Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session R28: Geophysical Fluid Dynamics: General |
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Chair: Glenn Flierl, MIT Room: 309 |
Tuesday, November 24, 2015 12:50PM - 1:03PM |
R28.00001: Eddy transport of reacting substances Glenn Flierl We examine an exact formulation of eddy fluxes\footnote{c.f. Kraichnan, R.H. (1987) Eddy Viscosity and Diffusivity: Exact Formulas and Approximations. {\sl Complex Systems}, {\bf 1}, 805-820.} but extended to tracers which react with each other. The resulting formula is evaluated using the lattice model approach,\footnote{Pierrehumbert, R.T. (2000) Lattice models of advection-diffusion. {\sl Chaos}, {\bf 10}, 61-74.} allowing not only control (including elimination) of sub-grid-scale diffusion and efficient enough computation to generate an adequate ensemble. The theory predicts that the flux is a non-local average of the mean gradients, even for passive scalars, and we can calculate the averaging kernel. The reaction terms alter the effective transport for a single scalar depending on decay time scale compared to that of the Lagrangian covariance. But, in addition, the eddies produce ``cross-fluxes'' whereby the transport of each tracer depends on the gradients of all of them. [Preview Abstract] |
Tuesday, November 24, 2015 1:03PM - 1:16PM |
R28.00002: Eulerian and Lagrangian statistics in fully developed rotating turbulent flows. Luca Biferale, Fabio Bonaccorso, Irene Mazzitelli, Alessandra Lanotte, Prasad Perlekar, Stefano Musacchio, Michel Hinsberg, Federico Toschi We present results concerning both Eulerian and Lagrangian statistics for turbulent under rotation at small and large Rossby numbers. Concerning the Eulerian statistics we discuss the effects of the presence of strong coherent large-scale vortical structures on the small-scale statistics. Concerning Lagrangian properties, we discuss the effects of preferential sampling at changing the inertial properties of the particles also due to the centrifugal and Coriolis forces. [Preview Abstract] |
Tuesday, November 24, 2015 1:16PM - 1:29PM |
R28.00003: L\'evy Dynamics of Stretching in 2-Dimensional Steady Random Flow Fields Marco Dentz, Tanguy Le Borgne, Daniel Lester, Felipe P. J. de Barros Stretching and compression of material fluid elements is key for the understanding and quantification of the mixing dynamics. For 2-dimensional steady random flows the elongation of a material strip $\rho(t)$ grows algebraically as $\rho(t) \propto t^{\gamma}$. The stretching exponent $\gamma$ depends on the heterogeneity strength. While the Poincar\'e-Bendixson theorem explains the absence of exponential stretching in steady $2d$ flows, the mechanisms of the algebraic stretching behavior and its relation to the flow statistics are not known. Here we formulate the deformation of a material fluid element in streamline coordinates, which unravels the dynamics of the stretching provess as a L\'evy walk. We provide an explicit relation between the stretching process and the flow heterogeneity and derive the scaling behavior of elongation with time. We find for the stretching exponent $\gamma$ is bounded between $1/2$ and $2$, where $\gamma = 1/2$ corresponds to weak heterogeneity and $\gamma = 2$ to strongly heterogeneous flow fields. [Preview Abstract] |
Tuesday, November 24, 2015 1:29PM - 1:42PM |
R28.00004: A Dynamical System Approach to the Surface Search of Debris from MH370 Ana M Mancho, V. J. Garcia-Garrido, S. Wiggins, C. Mendoza The disappearance of Malaysia Airlines flight MH370 on the morning of the 8th of March 2014 is one of the great mysteries of our time. One relevant aspect of this mystery is that not a single piece of debris from the aircraft was found during the intensive surface search carried out in the months following the crash. Difficulties in the search efforts, due to the uncertainty in the plane's final impact point and the time passed since the accident, brought the question on how the debris was scattered in an always moving ocean, for which there were multiple datasets that do not uniquely determined its state. Our approach to this problem is based on dynamical systems tools that identify dynamic barriers and coherent structures governing transport. By combining different ocean data with these mathematical techniques, we are able to assess the spatio-temporal state of the ocean in the priority search area at the time of impact and the following weeks. Using this information we propose a revised search strategy by showing why one might not have expected to find debris in some large search areas targeted by the search services and determining regions where one might have expected impact debris to be located and that have not been subjected to any exploration. [Preview Abstract] |
