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 L23: Minisymposium: Recent Advancements in Turbulent Mixing in Stratified Geophysical FlowsGeophysical Mini-Symposium Turbulence
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Chair: Jeffery Koseff, Stanford University, Stephan Monismith, Stanford University and Brian White, UNC Chapel Hill Room: 710 |
Monday, November 20, 2017 4:05PM - 4:31PM |
L23.00001: Energetics of stratified turbulent mixing at geophysical scales Alberto Scotti, Pierre-Yves Passaggia, Brian White Energy-based arguments provide a fundamental diagnostic tool in turbulent flows. In stratified incompressible flows, there are two reservoirs of energy, the kinetic and potential energy. However, the standard expression $E_{\rm p}=\rho gZ$ for the latter is not convex, and thus, within an energetic framework based on this definition, turbulent fluctuations have zero potential energy, a rather unsatisfactorily state of affairs. The solution is to modify the definition of potential energy to include only the portion that is effectively available. This introduces the concept of Available Potential Energy (APE). In this talk, we approach the problem of APE using a general framework which recovers the standard buoyancy-only dependent formulation in non-rotating systems. Unlike the standard formulation, rotation can be included in a natural way, in which case the Available Energy depends both on the buoyancy and potential vorticity distribution. We will show results from experiments of stratified mixing at oceanic values of the Gibson number conducted in our large flume. The goal of this experiments is to shed some light on the controversy surrounding the relationship between the mixing efficiency and the Gibson number. [Preview Abstract] |
Monday, November 20, 2017 4:31PM - 4:57PM |
L23.00002: High mixing efficiencies in buoyancy-driven flows Megan Davies Wykes The concept of a mixing efficiency is widely used to relate the amount of irreversible diabatic mixing to the amount of energy available in a stratified flow. In this talk, I will present the results of laboratory experiments that show that high mixing efficiencies ($\eta > 0.75$) can occur when Rayleigh--Taylor instability develops at an interface between two otherwise stably stratified layers. I will also highlight examples of `buoyancy-driven' mixing to demonstrate that the mixing efficiency depends not only on the specific characteristics of the turbulence in the region of the flow that is mixing, but also on the density profile in regions remote from where mixing physically occurs. [Preview Abstract] |
Monday, November 20, 2017 4:57PM - 5:23PM |
L23.00003: Kelvin-Helmholtz instability: the ``atom'' of geophysical turbulence? William Smyth Observations of small-scale turbulence in Earth's atmosphere and oceans have most commonly been interpreted in terms of the Kolmogorov theory of isotropic turbulence, despite the fact that the observed turbulence is significantly anisotropic due to density stratification and sheared large-scale flows. I will describe an alternative picture in which turbulence consists of distinct events that occur sporadically in space and time. The simplest model for an individual event is the ``Kelvin-Helmholtz (KH) ansatz'', in which turbulence relieves the dynamic instability of a localized shear layer. I will summarize evidence that the KH ansatz is a valid description of observed turbulence events, using microstructure measurements from the equatorial Pacific ocean as an example. While the KH ansatz has been under study for many decades and is reasonably well understood, the bigger picture is much less clear. How are the KH events distributed in space and time? How do different events interact with each other? I will describe some tentative steps toward a more thorough understanding. [Preview Abstract] |
Monday, November 20, 2017 5:23PM - 5:49PM |
