A numerical algorithm for solving a coupled problem of the air-sea-wave interaction

Abstract

The “partly coupled” algorithm and numerical schemes are developed to solve a coupled model of air-sea-wave interaction, using the matrix and simple pivotal-condensation methods. The “partly coupled” algorithm is used to handle boundary conditions at the air-sea interface to allow for solving systems of the atmospheric and oceanic equations, as two separate systems. This “partly coupled” algorithm is simpler, more effective, and requires less computing efforts to solve an air-sea-wave coupled model compared to the “fully coupled” algorithm developed by Ly [1] for solving a coupled model of the baroclinic atmospheric and oceanic boundary layers. In the numerical schemes, the buoyancy terms of dissipation and TKE budget equations are used as conditions for rearranging equation coefficient vectors to satisfy stability conditions. The mathematical coupled model of the air-sea-wave system is also presented. The model equations are written in the same form for both atmospheric and oceanic boundary layers, and include equations for momentum, the κ-ε turbulence scheme, and stratification in the atmospheric and oceanic boundary layers. In the model, ocean wind-induced wave effects are modeled by using boundary conditions for the turbulent energy dissipation at the interface in a κ-ε turbulence closure of the coupled model. Numerical experiments are designed for various geostrophic winds, wave heights, and wave ages under neutral atmospheric stratification to demonstrate an example in solving a coupled model of the air-sea-wave system. The numerical simulations show that surface wind-induced waves have strong effects on the basic physical characteristics of the air-sea system.