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By vertical boundary conditions, a spectral expansion of horizontal tide wave velocity is done in vertical direction in terms of a complete basis functions selected properly, hence a relation between tide levels and spectral components is found theoretically under condition of ignoring the horizontal friction stress and nonlinear effect. And a relation between bottom friction of tide current, which satisfies the viscous condition on sea bottom, and tide levels is determined. The relation is different from the relation of the traditional parameterizing of bottom friction. Moreover integration of the continuity equation and momentum equations is carried out in the vertical direction using zero flux condition on solid boundaries and inputting condition on open boundaries, and then a boundary value problem of elliptic form on the tide levels is constructed.
By vertical boundary conditions, a spectral expansion of horizontal tide wave velocity is done in vertical direction in terms of a complete basis functions selected properly, hence a relation between tide levels and spectral components is found theoretically under condition of ignoring the horizontal friction stress and nonlinear effect. And a relation between bottom friction of tide current, which satisfies the viscous condition on tide current, which satisfies the viscous condition on sea bottom, and tide levels is determined. The relation is different from the relation of the traditional parameterizing of bottom friction. equations is carried out in the vertical direction using zero flux condition on open boundaries, and then a boundary value problem of elliptic form on the tide levels is constructed.