Bulletin of the American Physical Society
62nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 54, Number 19
Sunday–Tuesday, November 22–24, 2009; Minneapolis, Minnesota
Session GS: Geophysical: Oceanographic II |
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Chair: Aline Cotel, University of Michigan Room: 200G |
Monday, November 23, 2009 8:00AM - 8:13AM |
GS.00001: Double Trouble: Internal Tide Attractors in Double Ridge Systems Paula Echeverri, Tite Yokossi, Neil Balmforth, Thomas Peacock A theoretical and experimental study is presented of the generation of internal tides by barotropic tidal flow over topography in the shape of a double ridge. A one-dimensional map is constructed that allows one to track the ray paths of waves reflecting between the ocean surface and topography, and this device is used to expedite the search for internal tide attractors between the ridges, these being attracting, closed ray paths. Calculations are then presented for the steady state scattering of internal tides from the barotropic tide. When attractors are present, these computations break down unless dissipation is also incorporated into the problem, in which case there is significantly enhanced energy conversion in the presence of attractors. We conclude with a direct comparison between theoretical predictions and the results of a laboratory experiment, as well as possible applications to geophysical locations. [Preview Abstract] |
Monday, November 23, 2009 8:13AM - 8:26AM |
GS.00002: Low-mode internal tide generation by topography: an experimental and numerical investigation Morris Flynn, Paula Echeverri, Tom Peacock, Kraig Winters We summarize recently published work (J.~Fluid Mech.) and analyze the low-mode structure of internal tides generated in laboratory experiments and numerical simulations by a two- dimensional ridge in a channel of finite depth. The height of the ridge is approximately half of the channel depth and the regimes considered span sub- to super-critical topography. For small tidal excursions, on the order of 1\% of the topographic width, our results agree well with linear theory. For larger tidal excursions, up to 15\% of the topographic width, we find that the scaled mode one conversion rate decreases by less than 15\%, in spite of nonlinear phenomena that break-down the familiar wave-beam structure and generate harmonics and inter- harmonics. Modes two and three, however, are more strongly affected. For this topographic configuration most of the linear baroclinic energy flux is associated with the mode-1 tide, so our experiments reveal that nonlinear behavior does not significantly affect the barotropic to baroclinic energy conversion in this regime, which is relevant to large scale ocean ridges. This may not be the case, however, for smaller scale ridges that generate a response dominated by higher modes. [Preview Abstract] |
Monday, November 23, 2009 8:26AM - 8:39AM |
GS.00003: A numerical study of oscillatory two-layer stratified flow over three-dimensional topography Laura Brandt, James Rottman A fully-nonlinear numerical model of two-layer stratified flow over three-dimensional topography is used to investigate the generation and propagation of interfacial waves by steady as well as oscillatory flows. Quantitative comparisons of the simulation results are made with shallow-water and weakly nonlinear theories. Qualitative comparisons are made with laboratory experiments and ocean observations. [Preview Abstract] |
Monday, November 23, 2009 8:39AM - 8:52AM |
GS.00004: Tidal flow over 3D topography generates out-of-forcing plane harmonics Benjamin King, Hepeng Zhang, Harry L. Swinney About 1 TW of mixing energy in the ocean comes from internal waves generated by tidal flow over bottom topography [1]. The generation of these waves in three dimensions (3D) remains poorly understood. We use a 3D axisymmetric Gaussian mountain as a model topographic feature and obtain numerical and experimental results for the internal wave field generated by tidal flow. The experiments use a model mountain in a 200 L tank, and particle image velocimetry for imaging. The numerical methods are the same as those in [2], and utilize a finite volume scheme to evaluate the 3D internal wave field. The stratification and forcing frequency are chosen such that 2$\omega <$ N (N is the buoyancy frequency), allowing the propagation of second harmonics. Surprisingly, when the maximum topographic slope exceeds the slope of second harmonic wave propagation, strong second harmonics are generated in the direction perpendicular to the tidal forcing direction. At high forcing amplitude, these harmonic waves have higher amplitude than the in-forcing-plane harmonics. \\[4pt] [1] W. Munk and C. Wunsch, Deep-Sea Res. I \textbf{45}, 1977 (1998)\\[0pt] [2] B. King, H. P. Zhang, and H. L. Swinney. Submitted to Phys. Fluids [Preview Abstract] |
Monday, November 23, 2009 8:52AM - 9:05AM |
GS.00005: The phase lead of shear stress in shallow-water flow over a perturbed bottom Paolo Luchini, Francois Charru Analysis of the flow over a slowly perturbed bottom (when perturbations have a typical length scale much larger than water height) is often based on the shallow-water (or Saint-Venant) equations, with the addition of a wall-friction term which is a local function of the mean velocity. By this choice small sinusoidal disturbances of wall stress and mean velocity are bound to be in phase with each other. In contrast, studies of shorter-scale disturbances have long established that a phase lead develops between wall stress and mean velocity, with a crucial destabilizing effect on sediment transport over an erodible bed. Our purpose here is to calculate the wall-stress phase lead under large-length-scale conditions, using asymptotic matching techniques for turbulent flow. This calculation provides significant corrections to the shallow-water model. [Preview Abstract] |
