Zonally propagating wave solutions of Laplace Tidal Equations in a baroclinic ocean of an aqua-planet
Zonally propagating wave solutions of Laplace Tidal Equations in a baroclinic ocean of an aqua-planet
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水行星斜压海洋中拉普拉斯潮汐方程的纬向传播波解
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发表时间：
2011
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通讯作者：
N. Paldor
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文献类型：
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作者：
Y. De;N. Paldor
尽管拉普拉斯潮汐方程（LTE）在近250年前就有了精确的表述，但这些方程在球形行星上的解析解只在缓慢旋转的行星上找到了波解色散关系的显式表达式，因此这些解与地球无关。最近，用Schr¨odinger方程逼近了旋转球面上对称赤道通道中LTE的解析解，该方程的能级产生了纬向传播波的色散关系，其本征函数决定了这些波的振幅的子午结构。用Schr¨odinger方程对球体（没有通道壁）上的LTE进行类似近似，可以得到斜压海洋相关参数范围内的带向传播波的精确解析解，在斜压海洋中，变形半径与地球半径之比很小。对于足够低的（经向）模态，解的振幅在一些热带外纬度消失，但这不是假定完全消失的。这些新发现的解并没有限制纬向波数的值小于子午波数，就像以前关于慢旋转球体的理论那样。
Despite the accurate formulation of Laplace’s Tidal Equations (LTE) nearly 250 years ago, analytic solutions of these equations on a spherical planet that yield explicit expressions for the dispersion relations of wave solutions have been found only for slowly rotating planets, so these solutions are of no relevance to Earth. Analytic solutions of the LTE in a symmetric equatorial channel on a rotating sphere were recently obtained by approximating the LTE by a Schr¨odinger equation whose energy levels yield the dispersion relations of zonally propagating waves and whose eigenfunctions determine the meridional structure of the amplitude of these waves. A similar approximation of the LTE on a sphere (with no channel walls) by a Schr¨odinger equation yields accurate analytic solutions for zonally propagating waves in the parameter range relevant to a baroclinic ocean, where the ratio between the radius of deformation and Earth’s radius is small. For sufficiently low (meridional) modes the amplitudes of the solutions vanish at some extra-tropical latitudes but this is not assumed abinitio. These newly found solutions do not restrict the value of the zonal wavenumber to be smaller than the meridional wavenumber as is the case in previous theories on a slowly rotating sphere.