The axisymmetric collapse of a mixed patch and internal wave generation in uniformly stratified fluid

Abstract

Laboratory experiments are used to investigate the axisymmetric collapse of a localized mixed region in uniformly stratified ambient. The collapsing fluid forms an intrusion and generates vertically propagating internal gravity waves in the stratified ambient. The speed of the intrusion is found to be (0.085±0.001)N0Hm where Hm is the depth of the mixed patch and N0 is the buoyancy frequency. Internal wave frequencies are set by the buoyancy frequency, (ω≃0.8N0), and the effective horizontal wavenumber is set by the radius of the cylinder so that kr≃2Rc. Vertical displacement amplitudes scale with the depth of the mixed patch according to |ξ|/(Hm/2)=0.032±0.002 and we find that about 2% of the available potential energy of the mixed region is extracted by the internal waves. Extrapolation of these results to oceanic circumstances of mixed region collapse beneath a hurricane gives a conservative estimate of the power extracted by internal waves during the lifecycle of the storm is estimated to range from 6×1010 to 4×1012 W. The corresponding power from all hurricanes averaged over the course of a year can range from 1×109 to 8×109 W.