Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session L34: Geophysical Fluid Dynamics: Stratified Flows IVGeophysical

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Chair: John McHugh, University of New Hamsphire Room: 102 
Monday, November 20, 2017 4:05PM  4:18PM 
L34.00001: Investigating the mechanism for layer formation in a stratified fluid: mixing due to a towed vertical rake of bars Jamie Partridge, Stuart Dalziel, Paul Linden A common feature of turbulent, stratified flows is layering of the density field. It has been observed, experimentally and numerically, that an initially linearly stratified system breaks down into a series of layers with a well defined length scale. Empirically, the length scale is found to scale linearly with $U/N^2$, with $U$ a typical velocity scale and $N^2$ the buoyancy frequency. Despite this empirical scaling, found across a variety of flow configurations, no universal underlying mechanism describing how the layering occurs has been found. We present new data from an experimental study investigating the flow and stratification that develops when an array of vertical bars is towed, back and forth, through an initially linearly stratified fluid. Particle image velocimetry (PIV) results are presented to provide further insight into the layering mechanism and how this may be related to other flow configurations. Of particular focus is the role of the internal wave field, generated by the towing motion, in establishing the layering. [Preview Abstract] 
Monday, November 20, 2017 4:18PM  4:31PM 
L34.00002: Characterising the structure of quasiperiodic mixing events in stratified turbulent TaylorCouette flow Kanwar Nain Singh, Jamie Partridge, Stuart Dalziel, C.P. Caulfield We present results from experiments conducted to study mixing in a twolayer stablystratified turbulent TaylorCouette flow. It has previously been observed that there is a quasiperiodic mixing event located at the interface separating the layers. We observe, through conductivity probe measurements, that the power of the mixing event in the frequency spectrum of the density data at the interface is higher when measured near the inner cylinder than in the middle of the annular gap. This is consistent with Oglethorpe's (2014) hypothesis that the mixing structure is triggered near the inner cylinder, and then advects and decays or disperses radially. We also observe that at $Ri = \frac{g'R_o}{(R_i\Omega_i)^2}\sim 7$, where $R_i$, $R_o$ are the inner and outer cylinder radius, respectively, $g'$ the reduced gravity characterising the density jump between the layers and $\Omega_i$ is the rotation rate of the inner cylinder, the power drops significantly at all radial locations, which is reminiscent of the onset of the enhanced flux regime as observed by Oglethorpe et al. (2013). We perform experiments to characterise the spatial extent and dynamics of this mixing structure using particle image velocimetry (PIV) giving further insights into this important mixing process. [Preview Abstract] 
Monday, November 20, 2017 4:31PM  4:44PM 
L34.00003: Effect of Prandtl number and bulk Richardson number on the secondary nonlinear dynamics of the TaylorCaulfield instability. Thomas Eaves, Neil Balmforth Layered density stratifications are ubiquitous in the natural environment. When such layered stratification is subject to a shear flow, the TaylorCaulfield instability can arise for arbitrarily large bulk Richardson number through the Dopplershifted interaction of internal gravity waves at the interfaces between density layers. Beyond this mechanistic description of the linear instability, only a few studies have investigated the nonlinear evolution of the primary linear instability, over relatively limited parameter ranges. Here we present a large number of twodimensional fully nonlinear simulations of the evolution of the TaylorCaulfield instability over a wide range of Prandtl and bulk Richardson numbers and identify three distinct regimes; a relatively quiescent wavelengthcascade of TaylorCaulfield instabilities at small bulk Richardson number, highly energetic and efficiently mixing dynamics at large bulk Richardson number, and reconfirmation of the emergence of parasitic nonlinear Holmboe waves at high Prandtl number. [Preview Abstract] 
Monday, November 20, 2017 4:44PM  4:57PM 
