Stefan G. Llewellyn Smith

Conversion of the Barotropic Tide

Using linear wave theory, the rate at which energy is converted into internal gravity waves by the interaction of the barotropic tide with topography in an ocean is calculated. Bell’s formula for the conversion rate is extended to the case of an ocean of finite depth H with weak two-dimensional topography h(x, y) and arbitrary buoyancy frequency N(z). Approximate solutions are computed using the WKB method, which reduce to the previous result for an ocean of infinite depth with constant stratification. The conversion rate for a finite-depth ocean can be substantially smaller than the infinite-ocean prediction when the length scale of the topography is of the same order as the horizontal wavelength of the internal tide. The conversion rate for two-dimensional Gaussian seamounts is calculated. Using observed statistics for the distribution of seamounts, the authors estimate 1/4 GW of conversion for a square of ocean floor of side 1000 km.

Resonance and propulsion performance of a heaving flexible wing

The influence of the bending rigidity of a flexible heaving wing on its propulsive performance in a two-dimensional imposed parallel flow is investigated in the inviscid limit. Potential flow theory is used to describe the flow over the flapping wing. The vortical wake of the wing is accounted for by the shedding of point vortices with unsteady intensity from the wing’s trailing edge. The trailing-edge flapping amplitude is shown to be maximal for a discrete set of values of the rigidity, at which a resonance occurs between the forcing frequency and a natural frequency of the system. A quantitative comparison of the position of these resonances with linear stability analysis results is presented. Such resonances induce maximum values of the mean developed thrust and power input. The flapping efficiency is also shown to be greatly enhanced by flexibility.

Tidal conversion at a very steep ridge

We obtain an analytic solution for the generation of internal gravity waves by tidal flow past a vertical barrier of height

Vortex shedding model of a flapping flag

b

Tidal Conversion at a Submarine Ridge

in a uniformly stratified ocean of depth

Dynamics of interfaces and layers in a stratified turbulent fluid

h\,{>}\,b

Numerical and Analytical Estimates of M2 Tidal Conversion at Steep Oceanic Ridges

and buoyancy frequency

Scattering of acoustic waves by a vortex

N

Enhanced dispersion of near-inertial waves in an idealized geostrophic è ow

. The radiated power (watts per metre of barrier) is