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 HS: Geophysical: Oceanographic III |
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Chair: Kyle Brucker, SAIC Room: 200G |
Monday, November 23, 2009 10:30AM - 10:43AM |
HS.00001: Numerical Simulations of Breaking Waves Douglas Dommermuth, Thomas O'Shea, Kyle Brucker The results of a set of numerical simulations of breaking waves are presented. The breaking waves are generated using a novel type of atmospheric forcing, which allows for wave breaking events characterized by strong plunging to weak spilling. The analysis of the wave breaking events consists of single point quantities, two-dimensional statistical quantities obtained by averaging, and three dimensional isocontours of instantaneous field variables. The single point quantities investigated include the kinetic and potential energies integrated over the computational volume. The effect of the atmospheric forcing on the late time asymptotic behavior of the kinetic and potential energies will be discussed. In terms of the two-dimensional statistical quantities: The use of binary and ternary averaged statistical quantities are compared, and it is found that statistics obtained by ternary averaging show better agreement with respect to the position of free surface than do those obtained by binary averaging. The amount of air entrained underneath the free surface is investigated both qualitatively and quantitatively. The three dimensional isocontours of vorticity show intense streamwise vorticity, or tubular structures, apparent during the strong plunging events. [Preview Abstract] |
Monday, November 23, 2009 10:43AM - 10:56AM |
HS.00002: Wave breaking onset and spectral distribution of energy loss due to laboratory generated breaking waves Zhigang Tian, Marc Perlin, Wooyoung Choi A study of wave breaking onset and energy loss due to wave breaking is presented. A global wave steepness parameter that accounts for spectral amplitude shape change is proposed. This parameter has a threshold of 0.25 for wave breaking onset and it correlated strongly with breaking energy loss. It exhibits reduced dependence on the shape of the wave spectrum, and it may be a better indicator for breaking onset and energy loss. Spatial evolution of frequency spectra is presented. Noticeable energy loss due to viscous effects is observed near the spectral peak. Spectral redistribution of energy due to wave breaking is presented. High frequency waves lose energy while low frequency components gain as much as 50{\%} of that energy loss. Energy near the spectral peak may increase or decrease, and is a function of the initial spectrum. In addition the change in the spatial distribution (i.e. wavenumber spectra) of energy loss will be presented. [Preview Abstract] |
Monday, November 23, 2009 10:56AM - 11:09AM |
HS.00003: A propagation model for internal waves generated by a localized source moving in an ocean thermocline James Rottman, Dave Broutman We develop a ray method for computing the propagation of internal waves generated by a localized source moving in an ocean thermocline. Previous work on this problem has involved an eigenfunction expansion. Eigenfunctions are often preferred over rays for regions such as the thermocline that have many ray reflections. Here we show that a ray method has some computational advantages over eigenfunctions, provided the rays are traced in Fourier space. The ray method does not require an eigenfunction solver and does not have the singularites that appear in the eigenfunction expansion. It does, however, require the correction of caustic singularities. For the thermocline problem, each ray has two caustics, one at each of the two the turning points that vertically trap the ray. Results for various buoyancy-frequency profiles will be presented and compared with previous computational techniques. [Preview Abstract] |
Monday, November 23, 2009 11:09AM - 11:22AM |
HS.00004: Numerical simulation of shear instabilities in interfacial gravity waves Oliver Fringer, Michael Barad We present simulations of shear instabilities in solitary-like interfacial gravity waves of depression using a Navier-Stokes solver that employs adaptive mesh refinement. The adaptive technique enables resolution of 0.20~m in a 500~m long wave which allows simulation of meter-scale Kelvin-Helmholtz (KH)-like billows that develop at the interface. In the presence of time-varying shear within the waves, an instability occurs only when a parcel of fluid is subjected to destabilizing shear long enough for KH-type billows to grow. While a necessary criterion for instability suggests that the Richardson number, $Ri$, must fall below the canonical value of 1/4, we find that a sufficient condition for instability occurs when $Ri < 0.1$. An alternate criterion for instability is given by a requirement that the growth rate time scale of the instability, $\tau_i$, satisfies $\tau_i<1.26T_w$, where $T_w$ is the time in which parcels of fluid are subjected to shear and stratification that satisfy $Ri<1/4$. This criterion can also be stated in terms of the width of the region in which $Ri<1/4$, $L_w$, which must satisfy $L_w > 0.86 L$ for instabilities to develop, where $L$ is the solitary wave half-width. Under any one of these three criteria, two-dimensional billows form at the wave troughs, and the billows subsequently break down via three-dimensional motions that decay once the wave-induced shear subsides in the trailing edge of the waves. [Preview Abstract] |
Monday, November 23, 2009 11:22AM - 11:35AM |
HS.00005: Near-bottom instabilities induced by nonlinear internal waves of depression Themistoklis Stefanakis, Peter Diamessis Results are presented from 2-D Direct Numerical Simulations (DNS) of the bottom boundary layer (bbl) in the footprint of fully nonlinear internal waves (NLIWs) of depression propagating in a uniform-depth two-layer system. Use of a spectral multidomain penalty method enables a robust and accurate description of the wave-induced bbl at values of Reynolds number (based on NLIW phase speed and wave-guide depth) as high as 100,000. The critical NLIW amplitude for global instability in the NLIW-driven bbl is identified as a function of Reynolds number, oncoming current strength and layer thickness ratio. The structure of of bbl vorticity and bottom shear stress fields is examined along with timeseries obtained of the near-bed vertical velocity fields obtained from Lagrangian and Eulerian virtual point sensors. DNS results are compared to recent laboratory observations, followed by a discussion of the underlying implications for the field. [Preview Abstract] |