L34.00004: Instability associated baroclinic critical layers in rotating stratified shear flow Chen Wang, Neil Balmforth When a vertically stratified fluid is subject to horizontal shear, a baroclinic critical layer of internal gravity waves can appear. It is where the wave's intrinsic frequency matches the fluid's buoyancy frequency and the baroclinicity becomes singular. The present research studies baroclinic critical layers associated with normal mode instability. The baroclinic critical layer makes localized large wave amplitude and abrupt phase change, as well as strong wavemean interaction and specially, it can make the flow unstable. In strongstratification flows, the baroclinic critical layer connects an incident inertialgravity travelling wave to an exponentially decaying amplitude, and in weakstratification flows, it connects a Kelvin wave to a standing inertialgravity wave. Moving the baroclinic critical layer into the domain will either make the originally neutral mode unstable or destroy that mode. We have specified the conditions of these two situations according to the conservation of pseudomomentum. The instability induced by baroclinic critical layer is very different from the previous known stratorotational instability (SRI): it is unstable for a continuous band of wavenumbers since resonance condition is not required. [Preview Abstract] 
Monday, November 20, 2017 4:57PM  5:10PM 
L34.00005: The stability of an overturning stratified fluid John McHugh Previous studies have shown that a weak vortex pair with horizontal axis that is released in a stratified fluid will quickly disintegrate, while a strong vortex pair will remain intact. The critical Froude number is unity, and values less than unity will disintegrate, as shown by Garten, et. al. (JFM, 1998) using twodimensional numerical simulations. An eigenvalue stability approach to this twodimensional configuration is difficult, as there is no equilibrium base flow for Froude number less than the critical value. Here we consider a similar configuration using a single vortex in three dimensions with a spiral density pattern. This spiral density is steady and approximates the flow that develops behind one side of a lifting surface. The disintegration still happens with a single vortex, since it is due to the inversion a statically stable density profile by the vortex motion. The base state flow is a distorted vortex, determined for weak stratification. Axial periodicity is assumed, which restricts the ratio of azimuthal to axial velocities to be constant. Only global stability is treated. The results show that the critical Froude number is strongly dependent on axial wavenumber. [Preview Abstract] 
Monday, November 20, 2017 5:10PM  5:23PM 
L34.00006: Stability criterion for stablystratified turbulent shear flows: Results of conditional averaging Robert Ecke, Philippe Odier Oceanic overflows, winddriven thermocline layers and river estuaries are geophysical examples of stablystratified shear flows. Our experimental realization of such flows consists of a turbulent wallbounded shear flow with lighter fluid injected at initial downstream velocity between 4 and 8 cm/s over a quiescent heavier fluid. We measure planar velocity and density fields usingPIV and PLIF, respectively. We consider 4 cases with initial bulk Richardson Number $0.25 < Ri_b < 1$ and determine the fraction of unperturbed interface defined using a Thorpe length analysis. We explore different definitions of gradient Richardson Number $Ri_g$ evaluated and conditionally averaged over unperturbed interface. A conventional choice in linear stability theory is $Ri_{g_0}$ where the gradients are evaluated at the interface position. Another that we denote $Ri_{g_m}$ (consistent with MilesHoward (MH) criterion) corresponds to the minimum value of $Ri_g$ as a function of vertical position. The second definition allows excellent comparison with linear stability theory and the MH criterion. For small Ri, there is robust KelvinHelmholtz instability (KHI) whereas for larger $Ri_g$ interfacial overturning is intermittent with infrequent KHI events and more frequent Holmboe instability. [Preview Abstract] 
Monday, November 20, 2017 5:23PM  5:36PM 
L34.00007: A new shortwave instability of stratified vortices Yuji Hattori, Shota Suzuki, Manish Khandelwal, Makoto Hirota The linear stability of stratified vortices is studied by local and modal stability analysis. Three vortical flows are considered: the twodimensional TaylorGreen vortices, the Stuart vortices, and the LambChaplygin vortex pair. A new shortwave instability is found by local stability analysis; it occurs on the streamlines near the heteroclinic orbits of the fluid particle which connect hyperbolic stagnation points. This instability emerges as the hyperbolic instability near the hyperbolic stagnation points, which cancels each other in the absence of stratification, survives through phase twist due to internal gravity waves. As a result the unstable regions appear as multiple bands whose number increases as stratification becomes strong; a simple model successfully predicts these bands. The direction of the wavevector is in good agreement with the structure of unstable eigenmodes obtained by modal stability analysis. Possible relation with the zigzag instability will be also discussed. [Preview Abstract] 
Monday, November 20, 2017 5:36PM  5:49PM 
