Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session R1: Geophysical: Ocean IV |
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Chair: Chris Rehman, Iowa State University Room: 22 |
Tuesday, November 20, 2012 1:00PM - 1:13PM |
R1.00001: The effects of a shear flow on lee waves Michael Patterson, Stuart Dalziel, Colm Caulfield, St\'ephane Le Brun We explore experimentally and theoretically the effects of a shear flow on lee waves that are generated by a stationary isolated three-dimensional obstacle in a low-Froude-number stratified flow. We observe that the uniform flow (beneath the shear layer) can be divided into two regions: an essentially two-dimensional flow around the base of the obstacle and a wave-generating flow over the top portion of the obstacle. The third region's structure is dependent on the sign of the shear, and is either a wave-free region above the critical height where the wave speed equals the local fluid speed or a region in which the waves are fully reflected. By separating the permanent waves produced into distinct categories, we compare detailed experimental measurements with theoretical predictions. Finally we examine the time-dependent establishment of the waves, including the transition from a uniform flow to a sheared flow. [Preview Abstract] |
Tuesday, November 20, 2012 1:13PM - 1:26PM |
R1.00002: Spatial structure of tidally generated internal waves Matthew Paoletti, Amadeus Dettner, Matthew Drake, Harry L. Swinney Tidal flow over bottom topography is one of the main sources of internal wave energy in the ocean, which may be converted into gravitational potential energy through mixing when the internal waves break. Internal wave breaking can occur when the destabilizing vertical shear of the waves overcomes the stabilizing effects of gravity. While past studies have determined the conversion rate of the tidal motions into internal wave energy, a general understanding of the spatial structure and shear profiles of tidally generated internal waves is lacking. Here, we present 2D experimental and computational studies of internal wave generation by tidal flow over several types of topographic ridges. For each topographic profile, we vary the criticality parameter, which is the ratio of the topographic slope to the wave beam slope, by independently changing the tidal frequency, stratification, and topographic slope. We also consider cases where the topography is beneath a turning depth, below which internal waves are evanescent owing to the weak stratification. The spatial structure of the internal waves is characterized by the velocity amplitude, principal wavenumber, width, and the local Richardson number, which determines the stability properties. [Preview Abstract] |
Tuesday, November 20, 2012 1:26PM - 1:39PM |
R1.00003: Energy flux of internal waves generated by tidal flow over topography beneath a turning depth Matthew Drake, M.S. Paoletti, F.M. Lee, P.J. Morrison, H.L. Swinney We present experimental and computational studies of internal gravity wave generation by tidal flow over 2D topography in a stably stratified fluid designed to model the deep ocean. King et al. found that there exist regions in the deep ocean where the buoyancy frequency (proportional to the square root of the density gradient) becomes less than the tidal frequency [King et al., J. Geophys. Res. 117, C04008 (2012)]. Below such ``turning depths'' the internal gravity waves become evanescent. The effect of turning depths on global internal wave generation has not been examined. Here we present experiments and 2D Navier-Stokes simulations that determine the far-field energy flux as a function of the distance of the turning depth above the topography. We examine how the energy flux depends on the tidal frequency, stratification, topographic profile, and the distance of the topography below the turning depth. [Preview Abstract] |
Tuesday, November 20, 2012 1:39PM - 1:52PM |
R1.00004: Generation of internal waves and boundary currents by tidal flow over 2D topography Amadeus Dettner, Matthew Paoletti, Harry L. Swinney The majority of internal wave energy in the ocean is produced by tidal flow over topography. Regions of critical topography, where the topographic slope is equal to the slope of the internal waves, is often believed to contribute most significantly to the radiated internal wave power. Here, we present 2D experimental and computational studies of internal wave generation by tidal flow over several types of topographic ridges. We vary the criticality parameter $\epsilon$, which is the ratio of the topographic slope to the wave beam slope, by independently changing the tidal frequency, stratification and topographic slope, which allows us to study subcritical ($\epsilon < 1$), critical ($\epsilon = 1$), and supercritical topography ($\epsilon > 1$). As in prior work [Zhang et al., {\em Phys. Rev. Lett.} (2008)], we observe resonant boundary currents for $\epsilon= 1$. However, we find that the normalized radiated power monotonically increases with $\epsilon$. We find that an appropriate normalization condition leads to a universal scaling of the radiated power as a function of $\epsilon$. [Preview Abstract] |
Tuesday, November 20, 2012 1:52PM - 2:05PM |
