Effect of rotation on the formation of hydraulic jumps

Solutions are found for a finite amplitude gravity wave in a rotating and homogeneous ideal fluid. Pressure is assumed to be hydrostatic, and gradients in one horizontal direction are set equal to zero. A theoretical analysis is made by modifying the nonlinear solution for the nonrotating case. This modification is according to a linear solution for waves in a rotating coordinate system, and it assumes that the rotational effects are small. The analytical solutions are compared with numerical solutions for the complete equations. Results are used to determine the delay in jump formation and the reduction in jump intensity due to rotation. In general, the study shows that both effects are exponentially dependent on the product of the length scale and rate of rotation, and they are inversely proportional to the square of the amplitude of the wave. It is concluded that the dispersion effects of rotation are unimportant in atmospheric situations where hydraulic jump analogies have been proposed.