On Surf Zone Fluid Dynamics

George Mellor Program in Atmospheric and Oceanic Sciences, Princeton University, Princeton, New Jersey

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Abstract

There have been several numerical models developed to represent the phase-averaged flow in the surf zone, which is characterized by kD less than unity, where k is wavenumber and D is the water column depth. The classic scenario is that of surface gravity waves progressing onto a shore that create an offshore undertow current. In fact, in some models, flow velocities are parameterized assuming the existence of an undertow. The present approach uses the full vertically dependent continuity and momentum equations and the vertically dependent wave radiation stress in addition to turbulence equations. The model is applied to data that feature measurements of wave properties and also cross-shore velocities. In this paper, both the data and the model application are unidirectional and the surface stress is nil, representing the simplest surf zone application. Breaking waves are described empirically. Special to the surf zone, it is found that a simple empirical adjustment of the radiation stress enables a favorable comparison with data. Otherwise, the model applies to the open ocean with no further empiricism. A new bottom friction algorithm had been derived and is introduced in this paper. In the context of the turbulence transport model, the algorithm is relatively simple.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: George Mellor, glmellor@princeton.edu

Abstract

There have been several numerical models developed to represent the phase-averaged flow in the surf zone, which is characterized by kD less than unity, where k is wavenumber and D is the water column depth. The classic scenario is that of surface gravity waves progressing onto a shore that create an offshore undertow current. In fact, in some models, flow velocities are parameterized assuming the existence of an undertow. The present approach uses the full vertically dependent continuity and momentum equations and the vertically dependent wave radiation stress in addition to turbulence equations. The model is applied to data that feature measurements of wave properties and also cross-shore velocities. In this paper, both the data and the model application are unidirectional and the surface stress is nil, representing the simplest surf zone application. Breaking waves are described empirically. Special to the surf zone, it is found that a simple empirical adjustment of the radiation stress enables a favorable comparison with data. Otherwise, the model applies to the open ocean with no further empiricism. A new bottom friction algorithm had been derived and is introduced in this paper. In the context of the turbulence transport model, the algorithm is relatively simple.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: George Mellor, glmellor@princeton.edu
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