R1.00005: Tidal conversion by a periodic array of ridges Likun Zhang, Matthew Paoletti, Harry Swinney The generation of internal waves by tidal flow over submarine topography such as ridges is the main source of internal tidal energy in the oceans. For multiple ridges the dependence of the radiated power on the ridge height and slope is different from that for an individual ridge, and for multiple ridges the power also depends on the spacing between the topographic features. Prior numerical and analytical studies on tidal generation by a periodic array of steep ridges suggest the possible saturation of conversion rate when the dimensionless height of the topography is large [S. Khatiwala, Deep-Sea Res. (2003); J. Nycander, J. Fluid. Mech. (2006); N. J. Balmforth and T. Peacock, J. Phys. Ocean. (2009)]. Here we perform 2D Navier-Stokes simulations and laboratory experiments on the generation of internal tides from a periodic array of supercritical barriers. We determine how the radiated power and saturation depend on the tidal flow, topography, and stratification. [Preview Abstract] |
Tuesday, November 20, 2012 2:05PM - 2:18PM |
R1.00006: Calculating viscous internal gravity waves Stefan Llewellyn Smith Internal gravity waves (IGWs) are ubiquitous features of the ocean and atmosphere, thought to be critical in global energy budgets. There has hence been much interest in developing simple models of IGW generation. However, only a few special solutions for simple geometries are known, and the hyperbolic spatial nature of the governing equations leads to numerical difficulties. At the same time, modern developments in laboratory techniques now reveal the quantitative effects of viscosity in experiments on IGW generation by oscillating bodies. Even fewer solutions are known when viscosity is present. We discuss boundary integral methods for viscous IGW generation, and present some results and applications. [Preview Abstract] |
Tuesday, November 20, 2012 2:18PM - 2:31PM |
R1.00007: Forcing of oceanic mean flows by dissipating internal tides Nicolas Grisouard, Oliver Buhler We present a theoretical study of the effective mean force exerted on an oceanic mean flow due to the presence of small-amplitude internal waves that are forced by a barotropic tide flowing over a topography and are also subject to dissipation. Although the details of our computation are quite different, we recover the main action-at-a-distance result familiar from atmospheric wave-mean interaction theory, namely that the effective mean force that is felt by the mean flow is located in regions of wave dissipation, and not necessarily near the topographic wave source. Specifically, using a perturbation series in small wave amplitude, we compute the three-dimensional leading-order wave field using a Green's function approach, derive an explicit expression for the leading-order effective mean force at the next order within the framework of generalized Lagrangian-mean theory, discuss in detail the range of situations in which a strong, secularly growing mean-flow response can be expected, and finally compute the effective mean force numerically in a number of illustrative examples with simple topographies. [Preview Abstract] |
Tuesday, November 20, 2012 2:31PM - 2:44PM |
R1.00008: Effect of slope criticality and tidal forcing on internal tide energetics at a model ridge Narsimha Rapaka, Bishakhdatta Gayen, Sutanu Sarkar Direct and large eddy simulations are performed to study the internal waves generated by the oscillation of a barotropic tide over a model ridge of triangular shape. The criticality parameter, defined as the ratio of the topographic slope to the characteristic slope of the tidal rays, is varied from subcritical to supercritical values. The barotropic tidal forcing is also systematically increased. Higher baroclinic modes are generated with increasing criticality parameter, resulting in generation of intensified beams near the topography in critical and supercritical cases. The radiated internal wave energy flux increases from subcritical to supercritical cases in laminar flow regime. In critical and supercritical cases with higher forcing, there is turbulence and significant reduction (as much as 25\%) of the radiated wave flux with respect to laminar flow results. Analysis of the baroclinic energy budget shows that the decrease in the radiated wave flux is associated with a decrease in energy conversion from the barotropic to baroclinic flow, caused by increased drag and mixing of momentum near the ridge, and additionally because of conversion to turbulence. [Preview Abstract] |
Tuesday, November 20, 2012 2:44PM - 2:57PM |
R1.00009: Numerical Simulation of Internal Tide Generation at a Continental Shelf Break Laura Brandt, James Rottman, Kyle Brucker, Douglas Dommermuth A fully nonlinear, three-dimensional numerical model is developed for the simulation of tidal flow over arbitrary bottom topography in an ocean with realistic stratification. The model is capable of simulating accurately at the generation of fine-scale internal wave tidal beams, their interaction with an ocean thermocline and the subsequent generation of solitary internal waves that propagate on this thermocline. Several preliminary simulation results are shown for uniform and non-uniform flow over an idealized two-dimensional ridge, which are compared with linear theory, and for flow over an idealized twodimensional continental shelf. [Preview Abstract] |
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