Coriolis effect on stationary nonlinear long wavelength water waves - revisited

Abstract

We revisit the problem of fully nonlinear, long wavelength waves in rotating shallow water, originally analyzed by Shrira [10], and here provide a physical interpretation which complements the original mathematical analysis. Our approach makes explicit use of the properties of the wave Bernoulli energy, and its integral, to elucidate the nature of the waves of the system. In particular, we show that it is the phenomenon of choked fbw, which occurs where the longitudinal fbw speed becomes critical, that prevents the formation of a solitary wave solution despite its necessary (but not sufficient) condition being satisffed for Froude numbers F < 1. On the other hand the supercritical case, F > 1, gives rise to nonlinear periodic waves, which are asymmetric with respect to their crests and troughs and, in the limiting case, become wedge-shaped waveforms of elevation when the local fbw speed approaches its critical value. These interesting properties are readily obtained from a simple graphical interpretation of the wave structure equation which reveals the compressive and rarefactive wave amplitudes as the intersections between the integral of the wave Bernoulli energy and an initial driver wave energy. Similar choked fbw behaviour is found in nonlinear waves in plasma physics systems, where the sonic point imposes restrictions on wave amplitudes and may also give rise to wedge-shaped waveforms.