The Collapse of an Axisymmetric Mixed Patch and Internal Wave Generation in Uniformly Stratified Fluid

Hurricanes are responsible for mixing localized patches of the upper ocean leaving cooler waters in their wakes. The region collapses into a stratified ambient forming an gravity current and generating internal waves beneath the mixed patch. In an effort to understand the axisymmetric collapse of a mixed patch into uniformly stratified fluid laboratory experiments are performed and wave properties are determined using a non-intrusive technique called Synthetic Schlieren. We find internal wave frequencies are set by the buoyancy frequency, $(\omega \approx 0.8 N_0)$ and that the horizontal wavelength is set by the radius of the cylinder so that $k_r \approx 2 R_c$. Vertical displacement amplitudes scale with the depth of the mixed patch according to $\left| \xi \right| / H_m = .016 \pm .001$ and we find that about $2 \%$ of the available potential energy of the mixed region is extracted by vertically propagating internal waves. The work presented here is a precursor to the more complicated rotating case which will more realistically simulate the oceanic example. Extrapolation of these results is certainly premature, but a conservative estimate of the energy extracted by internal waves through the process of mixed region collapse is on the order of $1$\,GW. That is an estimated $2$\,TW of power over the generation time and is comparable to the power exerted by tides and winds over the ocean.