L34.00008: Direct numerical simulation of turbulent plane Couette flow under neutral and stable stratification Evgeny Mortikov Direct numerical simulation (DNS) approach was used to study turbulence dynamics in plane Couette flow under conditions ranging from neutral stability to the case of extreme stable stratification, where intermittency is observed. Simulations were performed for Reynolds numbers, based on the channel height and relative wall speed, up to $2 \times 10^5$. Using DNS data, which covers a wide range of stability conditions, parameterizations of pressure correlation terms used in secondorder closure turbulence models are discussed. Particular attention is also paid to the sustainment of intermittent turbulence under strong stratification. Intermittent regime is found to be associated with the formation of secondary largescale structures elongated in the spanwise direction, which define spatially confined alternating regions of laminar and turbulent flow. The spanwise length of this structures increases with the increase in the bulk Richardson number and defines and additional constraint on the computational box size. In this work DNS results are presented in extended computational domains, where the intermittent turbulence is sustained for sufficiently higher Richardson numbers than previously reported. [Preview Abstract] 
Monday, November 20, 2017 5:49PM  6:02PM 
L34.00009: Detailed study of fluid flow in a stably stratified square liddriven cavity Bruno Welfert, Ke Wu, Juan Lopez A detailed numerical investigation of the fluid flow in a square liddriven cavity with stable temperature stratification in a comprehensive range of Reynolds and Richardson parameter values is presented (with Prandtl$=$1). Special attention is given to bifurcation mechanisms of the base steady state. Frequency analyses reveal an intricate pattern of responses when buoyancy and inertial effects compete. [Preview Abstract] 
Monday, November 20, 2017 6:02PM  6:15PM 
L34.00010: Fluid flow in a vertically oscillating, stably stratified cubic cavity Jason Yalim, Bruno Welfert, Juan Lopez, Ke Wu The dynamics of a fluid flow inside a vertically oscillating and stably stratified cubic cavity are investigated. Numerical simulations reveal an intricate pattern of states characterizing the response for each frequency and amplitude of the forced oscillations. It is shown how these states correspond to superpositions of internal wave modes associated to harmonic and subharmonic resonance tongues within the parameter space. The breaking of internal waves, which provides a mechanism for energy dissipation, is also illustrated. [Preview Abstract] 
Monday, November 20, 2017 6:15PM  6:28PM 
L34.00011: Velocity distribution around a sphere descending in a saltstratified water Hideshi Hanazaki, Shinsaku Akiyama, Shinya Okino When a sphere descends at constant speed in a saltstratified water, a thin and highspeed jet is often generated above the sphere. The phenomenon has first been observed by shadowgraph and then has been investigated numerically. In this study, a systematic measurement by particle image velocimetry (PIV) has been performed for a wide range of Froude number $Fr$ and Reynolds number $Re$, to actually observe the numerically simulated velocity distributions and confirm the accuracy of the numerical simulations for a very high Schmidt (Prandtl) number of $Sc=(Pr=)700$. The results show that the radius of the jet is proportional to both $Fr^{1/2}$ and $Re^{1/2}$, meaning that it is proportional to $\sqrt{Fr/Re}$ (when $F < 1$). The boundary layer on the sphere surface has a thickness comparable to the jet radius, and it is also proportional to $\sqrt{Fr/Re}$. These results are in agreement with the recent numerical simulations and a simple dimensional analysis. Typical diverging internalwave patterns, whose vertical wavelength has been predicted to be proportional to $Fr$, could also be observed. [Preview Abstract] 
Monday, November 20, 2017 6:28PM  6:41PM 
L34.00012: The fluid dynamics of deepsea mining Thomas Peacock, Andrew Rzeznik With vast mineral deposits on the ocean floor, deepsea nodule mining operations are expected to commence in the next decade. Among several fundamental fluid dynamics problems, this could involve plans for dewatering plumes to be released into the water column by surface processing vessels. To study this scenario, we consider the effects of nonuniform, realistic stratifications on forced compressible plumes with finite initial size. The classical plume model is developed to take into account the influence of thermal conduction through the dewatering pipe and also compressibility effects, for which a dimensionless number is introduced to determine their importance compared to the background stratification. Among other things, our results show that smallscale features of a realistic stratification can have a large effect on plume dynamics compared to smoothed profiles and that for any given set of environmental parameters there is a discharge flow rate that minimizes the plume vertical extent. Our findings are put in the context of nodule mining plumes for which the rapid and efficient resedimentation of waste material has important environmental consequences. [Preview Abstract] 
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