L23.00004: Interaction between double diffusion and differential diffusion in a stratified turbulent flow Chris Rehmann Experiments were used to explore the interaction between salt fingering and differential diffusion. Studies of ocean mixing have demonstrated preferential transport (or differential diffusion) of heat when a flow stratified with stable profiles of temperature and salinity is stirred weakly. Therefore, in a flow with an initial density ratio $R_\rho$ large enough to inhibit fingering, differential diffusion could reduce $R_\rho$ enough that salt fingers form. Experiments with stirring rods were conducted and characterized by $R_\rho$ and a turbulent Richardson number $Ri_T$. For $1< R_\rho < 3$, salt finger fluxes dominated and caused the salinity to mix faster than the temperature. For $R_\rho > 4$, differential diffusion fluxes dominated and caused temperature to mix faster than salinity. As expected from previous experiments, effects of differential diffusion were stronger for large $Ri_T$. However, although stronger turbulence was expected to disrupt salt fingers, effects of fingering were stronger for small $Ri_T$. Mixing efficiencies were largest for conditions conducive to differential diffusion. [Preview Abstract] |
Monday, November 20, 2017 5:49PM - 6:15PM |
L23.00005: The structure of shear instability at high Reynolds number W Rockwell Geyer Acoustic imaging of shear instabilities in a highly stratified estuary reveals a different structure than that observed in laboratory experiments and Direct Numerical Simulation. In these field observations, the mixing is accomplished by secondary instability within the braids, while the ``cores'' are relatively quiescent. This contrasts most experimental and DNS results that indicate the most intense mixing in the gravitationally unstable cores. New measurements obtained with a multibeam echosounder resolve the spatial structure and temporal evolution of shear instabilities in the highly stratified estuary. They confirm the key role of the braids in mixing through the development of secondary instabilities. They also indicate that the slope of the braids is relatively low, and the primary instability never steepens enough to ``roll up'' and generate gravitational instability in the core. Energetic secondary instabilities downstream of the inflection point appear to be the main agents of mixing. This structure is explained by the high Reynolds number conditions of the estuarine flow (Re$=$500,000), which permits the development of primary shear instabilities for Ri$\ge $0.2 as well as the development of fully turbulent secondary instabilities within the braid. Comparison with high Re DNS simulations suggest that the Reynolds number has a significant influence on the structure of instabilities at least up to Re$=$50,000. [Preview Abstract] |
Monday, November 20, 2017 6:15PM - 6:41PM |
L23.00006: Buoyancy fluxes in stratified flows: observations and parameterizations Stephen Monismith, Jeffrey Koseff, Ryan Walter, Michael Squibb, Brock Woodson, Kristen Davis, Geno Pawlak, Jamie Dunckley \textsc{We present a synthesis of observations of turbulent buoyancy fluxes, }\textsc{\textit{B}}\textsc{, made at five sites where flows and turbulence are primarily associated with internal waves, both breaking and non-breaking. In four cases, }\textsc{\textit{B}}\textsc{ was calculated from the covariance of velocity and density whereas in the fifth case, it was inferred from the rate of temperature variance dissipation,}$\chi $\textsc{. Overall, we find that the flux Richardson number, }\textsc{\textit{Ri}}$_{f}$\textsc{, depends on the Gibson number, }\textsc{\textit{Gi}}\textsc{ }$=$\textsc{ }$\varepsilon $\textsc{/}$\nu $\textsc{N}$^{\mathrm{2}}$\textsc{: when }\textsc{\textit{Gi}}\textsc{ \textless 100, }\textsc{\textit{Ri}}$_{f}$\textsc{ }$\approx $\textsc{ 0.27, and when }\textsc{\textit{Gi}}\textsc{ \textgreater 100 }\textsc{\textit{Ri}}$_{f}$\textsc{ }$\approx $\textsc{ 2.7 }\textsc{\textit{Gi}}$^{\mathrm{-0.5}}$\textsc{, in agreement with the functional relationship found originally using direct numerical simulation (DNS). Our observations do not match well other DNS-derived models that parameterize }\textsc{\textit{Ri}}$_{f}_{\mathrm{\thinspace }}$\textsc{in terms of the gradient Richardson number, }\textsc{\textit{Ri,}}\textsc{ or the turbulence Froude numbers, }\textsc{\textit{Fr}}$_{k}$\textsc{ and }\textsc{\textit{Fr}}$_{t}$\textsc{. Similarly, }\textsc{\textit{Ri}}$_{f}$\textsc{(}\textsc{\textit{Gi}}\textsc{) is found to be the same for all the covariance data sets, despite the fact that these 4 flows produce turbulence that falls in different regimes defined by several pairs chosen from the 5 non-dimensional numbers that the Buckingham }$\Pi $\textsc{ theorem shows may affect }\textsc{\textit{Ri}}$_{f}$\textsc{ . } [Preview Abstract] |
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