On the propagation of topographically trapped waves

Abstract

In the context of ageostrophic theory in a homogeneous ocean, a nondimensional number is determined which corresponds to the Ursell number for long gravity waves. It is defined as Q = NL ²/h ³, where N is the amplitude of the wave travelling along the long length-scale direction, L is its length and h (which for gravity waves is the water depth) is given by h=(l ⁴ f ²/g)^1/3. where l is the short length-scale, f the Coriolis parameter and g the acceleration due to gravity. The physical meaning of Q is as follows: if Q≪ O(1) the free evolution of the wave is linear and weakly dispersive, if Q = O(1) nonlinear and dispersive effects balance out and finally if Q ≫O(1) the evolution is nonlinear and non-dispersive. Expressions for the time scales for the development of dispersive and nonlinear effects are also determined. These results apply to topographically trapped waves, namely barotropic continental shelf and double Kelvin waves travelling along a rectilinear topographic variation.