Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session M31: Waves: Internal and Interfacial Waves |
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Chair: Michael R. Allshouse, University of Texas at Austin Room: 312 |
Tuesday, November 24, 2015 8:00AM - 8:13AM |
M31.00001: Internal wave bolus detection and analysis by a Lagrangian coherent structure method Michael R. Allshouse, G. Salvador-Vieira, Harry L. Swinney The shoaling of vertical mode internal waves on a continental shelf produces boluses, which are trapped regions of fluid that travel up the shelf with the wave. Unlike a propagating solitary wave, these boluses can transport material with the wave. Boluses have been observed to transport oxygen depleted water and induce rapid changes in temperature both of which have potential ramifications for marine biology. We extend a number of two-layer studies by investigating bolus generation and material transport in continuously stratified fluids. Laboratory experiments are conducted in a 4 m long tank and are complemented by 2-dimensional numerical simulations of the Navier-Stokes equations. The boundaries of a bolus are identified using a Lagrangian based coherent structure method relying on trajectory clustering. The time evolution of material transport by the bolus is investigated as a function of the stratification, wave properties, and the angle of the sloping topography. [Preview Abstract] |
Tuesday, November 24, 2015 8:13AM - 8:26AM |
M31.00002: Geometric focusing of internal waves: Experimental study Natalia Shmakova, Evgeny Ermanyuk, Bruno Voisin, Jan-Bert Fl\'or Mixing of the abyssal ocean plays a decisive role in large-scale ocean circulation and is believed to be caused by the nonlinear breaking of internal tides. Previous studies of two- and three-dimensional cases considered the generation of diverging waves by simple oscillating bodies such as a cylinder (e.g.\ Mowbray and Rarity 1967) or a sphere (e.g.\ King at al.\ 2009, Ermanyuk et al.\ 2011). We here consider converging waves as generated by a horizontally oscillating torus. The energy focuses and therefore the waves are more susceptible to overturning and breaking. LIF and PIV techniques are used to measure respectively the isopycnal displacement and the velocity. We have considered linear and nonlinear wave generation as a function of the Keulegan--Carpenter number, here adapted to the focusing waves. For small oscillation amplitude strong velocity amplification is observed in the focal zone, consistent with linear theory. Increasing the oscillation amplitude causes nonlinear effects and in particular the generation of higher harmonics and overturning in the focal zone. In addition, the focal zone acts as a wave source. Increase of the Stokes and Reynolds numbers leads to wave turbulence in the focal zone. [Preview Abstract] |
Tuesday, November 24, 2015 8:26AM - 8:39AM |
M31.00003: Internal wave focusing by annular forcing: theory Bruno Voisin, Evgeny Ermanyuk, Natalia Shmakova, Jan-Bert Fl\'or Among the various mechanisms susceptible of leading to local intensification of internal wave energy, followed by breaking and ultimately mixing, a specific three-dimensional mechanism has received little attention so far: the geometric focusing of waves emitted by horizontally curved oscillatory forcing. We present a linear theory of annular forcing, based on the assumption that the annulus is slender, namely of negligible local curvature. Both complete focusing by an axisymmetric annulus and partial focusing by a truncated or horizontally modulated annulus are considered. The case of a torus, either thin (i.e.\ hula-hoop-like) or thick (i.e.\ doughnut-like), is studied in detail. Focusing is seen to arise in both cases and to yield significant isopycnal slopes, close to overturning, even at low oscillation amplitude. This effect is all the more pronounced as the Stokes number gets higher and the wave structure changes from unimodal to bimodal. Flat circular Gaussian topography is considered next and compared to the earlier work of B\"uhler \& Muller (\emph{JFM} 2007) and Grisouard \& B\"uhler (\emph{JFM} 2012). The oceanic relevance of the analysis is finally discussed. [Preview Abstract] |
Tuesday, November 24, 2015 8:39AM - 8:52AM |
M31.00004: Nonlinear harmonic generation by diurnal tides Scott Wunsch Recent observations from the South China Sea have demonstrated that diurnal tides sometimes generate higher harmonics. Similar harmonic generation has been found in laboratory experiments and numerical simulations of internal wave beams refracting into a pycnocline. Here, a weakly nonlinear theory of internal wave refraction is applied to oceanic diurnal tides in an idealized stratification profile. The harmonic amplitude is calculated as a function of the tidal frequency and the pycnocline characteristics. The results indicate that harmonic generation by nonlinear refraction of diurnal tides is consistent with the South China Sea observations. [Preview Abstract] |
Tuesday, November 24, 2015 8:52AM - 9:05AM |
M31.00005: Convective Excitation of Internal Waves Daniel Lecoanet, Michael Le Bars, Keaton Burns, Geoffrey Vasil, Eliot Quataert, Benjamin Brown, Jeffrey Oishi We will present a joint experimental \& computational study of internal wave generation by convection. First we describe an experiment using the peculiar property of water that its density maximum is at $4^\circ C$. A tank of water cooled from below and heated from above develops a cold, convective layer near $4^\circ C$ at the bottom of the tank, adjacent to a hot stably stratified layer at the top of the tank. We simulate this setup in 2D using the open-source Dedalus code (dedalus-project.org). Our simulations show that waves are excited from within the convection zone, opposed to at the interface between the convective and stably stratified regions. Finally, we will present 3D simulations of internal wave excitation by convection in a fully compressible atmosphere with multiple density scaleheights. These simulations provide greater freedom in choosing the thermal equilibrium of the system, and are run at higher Rayleigh number. The simulated waves are then compared to analytic predictions of the bulk excitation model. [Preview Abstract] |
