On Fofonoff's Mode
The classical barotropic ocean model of Veronis (1966) is reexamined to verify the possible existence of Fofonoff's (1954) steady free inertial mode by considering the balance where J is the Jacobian, eta is the streamfunction of the horizontal velocity, and R is a parameter of nonlinearity. A linear functional relationship between the potential vorticity and the streamfunction and inertial boundary layers along the ocean basin was suggested by Fofonoff. However, the numerical integration showed that the system is barotropically unstable. The typical instantaneous field is given. The statistical equilibrium state eta is also given. Although it resembles Fofonoff's solution, it is maintained by the Reynolds stress field induced by the eddies in addition to the wind stress and dissipation. The plot of eta versus R delta sq +y is given. It is shown that the Fofonoff's linear relation between the potential vorticity and the streamfunction does not hold uniformly over the entire basin. The above results show that the Fofonoff's solution can not be realized physically.