Bulletin of the American Physical Society
72nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 64, Number 13
Saturday–Tuesday, November 23–26, 2019; Seattle, Washington
Session L33: Flow Instability: Geophysical |
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Chair: Bruce Sutherland, University of Alberta Room: 615 |
Monday, November 25, 2019 1:45PM - 1:58PM |
L33.00001: The Weakly Nonlinear Evolution of Superharmonics Generated by Model Oceanic Internal Tides Bruce Sutherland, Lois Baker It is now well-established that a vertically confined, horizontally periodic internal mode in non-uniformly stratified fluid self-interacts through the advection terms resulting in the forcing of superharmonics with double the horizontal wavenumber and frequency of the parent mode. The work presented here examines the linear and weakly nonlinear response to this forcing resulting from mode-1 "parent" waves in stratification typical of the ocean. It is shown that the forcing results in the excitation of a near-pure mode-1 ("sibling") internal wave with double the horizontal wavenumber of the parent, though the natural frequency of this mode differs slightly from double the frequency of the parent. As a result, the sibling wave first grows and decays, doing so periodically at the beat frequency set by the difference of the natural frequency of the mode and double the parent-mode frequency. A weakly nonlinear analysis is necessary to predict the maximum amplitude of the superharmonic. This considers how the interaction between the parent-mode and its superharmonic sibling put energy into or take energy out of the parent-mode. [Preview Abstract] |
Monday, November 25, 2019 1:58PM - 2:11PM |
L33.00002: Dynamic stability of a jet near a transition in static stability John McHugh The vertical profile of the Earth's atmosphere contains a sharp transition region at the tropopause between two roughly constant stability layers, and also jet streams at nearly the same altitude, with the jet stream core possible above or below the tropopause, depending on location. This proximity of the jet to the tropopause would be expected to greatly affect the dynamic stability of the jet, treated here with the jet modeled with the Bickley $sech^2$ profile and the tropopause modeled as a smooth transition region with a $\tanh$ profile. Stability results are obtained numerically using a Chebyshev collocation spectral method. The results show that the jet becomes more unstable as it is moved further beneath the tropopause. Corresponding two-dimensional direct numerical simulations of the flow confirm the initial growth rate, but then show that the most unstable mode achieves more kinetic energy when the jet is just above the tropopause. Overall, the results indicate that when a jet is above the tropopause, the configuration is more stable and more likely to produce a strong single unstable mode. Conversely, when a jet is below the tropopause, the jet is more likely to form a broad spectrum of motion. [Preview Abstract] |
Monday, November 25, 2019 2:11PM - 2:24PM |
L33.00003: Four wave interactions for internal waves Jean-Marc Chomaz, Sabine Ortiz Triadic instability is a very generic mechanism by which a primary wave of finite amplitude is destabilized by two secondary waves (daughter waves) forming a resonant triad. For gravity waves in the ocean, as shown by Phillips, O.M. (UPC, 1967), resonant triads form several continuous branches, which can be represented in two dimensions as resonant lines in the plane of the wave vector of one of the secondary waves. We show here that the crossing of two of these branches radically modifies the nature of triadic instability by coupling, no longer two daughter waves, but three that form two triads sharing one same wave. Instability is then reduced for the triad unstable in classical theory while the second triad, stable according to classical theory, is strongly destabilized. Building on McEwan, A.D. \& Plumb, R.A. (Dyn. Atm. \& Oceans, 1977), we show that this modification of triadic instability affects a finite region around the crossing point of resonant branches in the plane of wave vectors, region whose extent increases very rapidly as the amplitude of the primary wave increases. The direct calculation of instability modes by a Floquet method shows that, even for a very small amplitude of the primary wave (Froude number of about 0.01), the deviation from the classical theory. [Preview Abstract] |
Monday, November 25, 2019 2:24PM - 2:37PM |
