“Laplace derived the differential equations for a thin fluid on a sphere with no vertical motion, only horizontal motions, called a barotropic model. Ocean tides are caused by the horizontal gravitational force of Moon and Sun. The Earth rotates so we have Corriolis forces. A slope in the sea-surface also causes horizontal force. Bottom friction and/or lateral eddy dissipation.” Thus you can use the equation to compute for the ocean tides.

 

Source: http://wakes.uma.pt/cimar/PartII_lecture1.pdf

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