Tuesday, November 24, 2015 9:05AM - 9:18AM |
M31.00006: Simultaneous generation and scattering of internal tides by ocean floor topography Manikandan Mathur Internal waves play a significant role in the global energy budget of the ocean, with internal tides potentially contributing to the conversion of a large amount of mechanical energy into heat in the deep ocean. Several studies in the past decade have investigated internal tide generation and internal tide scattering by ocean floor topography, but by treating them as two separate, independent processes. In this talk, we use the recently developed Green function model (Mathur et al., J. Geophys. Res. Oceans, 119, 2165-2182, 2014), sans the WKB approximation, to quantify the extent to which internal tide generation (scattering) that results from barotropic (baroclinic) forcing on small- and large-scale topography in uniform and nonuniform stratifications is modified by the presence of a background baroclinic (barotropic) tide. Results on idealized topography, stratification and forcing will first be presented, followed by a discussion on the relevance of our studies in the real ocean scenario. [Preview Abstract] |
Tuesday, November 24, 2015 9:18AM - 9:31AM |
M31.00007: Linear waves in two-layer fluids over periodic bottoms Jie Yu, Leo Maas A new, exact Floquet theory is presented for linear waves in two-layer fluids over a periodic bottom of arbitrary shape and amplitude. A method of conformal transformation is adapted. The solutions are given, in essentially analytical form, for the dispersion relation between wave frequency and generalized wavenumber (Floquet exponent), and for the waveforms of free wave modes. The dispersion relation is the analogue of the classical Lamb's equation for a two-layer fluid over a flat bottom. For internal modes the interfacial wave shows rapid modulation at the scale of its own wavelength that is comparable to bottom wavelength, whereas for surface modes it becomes a long wave carrier for modulating short waves of bottom wavelength. The approximation using a rigid-lid is given. Sample calculations are shown, including the frequencies that are Bragg resonant. [Preview Abstract] |
Tuesday, November 24, 2015 9:31AM - 9:44AM |
M31.00008: An experimental investigation of evanescent wave~propagation~through a turning depth Allison Lee, Julie Crockett One well known method of internal wave generation is tidal flow over oceanic bathymetry. However, in some locations, the natural frequency of the deep ocean is less than the tidal frequency and thus only evanescent waves are generated. While evanescent waves generally dissipate quickly after formation, it is been observed that if these waves travel into a stronger stratification evanescent waves can become a propagating internal waves.~Here we present an experimental investigation of this internal wave generation mechanism. Specifically, internal wave energy transfer through a turning depth for a range of topography shapes, stratification profiles, and turning depth locations is explored. Energy transfer from evanescent to propagating waves is found to occur for both linear and exponential stratifications and increases as the turning depth approaches the topography. [Preview Abstract] |
Tuesday, November 24, 2015 9:44AM - 9:57AM |
M31.00009: Nonlinear effects on internal wave reflection at an interface John McHugh Internal waves impinging on an interface that has a sudden change in the first derivative of density are partially reflected, with a corresponding localized mean flow in the vicinity of the interface. Recent weakly nonlinear results have shown that this mean flow is discontinuous at the interface if the flow is inviscid. This recent theory showed that with continuous density at the interface, the linear interfacial conditions are asymptotically consistent, but only approximately balance overall momentum. The next level of nonlinear interfacial terms are now included here. Only several of the numerous terms are found to contribute significantly to the wave reflection, determined by numerical evaluation of all terms. Including these several terms has resulted in improved conservation of total momentum. The resulting nonlinear reflection coefficient depends strongly on wave parameters. [Preview Abstract] |
Tuesday, November 24, 2015 9:57AM - 10:10AM |
M31.00010: Boundary forced internal waves in a non-uniform stratification: diminution and resonant pathways to instability Sasan John Ghaemsaidi, Thomas Peacock We study the surface forcing of internal waves in a non-uniform stratification comprising a relatively thin, highly stratified upper layer sitting atop a deep, weakly stratified lower layer. Such a system theoretically yields a range of transmission features for harmonic boundary forcing, with the response ranging from diminution to resonant growth depending on the degree of coherence between the constitutive waves in the upper stratification layer. A series of laboratory experiments are performed in order to investigate the role of wave interference in tuning wave transmission. We find that the occurrence of destructive interference in the upper stratification naturally yields diminution of the transmitted wave. Conversely, constructive interference results in a notable amplification of the wave field over time scales on the order of the forcing period; the development of nonlinear wave-wave interactions due to wave amplification is observed over longer time scales. Good agreement is obtained between the experimental results and a weakly viscous, long wave model of our system within the linear regime. [Preview Abstract] |
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