Analytic solutions to long's model: A comparison of nonhydrostatic and hydrostatic cases

Summary In this paper, analytic solutions of the nonhydrostatic and hydrostatic forms of Long's model were obtained under two different sets of vertical boundary conditions: The first uses a sumusoidal obstacle at the lower boundary and a rigid-lid top for the upper boundary. The second set applies an isolated obstacle of the Witch of Agnesi type at the lower boundary, while still using a rigid lid at the top. Following the solution evaluations, comparisons between the nonhydrostatic and hydrostatic solutions were processed in order to describe several influences introduced by using the hydrostatic assumption in this model.Through comparisons we have found that, in the case of a sinusoidal lower boundary condition, the hydrostatic solution is obtained as the zero mode of the nonhydrostatic solution. The influence of the hydrostatic assumption on the model solution is trivial in this case. When an isolated lower boundary condition is applied, however, the solutions illustrate dramatic differences, showing the significance of the effect of hydrostatic assumption on this model's solutions. These effects vary considerably with the model parameters as well. The comparison results also reveal that the realization of the hydrostatic assumption in this model's solutions is accomplished through the vertical boundary conditions used in the model evaluations.With 5 Figures