The Analytical Solution of Mid-Latitude Free Vortex Wave of Two-Layer Barotropic Quasi-Equilibrium Ocean Model

A two-dimensional two-layer barotropic quasi-equilibrium ocean model considering Rayleigh dissipation is built, there are two kinds of situations in the model: One is the west coast of the ocean considered only, the other is the east and west coasts of the ocean taken into account. And both analytic solutions of the free vortex wave are given. The results show that, the forms of the solutions are wave packet, when only the west coast of the ocean is considered, whose carrier frequency is continuous spectrum; while both the east and west coasts of the oceans are taken into account, whose carrier frequency is discrete spectrum. And both cases have the same characteristics that: When carrier frequency is higher (period is shorter), the horizontal scale of wave packet is greater. For the excessive low-frequency fluctuations, the quasi-equilibrium assumption will be no longer applied. The period of wave package carrier frequency in the model is about 26 d to 24 a. Because friction is taken into account, the amplitude of wave packets decay exponentially with time, but the size of the coefficient of friction affects only the extent of wave packets decay without altering spatial structure. Finally, amplitude of the wave packet tends to 0, so the solution of the two-layer barotropic ocean model tends to particular solution of atmospheric wind field to forcing. In the model, carrier frequency of wave package spread westward; when the frequency is high, then the westward propagation is faster, and the characteristics and deformation of wave packets are obvious; while the frequency is low, then the westward propagation is slowly, and the waveform is close to plane simple harmonic wave. In the two-layer barotropic model, the flow of the upper flow field is similar to the barotropic model’s, while the lower ocean flow, whose velocity is the same as the upper ocean, the direction opposite. In the model, the nature of fluctuations is the quasi-equilibrium (quasi-non-divergence) vortex wave, when the friction is not too large while horizontal scale of fluctuations is greater than 10 km, the nature is quasi geostrophic Rossby waves.