Bulletin of the American Physical Society
61st Annual Meeting of the APS Division of Fluid Dynamics
Volume 53, Number 15
Sunday–Tuesday, November 23–25, 2008; San Antonio, Texas
Session GH: Internal Waves I |
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Chair: Thierry Dauxois, Laboratoire de Physique, ENS Lyon, France Room: 101B |
Monday, November 24, 2008 8:00AM - 8:13AM |
GH.00001: Internal Gravity Waves Generated by Convective Plumes Joseph Ansong, Bruce Sutherland Internal gravity waves are generated when a turbulent buoyant plume impinges the interface between a uniform density layer and a linearly stratified layer. Laboratory experiments are conducted in which a buoyant plume is released at the top of uniform-density layer. The penetration of the plume into the stable layer causes displacements of the isopycnals which results in the generation of radially and downward propagating waves away from the density interface. We examine the axisymmetric internal gravity waves and their relation to the properties of the plume at the density interface. The conical waves were analyzed using a newly-developed 3D Synthetic Schlieren method. The experiments show that less than five per cent of the plume's energy flux is lost to the waves. The results are related to atmospheric generation of gravity waves by deep convective clouds or thunderstorms through the mechanical oscillator effect. [Preview Abstract] |
Monday, November 24, 2008 8:13AM - 8:26AM |
GH.00002: Analyzing emission, reflection and diffraction of internal waves using the Hilbert transform Matthieu Mercier, Nicolas Garnier, Thierry Dauxois Hilbert Transform applied to two-dimensional internal waves allows a greater understanding of fundamental experiments such as diffraction and reflection. Robustness of this technique based on time and spatial filtering is tested through different types of internal waves generated using a recently developed wavemaker. The analysis of wavefields radiated by a slit and due to an incoming internal plane wave (whose wavelength is comparable to the width of the slit) reveals a diffraction-like pattern. Althouhg differences from the optical phenomenon due to the atypical nature of internal waves are evident, they can be explained with the same principle than ``classical'' diffraction. The study of reflection of internal plane waves using the Hilbert transform focuses on the search for a possible back-reflected beam. In the case of internal plane waves reflecting on a plane slope, no back-reflected beam is observed as predicted by theory. But the case of concave/convex surfaces remains opened. [Preview Abstract] |
Monday, November 24, 2008 8:26AM - 8:39AM |
GH.00003: A novel Internal Wave Generator for Oceanographic Application Thierry Dauxois, Matthieu Mercier, Denis Martinand, Louis Gostiaux, Thomas Peacock We present a new kind of generator of internal waves. It allows to reproduce in a laboratory different internal waves encountered in real oceanographic situations. We will focus our presentation on three different profiles. (i) Internal tide beams as emitted by topographic features analogous to the Thomas and Stevenson self-similar solution of linear viscous internal waves. (ii) Mode-1 internal tide as generated by barotropic tidal flow past ocean bathymetry. (iii) Plane waves beams as generally assumed in theoretical derivations. Several experimental applications will be presented, at small and large scales, together with numerical simulations. [Preview Abstract] |
Monday, November 24, 2008 8:39AM - 8:52AM |
GH.00004: Resonant generation of internal waves on a model continental slope Hepeng Zhang, Ben King, Harry L. Swinney We study internal wave generation in a laboratory model of oscillating tidal flow on a continental margin. Waves are found to be generated only in a near-critical region where the slope of the bottom topography matches that of internal waves. Fluid motion with a velocity an order of magnitude larger than that of the forcing occurs within a thin boundary layer above the bottom surface. The resonant wave is unstable because of strong shear; Kelvin-Helmholtz billows precede wave breaking. We construct a model to extrapolate our results to oceanic conditions. This work [1] provides a new explanation for the intense boundary flows on continental slopes. \\[3pt] [1] H. P. Zhang, B. King and Harry L. Swinney, Phys. Rev. Lett. 100, 244504 (2008). [Preview Abstract] |
Monday, November 24, 2008 8:52AM - 9:05AM |
GH.00005: Generation of internal waves by tidal flow over three-dimensional topography Benjamin King, Hepeng Zhang, Harry L. Swinney An understanding of the internal wave field generated by oscillatory tidal flow over three-dimensional topography is important for ocean models. Recent numerical work has compared the internal wave fields generated by 2D and 3D topography and found that 3D topography can be more than an order of magnitude less efficient at converting the M2 barotropic tide into internal waves.\footnote[1]{P. Holloway, M. Merrifield, J. Geophys. Res. {\bf 104}, 25,937 (1999)}$^,$\footnote[2]{J. R. Munroe, K. G. Lamb, J. Geophys. Res. {\bf 110}, C02001 (2005)} While the previous studies focus on the energy conversion rate, we perform experiments and simulations to examine the generation regions and flow fields in detail. In particular, we present results from numerical simulations of oscillatory flow past supercritical, 3-dimensional topography (a half-sphere on a flat plane). These results are compared to experiments performed on similar topography. In contrast to the 2D case, where all flow is forced to go over the topography, the 3D case has the added complexity that the oscillating flow can either go over or around the topography. We characterize the boundary layer near the topography, and show how regions containing large vertical motion lead to the observed angular dependence of the wave field. [Preview Abstract] |
