两层正压准平衡海洋模型的中纬度自由涡旋波动解

建立了具有瑞利摩擦且仅考虑大洋西海岸或同时考虑大洋东、西海岸的两层正压准平衡海洋模型,并做了解析求解,用以研究中纬度的自由涡旋波。得到的主要结论有:模型中该波动的解为波包。在仅考虑大洋西海岸时该波包的载频频率是连续谱;而同时考虑大洋东、西海岸时其为离散谱;且均有载频频率越高(周期越短)水平尺度越大的特点,对过分低频的波动,则会使准平衡的假定不再适用。模型中该波动波包载频的周期约在26天至24年。因考虑了摩擦,该波包的振幅随时间呈指数衰减,但摩擦系数的大小仅影响其衰减程度而不改变其空间结构,最终该波包振幅趋于0,故该两层正压海洋模型的解就趋于大气风场的强迫特解。模型中该波包的载频都是西传的;频率较高则西传较快,波包的特性和变形都很明显;频率低,则西传慢,其波形接近平面简谐波。在该两层正压模型中,该波动上层流场与正压模型中的流动类似,而下层海洋流动则其流速与上层海洋相同,而流向相反。该模型中该波动的性质是准平衡(准无辐散)的涡旋波,当摩擦不太大且其水平尺度在10km以上时,其性质则为准地转的Rossby波。

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.