15:00
Geophysical and astrophysical turbulence 2
Chair: Frederic Moisy
15:00
15 mins
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A statistical mechanics framework for the large-scale structure of a turbulent von K\'arm\'an flow
Berengere Dubrulle, Simon Thalabard, Brice Saint-Michel, Francois Daviaud, Eric Herbert
Abstract: Recent experimental results on large scale coherent steady states observed in experimental turbulent von K\'arm\'an flows are revisited from a statistical mechanics perspective. We argue that the coherent steady states may be described as the equilibrium states of ad hoc lattice models, that can be used to define global properties of von K\'arm\'an flows, such as their temperatures, their fugacity and so on.
The equilibrium description is then enlarged, in order to reinterpret a series of results about the stability of those steady states, their susceptibility to symmetry breaking, in the light of a deep analogy with the Curie-Weiss statistical theory of Ferromagnetism.
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15:15
15 mins
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Disentangling inertial waves from eddy turbulence in a forced rotating turbulence experiment
Antoine Campagne, Basile Gallet, Frédéric Moisy, Pierre-Philippe Cortet
Abstract: We present a spatio-temporal analysis of a statistically stationary rotating turbulence experiment, aiming to extract a signature of inertial
waves and to determine at what scales and frequencies they can be detected. This analysis is performed from two-point correlations of
temporal Fourier transform of the velocity fields obtained from time-resolved stereoscopic particle image velocimetry measurements
in the rotating frame. We quantify the degree of anisotropy of turbulence as a function of frequency and spatial scale normal to the
rotation axis. We show that this space-time-dependent anisotropy is well described by the dispersion relation of linear inertial waves at
large scale, while smaller scales are dominated by the nonlinear sweeping of the waves by the random motions at larger scales. This
sweeping effect is dominated here by the low-frequency quasi-two-dimensional component of the turbulence, a prominent feature of
our experiment which is not accounted for by the weak wave turbulence theory.
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15:30
15 mins
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Normal mode decomposition in direct numerical simulations of rotating-stratified turbulence
Corentin Herbert, Raffaele Marino, Annick Pouquet, Duane Rosenberg
Abstract: In the presence of solid-body rotation and density stratification, turbulent flows may exhibit an inverse as well as a direct cascade. We investigate the role of turbulence and waves in these energy cascades, focusing on the inverse cascade. This is done through a normal mode decomposition of the dynamical fields in a set of direct numerical simulations in terms of inertia-gravity waves and vortical modes. In agreement with theoretical arguments, we find that the vortical modes dominate the inverse cascade of energy.
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15:45
15 mins
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TURBULENT STRATIFIED SHEAR FLOW EXPERIMENTS: LENGTH SCALE COMPARISON
Robert Ecke, Philippe Odier
Abstract: Stratified shear flows are ubiquitous in geophysical systems such as oceanic overflows, wind-driven thermoclines, and atmo- spheric inversion layers. The stability of such flows is governed by the Richardson Number Ri which represents a balance between the stabilizing influence of stratification and the destabilizing influence of shear. For a shear flow with velocity difference U, density difference ∆ρ and characteristic length H, one has Ri = g(∆ρ/ρ)H/U^2 which is often used when detailed information about the flow is not available. A more precise definition is the gradient Richardson Number Rig = N^2/S^2 where the buoyancy frequency N = ((g/ρ)∂ρ/∂z)^{1/2}, the mean strain S = ∂U/∂z in which z is parallel to gravity and suitable ensemble or time averages define the gradients. We explore the stability and mixing properties of a wall-bounded shear flow over a range 0.1< Rig <1 using simultaneous planar measurements of density and velocity fields using Planar Laser-Induced Fluorescence (PLIF) and Particle Image Velocimetry (PIV), respectively. The flow, confined from the top by glass horizontal boundary, is a lighter alcohol-water mixture injected from a nozzle into quiescent heavier salt-water fluid with velocity between 5 and 10 cm/s and with a relative fractional density difference of 0.0026 or 0.0052. The injected flow is turbulent with Taylor Reynolds number between 50 and 100. We compare a set of length scales that characterize the mixing properties of our turbulent stratified shear flow including the Thorpe Length L_T, the Ozmidov Length L_o, the Ellison Length L_E, and turbulent mixing lengths L_m and L_ρ.
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16:00
15 mins
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Double diffusive convection between two parallel plates with different boundary conditions
Yantao Yang, Erwin P. van der Poel, Rodolfo Ostilla-Monico, Chao Sun, Roberto Verzicco, Siegfried Grossmann, Detlef Lohse
Abstract: We investigate the double diffusive convection between two parallel plates with either no-slip or free-slip boundary conditions. Direct numerical simulations have been conducted systematically for a series of control parameters. Salt fingers can be observed for both boundary conditions and all parameters explored. Compared to the no-slip case, salt fingers are stronger in the free-slip case, which is accompanied by larger salinity flux and flow velocity. For both boundary conditions, thin boundary regions develop adjacent to two plates. The salinity flux and the Reynolds number show similar dependences on the control parameter, namely, the Rayleigh number of the salinity field.
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16:15
15 mins
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The Göttingen rotating turbulent Rayleigh-Bénard convection facility
Dennis van Gils, Xiaozhou He, Guenter Ahlers, Eberhard Bodenschatz
Abstract: Thermally driven turbulent convection under the influence of global rotation is ubiquitous in nature. Well known examples are the outer convective shell of our Sun and the outer liquid core of the Earth. Trying to understand the underlying dynamics of such flows is highly challenging, not only because of the enormous range in length- and time-scales that are involved with these geo/astrophysical cases and the complex interaction of hydrodynamics with electromagnetism, but also because direct measurements on these systems are most often impossible to carry out. We gain access to direct measurements by isolating part of the problem: We focus solely on the hydrodynamical aspects of turbulent convection by performing experiments in the lab and making comparisons with direct numerical simulations (DNS). The canonical system that we use to study such flows is Rayleigh-B\'enard convection (RBC), the flow between a warm bottom plate and cold top plate, in a fluid-filled upright cylindrical cell that is rotating around its geometrical axis. This presentation will focus on the newly constructed rotating RBC facility at the Max Planck Institute for Dynamics and Self-Organization (MPIDS) in G\"ottingen.
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16:30
15 mins
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Similarities between 2D and 3D convection for large Prandtl number
Anando Chatterjee, Ambrish Pandey, Mahendra Verma, Biplab Dutta
Abstract: Using direct numerical simulations of Rayleigh-B\'enard convection (RBC), we perform a comparative study of the spectra and fluxes of energy and entropy for large and infinite Prandtl numbers in two (2D) and three (3D) dimensions. We observe close similarities between the 2D and 3D RBC, in particular the kinetic energy spectrum $E_u(k) \sim k^{-13/3}$, and the entropy spectrum exhibits a dual branch with a dominant $k^{-2}$ spectrum. We showed that the dominant Fourier modes in the 2D and 3D flows are very close.
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