Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session H28: Waves III |
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Chair: Reza Alam, University of California, Berkeley Room: Spirit of Pittsburgh Ballroom B/C |
Monday, November 25, 2013 10:30AM - 10:43AM |
H28.00001: A model for internal wave drift Fan Lin, James Munroe We studied the motion of neuturally buoyant spheres induced by internal waves in a linearly stratified fluid with moderate Reynolds number (200-300). The characteristic scale of the sphere is much smaller than the wavescale ($D/\lambda<0.05$) so we apply the Morison equation to model the motion of the spheres. In our 5-metre long wave tank, a mode-1 internal wave was generated by a wave generator to study the motion of the spheres. Experimental results show that similar to surface waves, there exists a wave induced drift of the sphere resulting from the phase lag between the motion of the sphere and the fluid. The magnitude and direction of the drift velocity $u_d$ can be affected by many parameters, including the initial phase of the wave generator, depth of the sphere, and the frequency of the internal waves. An empirical formula for $u_d$ will be introduced and will be compared to the theoretical results from a numerical simulation. For the vertical motion of the sphere, both the experiment and numerical simulation show that at low frequency of the internal waves $(\omega/N<0.2)$, a series of harmonics of $\omega$ appear in the vertical motion. [Preview Abstract] |
Monday, November 25, 2013 10:43AM - 10:56AM |
H28.00002: Weakly nonlinear models for internal waves Shengqian Chen, Roberto Camassa In the class of weakly nonlinear models for internal waves, some systems are solvable by the Inverse Scattering Transform (IST). However, these models have the drawback of being ill-posed, or highly oscillatory wavetrains may develop in the solution such as for the Korteweg de Vries equation, thereby preventing standard numerical approaches from achieving the desired accuracy. In this talk, we propose a regularized version of the ill-posed two-layer Kaup, and the solitary wave solution for the new model is provided. The particular nature of the ill-posedness of Kaup's system proves to be rather challenging for designing numerical solution algorithms, a situation that is completely by-passed by the new regularized Kaup system. We provide numerical evidence showing that our regularization has little influence on the prediction offered by IST: the soliton content of initial data based on Kaup's system is left basically intact by its regularized counterpart, as tested by the numerical simulations of the new model. [Preview Abstract] |
Monday, November 25, 2013 10:56AM - 11:09AM |
H28.00003: Particle dispersion induced by random internal waves Oliver Buhler, Nicolas Grisouard, Miranda Holmes-Cerfon This is a theoretical and numerical study of quasi-horizontal particle dispersion along stratification surfaces induced by random internal waves at small amplitude. The original motivation was small-scale particle dispersion in the deep ocean, but the theory is more general. The novelty is the realization that a small amount of wave dissipation can have a large impact on the dispersion process as measured by the Taylor diffusivity, for example. Basically, weak dissipation greatly strengthens the Taylor diffusivity, a fact that had been mostly overlooked in the literature so far. Here we present a combination of simple linear and nonlinear stochastic models as well as of fully nonlinear 3d simulations of the continuously stratified Boussinesq equations that explore this new situation. Particular attention is paid to the different power-law scalings of the Taylor diffusivity with wave amplitude that are obtained under different models for the wave dissipation, eg either due laminar viscous dissipation or due to nonlinear wave breaking. [Preview Abstract] |
Monday, November 25, 2013 11:09AM - 11:22AM |
H28.00004: Internal Wave Breaking From Parametric Subharmonic Instability James Munroe Parametric subharmonic instability is an energy transfer mechanism between internal waves from large to small spatial scales. In this type of resonant triad interaction, a parent wave of higher frequency destabilizes leading to the growth of two daughter waves with lower frequencies. In a laboratory experiment, a full-depth wave generator forces a high frequency vertical mode-1 wave and parametric subharmonic instability generates large amplitude, high vertical wave number waves. [Preview Abstract] |
Monday, November 25, 2013 11:22AM - 11:35AM |
H28.00005: Internal Waves Generated By A Horizontally Moving Source In A Thermocline - A WKB Approach Laura Brandt, Cecily Keppel, James Rottman, David Broutman A new, computationally efficient method is described for calculating the internal wavefield generated by a localized source moving horizontally within an ocean thermocline. The new method involves Fourier-space ray-tracing, instead of a more traditional Green's function approach with eigenfunction expansion. In addition to computational efficiency, the new method provides physical insight into how the wavefield is generated. The Fourier-space ray-tracing method reproduces all of the terms in the Green's function solution (not just the eigenfunctions) and provides a physical explanation of the significance of an eigenfunction derivative term in that solution. For validation, this new method is compared with and used to analyze and explain the various transverse and divergent wave modes observed in previously published experimental tank data. [Preview Abstract] |
