Waves in a rotating stratified fluid with laterally varying random inhomogeneities
We discuss the propagation and stability of internal waves in a rotating stratified unbounded fluid with randomly varying buoyancy frequency, N. The first order smoothing approximation is used to derive the mean wave dispersion relation when N is of the form N2=N 0 2 (1+εM), where N0=constant, 0<ε2<<1 and M is a centered stationary random function of the horizontal direction x. This form for M represents a stochastic model of the lateral variations in the temperature and salinity microstructure in the ocean. From the complex dispersion relation, expressions are obtained for the phase speed change and spatial growth rate (§ 2); in particular, attention is focused on the asymptotic behaviour of these expressions for short and long correlation lengths (§ 3).
KeywordsCorrelation Length Internal Wave Phase Speed Wave Dispersion Relation Spatial Growth Rate
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