Internal wave structure emitted by a horizontally oscillating sphere

International audienceAn oscillating body in a stratified fluid generates a double cone-shaped internal-wave pattern, the 3D analogue of the classic St.Andrew-cross. For sufficiently low frequency and large amplitude oscillations, higher-order wave harmonics may be generated along with the fundamental one. We present an experimental study of the 3D structure of first- and second-order wave fields emitted by a horizontally oscillating sphere. In contrast to the axisymmetric wave pattern found for a vertically oscillating sphere, for horizontal oscillations, the first- and higher-order-harmonic waves have different distributions of wave amplitudes in the azimuthal direction. The amplitude of the first-order waves is shown to follow the cosine dependence on the azimuthal angle, in accordance with theoretical predictions. The azimuthal distribution of the amplitude of the second-order waves gives evidence of a quadrupolar distribution, with four preferential directions of wave radiation in a horizontal plane, along the direction of oscillation and normal to it. Noteworthy is that the amplitudes of these second-order waves may exceed the amplitude of first-order waves

Internal-wave radiation by a horizontally oscillating body in a uniformly stratified fluid

International audienceIn this experimental-theoretical study we consider the waves emitted by a horizontally oscillating sphere in a linearly stratified fluid. In contrast to former investigations, the thus generated wave pattern is a-symmetric and three-dimensional. We consider large and small amplitude horizontal oscillations for different size spheres. The spatial structure of internal waves has a non-trivial dependence on the body geometry, direction and frequency of oscillations. The flowfield is measured quantitatively, using an alternative version of the synthetic schlieren technique. In addition we exploit the technique to visualise internal waves with fluorescein dye planes used by Hopfinger et al (Exp. in Fluids, 11, 1991) to measure the displacement field of the internal waves. For the theory a uniformly stratified viscous Boussinesq fluid of infinite extent is considered, with small viscosity and the boundary layer on the body surface neglected. For small amplitude oscillations, the comparison with the theory is good, with the near-field theory being in very good agreement with the experimental results and the far field theory slightly overestimating the wave amplitude

Energy cascade in internal wave attractors

One of the pivotal questions in the dynamics of the oceans is related to the cascade of mechanical energy in the abyss and its contribution to mixing. Here, we propose internal wave attractors in the large amplitude regime as a unique self-consistent experimental and numerical setup that models a cascade of triadic interactions transferring energy from large-scale monochro-matic input to multi-scale internal wave motion. We also provide signatures of a discrete wave turbulence framework for internal waves. Finally, we show how beyond this regime, we have a clear transition to a regime of small-scale high-vorticity events which induce mixing. Introduction

Three dimensional internal-wave radiation by a horizontally oscillating body in a uniformly stratified fluid

International audienceThe energy radiated by a vertically oscillating sphere in a uniformly stratified fluid has, in shadowgraph and schlieren images, the well known "St. Andrew cross" ray pattern. Since the wave length does not appear in the dispersion relation, the spatial structure of internal waves has non-trivial dependence on the body geometry, direction and frequency of oscillations, and the viscosity. In contrast to former investigations, in the present investigation we consider the asymmetric 3D wave pattern for large and small amplitude horizontal oscillation of different size spheres. New experimental techniques are explored. For small oscillations good agreement is found with linear theory; in addition to comparison between experimental data and theoretical (near-field) solution we also present the comparison between the far-field and near-field solutions

First and second harmonic internal waves from a horizontally oscillating sphere

International audienceA horizontally oscillating sphere in a density-stratified fluid is studied experimentally and theoretically, as a paradigm of the generation of three-dimensional internal tides by supercritical topography. The experiments implement a novel technique for the measurement of the spatial structure of internal wave fields, based on horizontal fluorescent dye planes and a mobile vertical laser sheet; they are compared with an original linear theory. Spectral analysis reveals the presence of two harmonics, namely a first harmonics at the fundamental frequency and a second harmonics at twice this frequency. The first harmonics has a dipolar structure, an amplitude varying linearly with the amplitude of oscillation, and is quantitatively described by the theory. The second harmonics is present at amplitudes of oscillation higher than one tenth of the sphere radius and has a quadrupolar structure. Its amplitude varies quadratically with the amplitude of oscillation, and may exceed the amplitude of the first harmonics. At frequencies smaller than half the buoyancy frequency, the second harmonics is evanescent and confined to the vicinity of the sphere; at frequencies larger than half the buoyancy frequency, it propagates away

