Bulletin of the American Physical Society
69th Annual Meeting of the APS Division of Fluid Dynamics
Volume 61, Number 20
Sunday–Tuesday, November 20–22, 2016; Portland, Oregon
Session E1: MiniSymposium: GeophysicalTurbulence Induced by Flow over Topography IIIInvited

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Chair: Ruth Musgrave, Massachusetts Institute of Technology Room: A105 
Sunday, November 20, 2016 5:37PM  6:03PM 
E1.00001: Internal waves trapped below a virtual seafloor Invited Speaker: Harry Swinney Numerical simulations of tidal flow over random topography with the ocean seafloor spectrum reveal that the timeaveraged tidal energy converted into far field internal wave radiation arises only from topography that rises above a local ``virtual'' seafloor (Zhang and Swinney, Phys. Rev. Lett. 112, 104502 (2014)). For topography below the virtual seafloor, destructive wave interference leads to no timeaveraged far field internal wave power. The concept of a virtual floor extends the applicability of linear theory to global predictions of the conversion of tidal energy into internal wave energy in the oceans. The simulations show that for increasing topographic RMS height the emergent interference of internal waves from neighboring generation sites leads to a transition in the radiated power dependence on topographic height from quadratic to linear. The internal wave power radiated by random topography is found to increase as the horizontal spatial resolution scale is decreased, down to a length scale of typically 300 m, but smaller scales generate at most a few percent of the radiated power (Zhao, Zhang, and Swinney, Geophys. Res. Lett. 42, 80818087 (2015)). Tidal flow past 3D seamounts generates much less total internal wave power than that radiated by quasi2D ridges (Zhang, Swinney, Comino, and Buijsman (2016)). [Preview Abstract] 
Sunday, November 20, 2016 6:03PM  6:29PM 
E1.00002: On turbulent mixing in stably stratified geophysical flows Invited Speaker: Karan Venayagamoorthy The understanding and quantitative prediction of diapycnal (irreversible) mixing of density and momentum in geophysical flows remains an important ongoing challenge. This is not surprising given the complexity introduced into most geophysical flows by factors such as density stratification, complex topography and a host of physical phenomena associated with such flows. However, accurate prediction of the smallscale irreversible mixing induced by turbulent processes is critical for many applications such as the prediction of heat fluxes and global circulation in oceanic flows. From a practical standpoint, a major goal is the {\bf{inference}} of turbulent heat and momentum fluxes using indirect measurements in field studies of geophysical flows. This usually involves the need to either measure directly or infer two key quantities namely: (1) the rate of dissipation of turbulent kinetic energy $\epsilon$, and (2) the mixing efficiency $R_f^*$, which is a measure of the amount of turbulent kinetic energy that is irreversibly converted into background potential energy, respectively. Indirect estimates of $\epsilon$ in oceanic flows has been traditionally achieved by assuming a linear relationship between the Thorpe (vertical overturn) length scale $L_T$ and the Ozmidov scale $L_O$. This approach is particularly attractive since the vertical scales of overturns can be readily obtained using a sorting algorithm from inversions in standard density profiles obtained from ConductivityTemperatureDepth (CTD) measurements in the ocean. Hence, $L_T$ is essentially a kinematic scale that provides a description of the turbulence at a given sampling location. On the other hand, $L_O$ is a representative dynamic length scale of the largest eddy that is unaffected by buoyancy. A review of a number of recent studies that were conducted in our research group will be presented in this talk to highlight the lack of a linear relationship between $L_T$ and $L_O$. These studies indicate that inferred estimates of $\epsilon$ may be biased high by up to an order of magnitude or more especially for large overturns in the ocean. An alternative unifying framework using a twodimensional parameter space based on a buoyancy strength parameter (i.e. an inverse Froude number) and a shear strength parameter will be discussed to characterize the scaling correspondence of the overturning length scale with pertinent turbulent length scales. The second key quantity that is a necessary ingredient for the inference of diapycnal mixing from oceanic measurements is the flux Richardson number $R_f^*$. To date, however, no unifying parameterization of $R_f^*$ exists due to both the variability inherent in geophysical flows as well as certain ambiguities that are introduced in descriptions based on illconditioned single parameters. A discussion on the mixing efficiency and implications for estimates of diapycnal mixing in geophysical flows will also be presented. [Preview Abstract] 
Sunday, November 20, 2016 6:29PM  6:55PM 
E1.00003: Internal Hydraulic Jumps in Shallow Flows over Topography Invited Speaker: Kelly Ogden A barotropically forced stratified flow over topography can generate an internal hydraulic jump with upstream shear. The structure and mixing of these jumps are investigated theoretically and numerically. The effect of upstream shear on simplified jumps in twolayer flows without topography results in jump types such as undular bores, smooth front turbulent jumps, and fully turbulent jumps (Ogden and Helfrich, 2016). Increased shear results in entrainment across the jump with jump structures that resemble expanding shear layers. The addition of topography increases the number of qualitative jump types. Idealized simulations are conducted to characterize the types of jumps that can occur under various parameter regimes. The effect of parameters such as the volume flow rate and topographic height are considered. Flow structures including firstmode jumps with wave overturning and highermode jumps with wedges of homogeneous stagnant fluid are found. The degree of mixing and the mass budget of the developing stagnant wedge illuminate the important physical characteristics of each jump type. Existing hydraulic jumps in the environment are compared to the parameter regimes the identified jump types. The applicability of twolayered theories for studying these jumps is also considered. [Preview Abstract] 
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