Monday, November 25, 2013 11:35AM - 11:48AM |
H28.00006: Stability of internal wave beams to three-dimensional modulations T.R. Akylas, T. Kataoka The linear stability of uniform, plane internal wave beams with locally confined spatial profile, in a stratified fluid of constant buoyancy frequency, is discussed. The associated eigenvalue problem is solved asymptotically, assuming perturbations of long wavelength relative to the beam width. In this limit, instability is found only for oblique disturbances which vary in the along-beam and the horizontal transverse directions. Progressive beams, which transport energy in one direction and are directly relevant to internal tides, are unstable if the beam steepness exceeds a certain threshold value, whereas purely standing beams are unstable even at infinitesimal steepness. A distinguishing feature of this three-dimensional modulational instability is the generation of circulating horizontal mean flows at large distances from the vicinity of the beam. [Preview Abstract] |
Monday, November 25, 2013 11:48AM - 12:01PM |
H28.00007: Interactions between capillary wave turbulence and hydrodynamics turbulence Michael Berhanu, Leonardo Gordillo, Timothee Jamin, Eric Falcon We report experiments on capillary wave turbulence at the air-water interface. The field of wave elevation is measured using Diffusing Light Photography method. When wave turbulence regime is reached, we observe power-law spectra of wave elevation, both in frequency and in wave number, whose exponents are found in agreement with the predictions of capillary wave turbulence theory, although some hypotheses are not fulfilled. By the means of a laser sheet, we complete our observations by measuring in the same conditions in a vertical plane, the space-time deformation of the free surface using a Radon transform and the corresponding velocity field using 2D PIV algorithms. We aim to characterize vorticity generation by the waves and interaction between wave turbulence and hydrodynamics turbulence. These phenomena could indeed increase strongly the effective dissipation of non-linear propagating waves. [Preview Abstract] |
Monday, November 25, 2013 12:01PM - 12:14PM |
H28.00008: On the unsteady gravity-capillary wave pattern found behind a slow moving localized pressure distribution N. Masnadi, J.H. Duncan The non-linear response of a water surface to a slow-moving pressure distribution is studied experimentally using a vertically oriented carriage-mounted air-jet tube that is set to translate over the water surface in a long tank. The free surface deformation pattern is measured with a full-field refraction-based method that utilizes a vertically oriented digital movie camera (under the tank) and a random dot pattern (above the water surface). At towing speeds just below the minimum phase speed of gravity-capillary waves ($c_{min}\approx23$ cm/s), an unsteady V-shaped pattern is formed behind the pressure source. Localized depressions are generated near the source and propagate in pairs along the two arms of the V-shaped pattern. These depressions are eventually shed from the tips of the pattern at a frequency of about 1 Hz. It is found that the shape and phase speeds of the first depressions shed in each run are quantitatively similar to the freely-propagating gravity-capillary lumps from potential flow calculations. In the experiments, the amplitudes of the depressions decrease by approximately 60 percent while travelling 12 wavelengths. The depressions shed later in each run behave in a less consistent manner, probably due to their interaction with neighboring depressions. [Preview Abstract] |
Monday, November 25, 2013 12:14PM - 12:27PM |
H28.00009: 3D Solitons of Capillary-Gravity and Flexural-Gravity Waves Reza Alam In the context of nonlinear water wave theory an intriguing question has always been if fully-localized 3D wave structures, counterparts of 2D solitons, can exist. These structures are important because, if exist, they can transport mass, momentum and energy over long distances. For pure gravity waves this possibility is already ruled out, but- as we will discuss- few limiting cases of capillary-gravity and flexural-gravity wave equations admit such solutions in the form of dromions and lumps. Here we show that weakly nonlinear flexural-gravity wave packets, such as those propagating on the surface of ice-covered waters, admit three-dimensional fully localized solutions in the form of dromions. This study is motivated by observations of (relatively) large amplitude localized waves deep inside the ice-pack in polar waters. For capillary-gravity wave classical theory obtains dromions for shallow-water and strong surface tension (Bond number, Bo, greater than 1/3). Here we show that capillary-gravity dromions exist beyond this limit for a broad range of finite water depths as well as for sub-critical Bond numbers, i.e. for Bo $<$ 1/3. [Preview Abstract] |
Monday, November 25, 2013 12:27PM - 12:40PM |
H28.00010: Capillary Gravity Waves over an Obstruction - Forced Generalized KdV equation Jeongwhan Choi, S.I. Whang, Shu-Ming Sun Capillary gravity surface waves of an ideal fluid flow over an obstruction is considered. When the Bond number is near the critical value 1/3, a forced generalized KdV equation of fifth order is derived. We study the equation analytically and numerically. Existence and stability of solutions are studied and new types of numerical solutions are found. [Preview Abstract] |
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