Monday, November 23, 2009 11:35AM - 11:48AM |
HS.00006: Backscatter in Large-Scale Flows Balu Nadiga Downgradient mixing of potential-voriticity and its variants are commonly employed to model the effects of unresolved geostrophic turbulence on resolved scales. This is motivated by the (inviscid and unforced) particle-wise conservation of potential-vorticity and the mean forward or down-scale cascade of potential enstrophy in geostrophic turubulence. By examining the statistical distribution of the transfer of potential enstrophy from mean or filtered motions to eddy or sub-filter motions, we find that the mean forward cascade results from the forward-scatter being only slightly greater than the backscatter. Downgradient mixing ideas, do not recognize such equitable mean-eddy or large scale-small scale interactions and consequently model only the mean effect of forward cascade; the importance of capturing the effects of backscatter---the forcing of resolved scales by unresolved scales---are only beginning to be recognized. While recent attempts to model the effects of backscatter on resolved scales have taken a stochastic approach, our analysis suggests that these effects are amenable to being modeled deterministically. [Preview Abstract] |
Monday, November 23, 2009 11:48AM - 12:01PM |
HS.00007: Extension of Brinkman Penalization for Ocean Circulation Modeling using Adaptive Wavelet Collocation Method Shanon Reckinger, Oleg V. Vasilyev This work improves the representation of continental topology and bottom bathymetry for use in ocean circulation models through an extension of the Brinkman penalization method. Due to the complicated geometry inherent in ocean boundaries, the stair-step representation used in the majority of current global ocean circulation models causes large accuracy and stability problems. Brinkman penalization is a numerical technique used to enforce no slip boundary conditions through the addition of a term to the governing equations. When coupled with the Adaptive Wavelet Collocation Method, which solves the penalized equations on a temporally and spatially varying mesh, the flow near the boundary can be well defined for less computational cost. The talk presents an extension of this technique to slip boundary conditions and is applied to the various sets of equations that govern ocean circulation. The solution using this new penalization converges to the numerical solution with traditional boundary conditions similarly to the order $\eta$ convergence of the Brinkman penalization method that enforces no slip conditions. [Preview Abstract] |
Monday, November 23, 2009 12:01PM - 12:14PM |
HS.00008: Detached eddy simulation of separated flow in the near-wake of a sphere moving through a stratified fluid T.S. Orr, J.A. Domaradzki, G.S. Constantinescu Separated turbulent flows generated by submersed bodies in stratified fluids have been investigated in numerous experiments and numerical simulations. At high Reynolds numbers the numerical simulations are unable to resolve both a flow around the body and in the far-wake, which is the region of interest in such investigations. Because of that, in the far-wake simulations, the body is not simulated directly, but an initial condition is constructed using limited information from experiments for the near-wake properties. However, such initializations suffer from the lack of information about density field, which is difficult to measure. To obtain such information we perform DES of a flow around a sphere moving through a stably stratified fluid employing a body-fitted viscous flow solver in generalized curvilinear coordinates. The DES method based on the Spalart-Allmaras turbulence model is used to model the momentum equation as well as the density perturbation equation in the Boussinesq approximation. The simulations are validated by comparison with experimental data collected at USC at a $Re=5000$ and $Fr=4$ and then parameter space is extended to cover several other values of Re and Fr of interest. [Preview Abstract] |
Monday, November 23, 2009 12:14PM - 12:27PM |
HS.00009: New Lagrangian tools for describing transport in aperiodic time dependent flows: a case study of the Kuroshio current Ana M. Mancho, Carolina Mendoza In recent years there has been a lot of progress in the application of dynamical systems concepts to the description of transport in oceanic flows. In these flows the classical dynamical system theory does not apply since they are aperiodic and finite-time defined. Recently, for describing these flows a new definition of distinguished trajectory has been proposed (Madrid {\&} Mancho, Chaos, 2009). Distinguished trajectories act as organizing centres of the geometrical template of aperiodic time-dependent flows, like fixed points and periodic orbits do in time independent or periodic flows. The computation of distinguished trajectories makes use of a function $M$ of which we show contains a lot of Lagrangian information. In this presentation I will discuss how the visualization of this function $M$, allows identifying relevant Lagrangian features at a glance. In particular we report an application to real altimetry data taken from satellite in the area of the Kuroshio current. The function $M$ also determines the stable and unstable subspaces of the distinguished hyperbolic trajectories which are tangent to the invariant manifolds. From the computation of stable and unstable manifolds we report an accurate description of transport routes in this region. [Preview Abstract] |
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