L33.00004: Linear instability of the Prandtl model for stratified slope flows Inanc Senocak, Cheng-Nian Xiao Ludwig Prandtl dedicated the last three pages in the authorized translation of his famous book ``Essentials of Fluid Dynamics'' to describe mountain and valley winds in stratified air. The exact solution assumes the presence of a constant linear background stratification above a sloped surface of infinite extent in all directions with a constant heating or cooling applied to it. Over the years, the Prandtl model has been found to describe the flow profile of katabatic winds observed in nature. Despite the usefulness of the Prandtl model, its stability characteristics have gone unexplored for many decades since its publication. In the present work, we use linear modal analysis and direct numerical simulations to uncover two types of flow instabilities in the Prandtl model for anabatic and katabatic slope flows. These instabilities manifest themselves as a function of the slope angle, the Prandtl number and a newly introduced stratification perturbation parameter, which is a measure of the relative importance of the surface heat flux with respect to the background stratification. We investigate the characteristics of these instabilities as a function of the aforementioned dimensionless parameters and highlight their differences under katabatic and anabatic scenarios. [Preview Abstract] |
Monday, November 25, 2019 2:37PM - 2:50PM |
L33.00005: Analysis of linear stability for katabatic slope flows subject to ambient winds Chengnian Xiao, Inanc Senocak In the original Prandtl model, the slope flows are purely gravity driven due to thermal forcing imposed at the surface. The extended Prandtl model incorporates the presence of ambient winds to better approximate nocturnal flows profiles in sloped terrain or over (Ant-)arctic ice sheets than does the original model. In an effort to establish the set of dimensionless numbers governing the slope flows, we investigate the linear stability of such generalized slope flows with the help of modal analysis and direct numerical simulations for a range of slope angles. In order to fully describe the stability behavior of slope flows subject to ambient winds, we introduce a new dimensionless number in addition to the recently introduced stratification perturbation parameter. This new dimensionless number is a measure of the relative importance of the inertia of ambient winds with respect to total damping effects in the background medium. The effect of ambient winds measured by this new parameter on the stability behavior of the extended Prandtl slope flow configuration will be investigated, and major differences to the basic Prandtl model will be highlighted [Preview Abstract] |
Monday, November 25, 2019 2:50PM - 3:03PM |
L33.00006: Shear instabilities in laboratory arrested salt-wedge flows Adam Jiankang Yang, Edmund Tedford, Jason Olsthoorn, Gregory Lawrence The spatial variation in the properties of an arrested salt wedge and its resulting Holmboe instabilities have been investigated, both analytically and in the laboratory. In the laboratory particle image velocimetry and laser induced fluorescence are used to obtain flow velocities and the height of the density interface. The positive and negative Holmboe wave modes are separated by the 2D Fourier transform. An analytical solution for the profile of interface height, in the absence of interfacial flow instabilities, has been developed from two-layer internal hydraulic theory. The evolution of the velocity profile is predicted using a momentum diffusion equation following a Lagrangian frame of reference along the interface of the salt wedge. The centre of the shear layer is predicted to lie above the density interface, with this offset decreasing in the downstream direction. Due to the offset and lower boundary, the growth rate of the negative instability is smaller than that of the positive instability. Our theoretical predictions are in good agreement with the laboratory measurements. [Preview Abstract] |
Monday, November 25, 2019 3:03PM - 3:16PM |
L33.00007: Halite precipitation from double-diffusive salt fingers in the Dead Sea: Numerical simulations Raphael Ouillon, Nadav Lensky, Vladimir Lyakhovsky, Ali Arnon, Eckart Meiburg Thick, extensive salt layers are commonly found in the Earthâ€™s geological record and formed as a result of a negative water balance in hypersaline lakes saturated in salt. Today, the Dead Sea is considered to be the only modern analog to these deep hypersaline lakes. Recent field work conducted by the Geological Survey of Israel showed that during the dry summer season, the top layer of the Dead Sea is warmer, saltier and undersaturated in salt, and that double-diffusive convection is responsible for delivering dissolved salt from the top layer to the bottom layer, resulting in continuously supersaturated bottom layer and seasonally undersaturated top layer. We present numerical simulations of this double-diffusive process directly based on measurements from the field work. The simulations account for the phase change from dissolved to crystalline salt, and for the settling of the salt crystals. We show that no other physical mechanism than double-diffusion is required in order to generate sufficient transport of salt and obtain the salinity and temperature profiles measured in the summer in the Dead Sea. The combined field measurements and numerical simulations paint a novel and promising picture for the mechanisms of salt deposition in the historical record. [Preview Abstract] |
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