E. V. Ermanyuk

Spatial structure of first and higher harmonic internal waves from a horizontally oscillating sphere

An experimental study is presented on the spatial structure of the internal wave field emitted by a horizontally oscillating sphere in a uniformly stratified fluid. The limits of linear theory and the nonlinear features of the waves are considered as functions of oscillation amplitude. Fourier decomposition is applied to separate first harmonic waves at the fundamental frequency and higher harmonic waves at multiples of this frequency. For low oscillation amplitude, of 10 % of the sphere radius, only the first harmonic is significant and the agreement between linear theory and experiment is excellent. As the oscillation amplitude increases up to 30 % of the radius, the first harmonic becomes slightly smaller than its linear theoretical prediction and the second and third harmonics become detectable. Two distinct cases emerge depending on the ratio Ω between the oscillation frequency and the buoyancy frequency. When Ω > 0.5, the second harmonic is evanescent and localized near the sphere in the plane through its centre perpendicular to the direction of oscillation, while the third harmonic is negligible. When Ω < 0.5, the second harmonic is propagative and appears to have an amplitude that exceeds the amplitude of the first harmonic, while the third harmonic is evanescent and localized near the sphere on either side of the plane through its centre perpendicular to the direction of oscillation. Moreover, the propagative first and second harmonics have radically different horizontal radiation patterns and are of dipole and quadrupole types, respectively.

Internal wave focusing by a horizontally oscillating torus

This paper presents an experimental study on internal waves emitted by a horizontally oscillating torus in a linearly stratified fluid. Two internal wave cones are generated with the kinetic energy focused at the apices of the cones above and below the torus where the wave amplitude is maximal. Their motion is measured via tracking of distortions of horizontal fluoresce in dye planes created prior to the experiments and illuminated by a vertical laser sheet. The distortion of the dye planes gives a direct access to the Lagrangian displacement of local wave amplitudes and slopes, and in particular, allows us to calculate a local Richardson number. In addition particle image velocimetry measurements are used. Maximum wave slopes are found in the focal region and close to the surface of the torus. As the amplitude of oscillations of the torus increases, wave profiles in the regions of maximum wave slopes evolve nonlinearly toward local overturning. A theoretical approximation based on the theory of Hurley & Keady is presented and shows, for small amplitudes of oscillation, a very reasonable agreement with the experimental data. For the focal region the internal wave amplitude is found to be overestimated by the theory. The wave breaking in the focal region is investigated as a function of the Keulegan-Carpenter number,

Taylor–Couette flow in a two-layer stratified fluid: instabilities and mixing

K_e = A/a

Generation of higher harmonic internal waves by oscillating spheroids

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Geometric focusing of internal waves: Experimental study

A

Internal wave focusing by annular forcing: theory

the oscillation amplitude and a the short radius of the torus. A linear wave regime is found for

Focalisation linéaire d'ondes internes par un tore oscillant

K_e 0.8

First and second harmonic internal waves from a horizontally oscillating sphere

. For large forcing, the measured wave amplitude normalized with the oscillation amplitude decreases almost everywhere in the wave field, but increases locally in the focal region due to nonlinear effects. Due to geometric focusing the amplitude of the wave increases with

sphere, with application to internal tides

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Structure of baroclinic flows around seamounts

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