Effects of rotation on internal solitary waves

We numerically investigate the propagation of internal solitary waves under the Coriolis effect using a three-dimensional hydrodynamic model, which employs a periodic boundary condition in the transverse direction of propagation. As the Rossby number decreases, the group velocity and representative length of the wave train also decrease. Intriguingly, the speed of the waves inside the wave train equals the difference in group velocities between no rotation and rotation when the Rossby number is more than 3. Our energy analysis found that the kinetic energy must be greater than the potential energy. Moreover, the kinetic energy in the transverse direction is necessary for stable propagation of the wave train. The total and kinetic energies were confirmed to have lower attenuation rates as the Rossby number increased. In contrast, the potential energy had a lower attenuation rate for smaller Rossby numbers, suggesting that kinetic energy determines energy attenuation for such numbers. As for the real scale phenomena, the present results revealed that significant energy attenuation of the internal solitary waves due to the rotation can be expected in areas less than a nondimensional water depth of 0.84, and where the nondimensional longwave speed is less than 0.55.