Monday, November 23, 2009 9:05AM - 9:18AM |
GS.00006: Hydrodynamic instability and rip current generation Jie Yu, Ali Marjani Rip currents are jet-like offshore flows which are part of the horizontal cell circulations originating inside the surf zone. It is generally acknowledged that alongshore variations in the wave field are essential to rip current generation, however, such a variability can arise from a variety of processes. We present here a linear instability analysis and show that the coupling of waves and evolving currents can lead to a positive feedback, generating rip currents in a system initially alongshore uniform. Preliminary results based on a simplified beach profile show that circulations with alongshore spacing of a few hundreds meters can be initiated by the instability on beaches of typical water depth. Qualitative agreements with observations of natural rip currents are obtained. Extension to complex beach bathymetry is made, and some results are discussed. [Preview Abstract] |
Monday, November 23, 2009 9:18AM - 9:31AM |
GS.00007: Resonant forcing of nonlinear internal waves by a density current released into a two-layer fluid Brian White, Karl Helfrich The propagation of a density current released by a dam break into
a fluid with two-layer stratification is a geophysical fluid
dynamics problem relevant to the ocean and atmosphere. Analogous
to topographic forcing, a transcritical resonance is observed
when the speed of the density current falls within a range,
$c_l |
Monday, November 23, 2009 9:31AM - 9:44AM |
GS.00008: Sediment wave formation by unstable internal waves in a turbidity current boundary layer Lutz Lesshafft, Brendon Hall, Eckart Meiburg, Ben Kneller The bedform of sediment that is deposited from turbidity currents onto the ocean floor is often found to exhibit long-wavelength variations, with crest lines perpendicular to the flow direction (``sediment waves''). A temporal stability analysis, based on the 2D Navier--Stokes equations, reveals the presence of unstable internal waves in the bottom boundary layer of a turbidity current. Instability arises from the interaction between the current and the sediment bed, via the competing effects of particle deposition and erosion. Due to the velocity and density variations within the boundary layer, near-stationary internal waves near the bottom may exist under both sub- and supercritical outer flow conditions. Unstable internal waves display long wavelengths and are typically found to slowly travel upstream. Both features are in qualitative agreement with field observations on sediment waves. [Preview Abstract] |
Monday, November 23, 2009 9:44AM - 9:57AM |
GS.00009: Critical Richardson Numbers in Breaking Internal Waves Cary Troy, Erin Hult, Jeffrey Koseff The breaking of internal waves is known to be responsible for much of the vertical mixing observed in the ocean, large lakes, and the atmosphere. In order to both correctly model and correctly infer the mixing associated with breaking internal waves, a thorough understanding of the instability mechanism driving these turbulent events is crucial. In this study, a primary indicator of turbulence in stratified flows, the gradient Richardson number (Ri), is examined for internal waves on the verge of instability. We use simultaneous high-resolution scalar (Planar Laser-Induced Fluorescence, PLIF) and velocity (Digital Particle Image Velocimetry, DPIV) measurement techniques to infer the gradient Richardson number of breaking and near-breaking progressive internal waves in a laboratory channel. The results show important deviations from the oft-assumed canonical stability limit of Ri=1/4, which we attribute to the unsteadiness of the internal wave-generated shear driving the instability. Results are compared to inviscid theory based on the normal modes equation. These results have important implications for the diagnosis of turbulent mixing in stratified environments. [Preview Abstract] |
Monday, November 23, 2009 9:57AM - 10:10AM |
GS.00010: Dissipation Mechanisms of Internal Solitary-like Waves in the Ocean Kevin Lamb Internal solitary-like waves (ISWs) are ubiquitous, highly energetic features in the coastal ocean where they are predominately generated by tide-topography interaction. There are many unanswered questions about the generation and fate of these waves and a better understanding of these processes is necessary for developing parameterizations of their effects for use in large scale models. Several sets of observations have suggested that the mixing associated with ISW trains is important for setting the stratification in some regions of the coastal ocean (e.g, the Scotian Shelf and the Portuguese Shelf). This talk will begin with a discussion of the energetics of large amplitude internal waves. I will then discuss three dissipation mechanisms for ISWs and consequences for mixing: instabilities in the bottom boundary layer, the breaking of shoaling waves, and shear instabilities in the pycnocline. Results from 2D numerical simulations will be presented for all three mechanisms, with a focus on shear instabilities. 3D simulations of shear instabilities have recently been initiated. It is hoped that results from these simulations will also be presented. [Preview Abstract] |
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