Monday, November 24, 2008 9:05AM - 9:18AM |
GH.00006: Three dimensional internal-wave radiation by a horizontally oscillating body in a uniformly stratified fluid Evgenyi Ermanyuk, Jan-Bert Flor, Bruno Voisin The energy radiated by a vertically oscillating sphere in a uniformly stratified fluid~has, in shadow-graph 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~\textit{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. [Preview Abstract] |
Monday, November 24, 2008 9:18AM - 9:31AM |
GH.00007: Nonlinear Characteristics of Internal Wave Reflection from Sloping Topography Bruce Rodenborn, Daniel Kiefer, Hepeng Zhang, Harry L. Swinney Internal waves are generated in the oceans by surface waves and abyssal tidal flow over the ocean floor. The interaction among these waves and their reflection from the ocean floor are believed to cause mixing necessary to support thermohaline circulation.\footnote[1]{W. Munk and C. Wunsch, Deep-Sea Res. I {\bf 45}, 1977-2010 (1998)} The reflection of internal waves is often treated as a linear or a weakly nonlinear and inviscid problem\footnote[2]{T. Dauxois and W.R. Young, J. Fluid Mech. {\bf 390}, 271-295 (1999)}, but the full nonlinear effects generate higher harmonics and mixing. We use Particle Image Velocimetry to study the reflection of internal waves from a sloping bottom boundary in a laboratory tank. The experiments are modeled using a 2-D pseudo-spectral numerical simulation that solves the nonlinear problem in the Boussinesq approximation. The kinetic energy density of harmonics generated upon wave reflection from the boundary is examined as a function of the boundary angle and wave angle. Certain harmonics are found to be missing, in accord with recently derived selection rules.\footnote[3] {C.H. Jiang and P.J. Marcus, preprint, (2008)} [Preview Abstract] |
Monday, November 24, 2008 9:31AM - 9:44AM |
GH.00008: A New Branch of Internal Inertial-Gravity Waves in Rotating Flows: Interactions, Selection Rules, Refraction and Roll-Up into Vortices Chung-Hsiang Jiang, Philip Marcus In most atmospheric and oceanographic applications, the Coriolis parameter $f$ is much less than the Brunt-Vaisala frequency $N$, and internal gravity waves with frequency $\omega$ exist when $f < \omega \le N$. However, in many astrophysical applications, such as protoplanetary disks where planets form, there are large regions close to the disk's mid-plane where $N < f$. In those regions a new branch of internal inertial-gravity waves exists with $N < \omega \le f$. These waves have selection rules that determine when their nonlinear interactions can produce harmonics. Collimated beams of these waves travel in straight lines when $N$ and $f$ are constant, but in in regions where either varies with location, the waves refract and the beams bend. Bent, collimated beams of these new waves are ubiquitous in our numerical simulations of protoplanetary disks. When the refraction and bending are large, we find that large amplitude waves ``break'' and spawn vertically-aligned vortices with Rossby numbers less than unity. [Preview Abstract] |
Monday, November 24, 2008 9:44AM - 9:57AM |
GH.00009: Practical Modeling of Internal Wave Tunneling in Variable Ocean Currents James Rottman, Dave Broutman The purpose of this research is to develop a practical Fourier-ray method for computing the propagation of internal waves through current fluctuations in the upper ocean. In particular, we are concerned with modeling wave transmission through thin evanescent layers, a process that cannot be described by ray theory alone. We discovered that the maximum transmission is associated with waves that have four, not two, nearby turning points. The theory for four turning points is not well advanced and is far less practical for computation. For these waves we use a numerical integration of the Taylor-Goldstein equation that is new is two ways. First, we only apply the numerical integration to a small portion of the wavenumber spectrum, namely those components with more than two nearby turning points. We can vectorize the numerical integration of these components over horizontal wavenumbers. Secondly, we do not attempt to find the long-time steady-state solutions, which can have resonant singularities, but instead we find the numerical solution for one reflection from (and one transmission through) the evanescent region, and then add in phase-shifted copies of this solution to account for the contribution for further reflections. [Preview Abstract] |
Monday, November 24, 2008 9:57AM - 10:10AM |
GH.00010: Reynolds Number Dependence of Internal Gravity Wave Dynamics near a Critical Level A. Abdilghanie, P. Diamessis, J. Rottman The interaction of an internal gravity wave packet with a steady background shear flow near a critical level is studied through two-dimensional numerical simulations. Use of a spectral multidomain penalty method and spectral filtering ensures numerical stability without sacrificing spectral accuracy at high Reynolds numbers, where simulations are typically under-resolved. The spatial adaptivity of the multidomain scheme enables flexible resolution of the critical layer region. A mechanical forcing technique is used to generate a vertically localized monochromatic wave-packet propagating towards the background current. The behavior of the waves near the critical level is studied for low and finite amplitude waves. Momentum transfer between the waves and the mean flow is carefully assessed over a broad range of Reynolds numbers. The effect of Reynolds number is also considered in terms of the role of shear intensification and static instabilities to the ensuing wave behavior near the critical level. [Preview Abstract] |
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