On the multiple solutions to a three-coefficient spectral model of wind-driving ocean current equation

In this paper, a research on the problem of multiple solutions of the three-coefficient low-spectrum model for the quasi-geostrophic ocean current equation with forcing and dissipation terms is carried out. The state of the ocean current under wind conditions such as those of typhoon is discussed carefully and the relations between the multiple solutions and the coefficientsR and ε are analyzed. It is seen that in an approximate triangular region with the Rossby-coefficientR less than 0.5, and the friction-coefficient ε less than 0.22, there exist three equilibrium solutions, among which two are stable and one is unstable. For the former, the coefficientA orB in the expansion is rather large, while for the latter.A orB is relatively small. They respectively imply how much the ocean energy is fed back from the wind stress and the solution with a largeA is much more stable than that with a largerB. Institute of Systems Science, Academia Sinica The project partly supported by the national project of 75-76-01-03 “Study on numerical prediction of the South China Sea current”.