Tuesday, November 24, 2015 1:42PM - 1:55PM |
R28.00005: Lagrangian coherent structures in the Gulf Stream Yi Liu, Chris Wilson, Melissa Green Finite-time Lyapunov exponent (FTLE) is calculated to identify Lagrangian coherent structures in the Gulf Stream region. The velocity fields are determined using the geostrophic velocities derived from satellite altimetry data. The coherent structures in and around the Gulf Stream are delineated by the both positive and negative FTLE ridges, and represent boundaries between dynamically distinct regions that are important to investigate transport and mixing processes in the ocean. Alternating positive and negative FTLE ridge patterns are found to line the meandering jet, which indicate the regions of entrainment and detrainment along the jet. Results compare well with the Bower kinematic model of a meandering jet, although it is clear that the kinematic model is an over-simplification of the jet dynamics, and studying the dynamics of vortex interaction with the jet is important for understanding fluid transfer in the Gulf Stream region. [Preview Abstract] |
Tuesday, November 24, 2015 1:55PM - 2:08PM |
R28.00006: Vortex Ring Induce Mixing: A Mixing Model Jason Olsthoorn, Stuart B. Dalziel The parameterization of stratified turbulent mixing is key to developing large scale simulations of geophysical flows. Stratified mixing if often quantified through its mixing efficiency, a quantity that has been reported to vary significantly depending on the mixing mechanism. In the work presented here, we will investigate periodically-forced, externally-mixed stratified flows where the mixing mechanism is produced external to the mixing location. The mixing induced by vortex rings is a frequently studied phenomena as it is often compared with the eddies of fully developed turbulence. We continue this work experimentally with the aid of modern measurement techniques. Additionally, we have developed a one-dimensional model of vortex-ring-induced mixing and compare this model with both laboratory and numerical experiments. The results of the density field evolution, and the mixing efficiency, demonstrate a quantitative agreement between the model and experiments. [Preview Abstract] |
Tuesday, November 24, 2015 2:08PM - 2:21PM |
R28.00007: On accuracy of overturn-based estimates of turbulent dissipation in a Luzon Strait model simulation with realistic topography Masoud Jalali, Vamsi Chalamalla, Sutanu Sarkar Oceanic density overturns are commonly used to estimate the dissipation rate of turbulent kinetic energy using the Thorpe sorting method. However, the accuracy of the dissipation estimate under different conditions is unclear. To assess the accuracy of Thorpe estimates of turbulence dissipation, 3D LES are performed with scaled semidiurnal frequency in a scaled down model of Luzon strait topography. The Thorpe-scale method is found to be able to qualitatively estimate the spatial distribution and phasing of dissipation rate but there are quantitative errors. It overestimates the magnitude of dissipation in locations with strong convectively driven turbulence. The extent of overestimation in the case of Luzon strait is up to more than one order of magnitude. However, the Thorpe estimate has reasonably good agreement with the dissipation in regions with shear-driven turbulence. An alternative model based on a modified estimate of the Thorpe scale from the vertical profile of density is introduced. This method is able to estimate convectively driven dissipation more accurately, although it is less accurate in regions with shear driven turbulence such as downslope jets. Both methods of inferring dissipation rate exhibit phase difference with respect to the value in the simulations. [Preview Abstract] |
Tuesday, November 24, 2015 2:21PM - 2:34PM |
R28.00008: From convection rolls to finger convection in double-diffusive turbulence Yantao Yang, Roberto Verzicco, Detlef Lohse The double diffusive convection (DDC), where the fluid density depends on two scalar components with very different molecular diffusivities, is frequently encountered in oceanography, astrophysics, and electrochemistry. In this talk we report a systematic study of vertically bounded DDC for various control parameters. The flow is driven by an unstable salinity difference between two plates and stabilized by a temperature difference. As the relative strength of temperature difference becomes stronger, the flow transits from a state with large-scale convection rolls, which is similar to the Rayleigh-B\'{e}nard (RB) flow, to a state with well-organised salt fingers. When the temperature difference increases further, the flow breaks down to a purely conductive state. During this transit the velocity decreases monotonically. Counterintuitively, the salinity transfer can be enhanced when a stabilising temperature field is applied to the system. This happens when convection rolls are replaced by salt fingers. In addition, we show that the Grossmann-Lohse theory originally developed for RB flow can be directly applied to the current problem and accurately predicts the salinity transfer rate for a wide range of control parameters. [Preview Abstract] |
