Three-dimensional simulation of wave-induced circulation: Comparison of three radiation stress formulations

Abstract

[1] A three-dimensional current-wave modeling system, Curvilinear-grid Hydrodynamics 3D (CH3D)-Simulating Waves Nearshore (SWAN), has been used to simulate wave-induced circulation and compare the performances of three radiation stress (RS) formulations: two depth-dependent formulations (M08 by Mellor (2008) and X04 by Xia et al. (2004)) and one depth-independent formulation (LHS by Longuet-Higgins and Stewart (1964)). While all are based on linear wave theory, LHS uses the vertically integrated equations of motion, and M08 and X04 consider the three-dimensional equations of motion. Results of CH3D-SWAN with three RS formulations are compared with steady state wave setup, observed data in an undertow experiment by Ting and Kirby (1994) (TK94), and observed data in a laboratory fringing reef. All three RS formulations reproduce the analytical solution of wave setup very well. Simulated wave-induced currents and turbulence for TK94 are the best when M08 is used and worst when X04 is used, apparently due to the errors in the X04 formulation. All three RS formulations give good simulation of wave setup in the fringing reef. Wave-induced currents in the fringing reef simulated by the three RS formulations are quite different: M08 produces a single large clockwise gyre in the x-z plane, LHS produces a weaker gyre, and X04 produces a clockwise gyre plus a counterclockwise gyre inside the surf zone. Using the CH3D-Storm Surge Modeling System and M08, storm surge and currents in the Outer Banks and Chesapeake Bay during Hurricane Isabel are simulated. Compared to the earlier simulation obtained with the LHS, M08 produces similar storm surge but slightly improved the wave-induced currents.