interactions

### ASJC Scopus subject areas

- Environmental Engineering
- Ocean Engineering

### Cite this

*Coastal Engineering*,

*90*, 64-84. https://doi.org/10.1016/j.coastaleng.2014.04.009

**Interaction of dispersive water waves with weakly sheared currents of arbitrary profile.** / Son, Sang Young; Lynett, Patrick J.

Research output: Contribution to journal › Article

*Coastal Engineering*, vol. 90, pp. 64-84. https://doi.org/10.1016/j.coastaleng.2014.04.009

}

TY - JOUR

T1 - Interaction of dispersive water waves with weakly sheared currents of arbitrary profile

AU - Son, Sang Young

AU - Lynett, Patrick J.

PY - 2014/1/1

Y1 - 2014/1/1

N2 - A set of depth-integrated equations describing combined wave-current flows is derived and validated. To account for the effect of turbulence induced by interactions between waves and currents with arbitrary horizontal vorticity, new additional stress terms are introduced. These stresses are functions of a parameter b that relates the relative importance of wave radiation stress and bottom friction stress to the wave-current interaction. To solve the equations, a fourth-order MUSCL-TVD scheme with an approximate Riemann solver is adopted. As a first-order check of the model, the Doppler shift effect and wave dispersion over linearly sheared currents are analytically shown to be retained appropriately in the equation set. The model results are then validated through comparisons with three experimental data sets. First, based on the experiments of Kemp and Simons (1982, 1983), a reasonable functional form of b is estimated. Second, simulations examining the propagation of a weakly dispersive wave over a depth-uniform or linearly sheared current are performed. Finally, the model is applied to a more complex configuration where bichromatic waves interact with spatially varying currents. Simulated results indicate that the model is capable of predicting nearshore interactions of waves with currents of arbitrary vertical structure. One of the unique properties of the developed model is its ability to assimilate an external current field from any source, be it from a circulation model or an observation, and predict the interaction of a nonlinear and dispersive wave field with that current. •Examine nonlinear waves interacting with a current of arbitrary vertical structure•Employ depth-integrated, Boussinesq-type approach•The model accurately predicts the combined wave-current velocity structure.•The approach can assimilate external current field from any source.

AB - A set of depth-integrated equations describing combined wave-current flows is derived and validated. To account for the effect of turbulence induced by interactions between waves and currents with arbitrary horizontal vorticity, new additional stress terms are introduced. These stresses are functions of a parameter b that relates the relative importance of wave radiation stress and bottom friction stress to the wave-current interaction. To solve the equations, a fourth-order MUSCL-TVD scheme with an approximate Riemann solver is adopted. As a first-order check of the model, the Doppler shift effect and wave dispersion over linearly sheared currents are analytically shown to be retained appropriately in the equation set. The model results are then validated through comparisons with three experimental data sets. First, based on the experiments of Kemp and Simons (1982, 1983), a reasonable functional form of b is estimated. Second, simulations examining the propagation of a weakly dispersive wave over a depth-uniform or linearly sheared current are performed. Finally, the model is applied to a more complex configuration where bichromatic waves interact with spatially varying currents. Simulated results indicate that the model is capable of predicting nearshore interactions of waves with currents of arbitrary vertical structure. One of the unique properties of the developed model is its ability to assimilate an external current field from any source, be it from a circulation model or an observation, and predict the interaction of a nonlinear and dispersive wave field with that current. •Examine nonlinear waves interacting with a current of arbitrary vertical structure•Employ depth-integrated, Boussinesq-type approach•The model accurately predicts the combined wave-current velocity structure.•The approach can assimilate external current field from any source.

KW - Following currents

KW - Opposing currents

KW - Radiation stress

KW - Sheared currents

KW - Turbulence mixing

KW - Wave-current interactions

UR - http://www.scopus.com/inward/record.url?scp=84899509585&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84899509585&partnerID=8YFLogxK

U2 - 10.1016/j.coastaleng.2014.04.009

DO - 10.1016/j.coastaleng.2014.04.009

M3 - Article

AN - SCOPUS:84899509585

VL - 90

SP - 64

EP - 84

JO - Coastal Engineering

JF - Coastal Engineering

SN - 0378-3839

ER -