Tuesday, November 24, 2015 2:34PM - 2:47PM |
R28.00009: Mixing in the spiral roll state in heat convection between concentric double spherical boundaries Tomoaki Itano, Takahiro Ninomiya, Kohei Iida, Masako Sugihara-Seki Recent studies have indicated that the spherical Rayleigh B\'enard convection provides a variety of non-trivial (convective) flow states bifurcating from the (conductive) static state at the onset of instability. In the present study, focusing on one of them, "spiral roll state", which was originally explored by Zhang et al.(2002), we elucidated the following three points of the state; (1) the state exists even in a fairly thicker gap than expected in the previous study, and (2) it is an exact autonomously rotating wave solution, and (3) the state bifurcates directly from the static state at the onset of instability. It is of great interest that this state involves globally mixing through the whole domain beyond a cell which would be formed by the other highly-symmetric nontrivial steady states bifurcating at the onset. [Preview Abstract] |
Tuesday, November 24, 2015 2:47PM - 3:00PM |
R28.00010: The Modified Rayleigh-Benard Convection Problem and its Application to Permafrost Methane Emission Modeling Ivan Sudakov, Sergey Vakulenko The original Rayleigh-Benard convection is a standard example of the system where the critical transitions occur with changing of a control parameter. We will discuss the modified Rayleigh-Benard convection problem which includes the radiative effects as well as the specific gas sources on a surface. Such formulation of this problem leads to identification a new kind of nonlinear phenomenon, besides the well-known Benard cells. Modeling of methane emissions from permafrost into the atmosphere drives to difficult problems, involving the Navier-Stokes equations. Taking into account the modified Rayleigh-Benard convection problem, we will discuss a new approach which makes the problem of a climate catastrophe in the result of a greenhouse effect more tractable and allows us to describe catastrophic transitions in the atmosphere induced by permafrost greenhouse gas sources. [Preview Abstract] |
Tuesday, November 24, 2015 3:00PM - 3:13PM |
R28.00011: Transition to Turbulence in the Infrared - Revisited Richard Leighton, Geoffrey B. Smith A serendipitous observation of the transition to turbulence of a wind driven free-surface at the University of Delaware Air-Sea Interaction Laboratory led the 1998 'Gallery of Fluid Motion: Transition to turbulence in the infrared'. This transition, via the formation of Langmuir cells is being examined numerically. Simulations are performed of a strongly shear driven air-water interface, modeled as a flat interface with a specified Stokes drift and a constant heat flux cooling the interface. The simulations are initialized with a weak random flow field and allowed to evolve under the influence of constant shear and heat flux. Like the original experiment, the flow is slow to setup, but transition occurs quickly. The scaling and energetics will be discussed. [Preview Abstract] |
Tuesday, November 24, 2015 3:13PM - 3:26PM |
R28.00012: Self-similar behavior of non-planar non-circular gravity currents Thomas Bonometti, Nadim Zgheib, S. Balachandar This work reports some new aspects of non-planar non-circular gravity currents obtained from laboratory experiments, fully resolved simulations and box models. We show that these currents eventually reach a self-similar regime during which the local front propagation scales as the square root of time as in circular releases. In particular, the front has a self-similar shape that primarily depends on the aspect ratio of the initial release. The extended box model recently reported in [Zgheib \textit{et al.} 2014 \textit{Theor. Comput. Fluid Dyn.} \textbf{28}, 521-529] is used to propose a relation for the self-similar horizontal aspect ratio of the propagating front as a function of the initial horizontal aspect ratio. The experimental and numerical results are in good agreement with the proposed relation. [Preview Abstract] |
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