Evolution Equations for Weakly Nonlinear, Long Internal Waves in a Rotating Fluid

Evolution equations are derived for weakly nonlinear, long internal waves in a frame of reference rotating about the vertical axis. When the internal Rossby radius is at most comparable with the wavelength, the evolution equation is a Korteweg‐de Vries equation for shallow fluids, and its counterpart for deep fluids. To leading order the transverse structure is that for a linear internal Kelvin wave. For weaker rotation when effects due to the internal Rossby radius are comparable with the effects due to nonlinearity and dispersion, the evolution equation is a rotation‐modified two dimensional Korteweg‐de Vries equation for shallow fluids, or its counterpart for deep fluids. Some comparisons are made with the recent experiments of Maxworthy (1983).