Internal wave focusing by a horizontally oscillating torus: nonlinear aspects

International audienceDissipation due to nonlinear breaking of internal tides is believed to play an important role in the mixing of the abyssal ocean, and therefore in the large-scale ocean circulation. In the laboratory, we generate the internal waves by an oscillating objects in a linearly stratified fluid. Over the past five decades the dynamics of particularly diverging internal waves have been considered, such as generated by cylinder (Mowbray & Rarity, 1967) or spheroid (Ermanyuk et al., 2011; Shmakova et al. 2017). However, the localized zones representing hot spots for incipient overturning may occur close to curved topographies owing to the concentration of energy due to wave focusing (Buijsman et al. 2014, Peliz et al. 2009). Ermanyuk et al. (2017) showed experimentally with a horizontally oscillating torus that in a linear regime the wave amplitude amplifies in the focal zone and increases linearly with increasing oscillation amplitude. Here we investigate weakly nonlinear and nonlinear effects of focusing internal waves generated by a torus with radius $b$ and a circular cross-section of radius a oscillating horizontally with amplitude A. LIF and PIV techniques are used to measure the isopycnal displacement and the velocity, respectively. The nonlinear effects are investigated in terms of wave slopes as a function of newly developed focusing number defined as {Fo} = (A/a)\epsilon^{−1/2}f(\theta), which includes the amplitude increase due to focusing as epsilon^{1/2} = \sqrt{b/a} and the variation in energy with the propagation angle theta. The data obtained for different sizes tori predict the wave breaking for the critical value of {Fo}=0.23. Below this value, nonlinear effects in the focal zone arise in the generation of the vertical mean flow and evanescent higher harmonics. Above the critical number the focal region is unstable due to triadic wave resonance (TRI) that is formed of the fundamental wave and two subharmonic waves generated in the focal zone. The observed TRI in three dimensional flow resembles closely the resonance obtained by Bourget et al. (2013) for a two-dimensional flow due to the symmetry of our problem, and thus with the amplitude maximum in the symmetry plane (Shmakova et al., 2019)

Focalisation linéaire d'ondes internes par un tore oscillant

Parmi les phénomènes susceptibles de provoquer localement une intensification de l'amplitude des ondes internes dans un fluide stratifié, et ainsi de conduire au mélange, figure un phénomène spécifiquement tridimensionnel : la focalisation géométrique causée par la forme de l'émetteu

Generation of higher harmonic internal waves by oscillating spheroids

International audienceOscillating bodies in stratified fluids may emit higher harmonics in addition to fundamental waves. In the present experimental study, we consider higher harmonics of an internal wave field generated by a horizontally oscillating spheroid in a linearly stratified fluid for moderate to high oscillation amplitudes, i.e., scaled oscillation amplitude A/a≥0.5, with a the minor radius of the spheroid. Three different spheroid shapes are tested. The results are discussed in the context of the different theories on the generation of higher harmonics. Higher harmonics are observed at the intersections of fundamental wave beams, and at the critical points of the topography where the topographic slope equals the wave slope. The velocity amplitudes of the fundamental, second, and third harmonic waves grow respectively linearly, quadratically, and with the third power of the scaled oscillation amplitude A/a. Though these amplitudes are generally higher when the object's slope is larger, the increase in amplitude above and below the axisymmetric oscillating objects is found to be due to the effect of focusing. In order to discern the relative importance of the harmonics to the fundamental wave, the horizontal structure of the wave amplitude is measured. The results suggest that the nth harmonic of the internal wave field is associated with a radiation diagram corresponding to a multipole of order 2n, with 2n directions of propagation