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10:45   Two-dimensional Turbulence 2 10:45 15 mins #41 Lagrangian pair dispersion in generalized two-dimensional turbulence Stefano Berti, Alexis Foussard, Xavier Perrot, Guillaume Lapeyre Abstract: The statistical properties of turbulent flows depend on the degree of locality of energy transfers among scales, namely on whether, at a given scale, the transfer is due to eddies of size comparable to the considered scale or to larger ones. Such locality characteristics of the Eulerian flow field may impact the relative dispersion of passively transported Lagrangian tracers. To explore the relation between the locality of energy transfers and the statistical properties of dispersion we consider a class of generalized two-dimensional flows, obtained from the so-called α-turbulence model, theoretically possessing different properties in terms of locality of energy transfers. Two important models of geophysical interest belong to this class: the barotropic quasi-geostrophic (QG) model and the surface quasi-geostrophic (SQG) one. All the considered dynamics are characterized by the conservation of an active tracer along the geostrophic flow with a direct cascade of tracer variance to small scales. The relative dispersion statistics in the direct cascade range of α−turbulent flows are examined, both as a function of time and as a function of scale, and compared to predictions based on phenomenological arguments assuming the locality of the cascade. We find that the dispersion statistics follow the predicted values from local theories, as long as the parameter α is small enough (dynamics close to those of the SQG model), for sufficiently small initial pair separations. In contrast, non-local dispersion is observed for the QG model, a robust result when looking at relative displacement probability distributions. 11:00 15 mins #311 THE DECAY OF TWO-DIMENSIONAL TURBULENCE IN SOAP-FILM FLOWS Zeyou Zhou, Haitao Xu Abstract: Vertical soap-film flows are very often used as a laboratory example of two-dimensional turbulence [3], due to its large aspect ratio in the flow direction and in the film-thickness direction, which could easily reach 4 to 5 orders of magnitudes. We set up a vertical soap-film flow that can reach a steady mean flow velocity in the range of 1􀀀3m=s and film thickness of 4 􀀀 9 m. The turbulence was created by inserting an array of equally spaced round-rods into the film. The spacing of the rods is M = 5mm, and we performed measurements at distances of 12M 􀀀 100M downstream the rods. The flow was seeded with 1 m polystyrene tracer particles and illuminated by a pulsed Nd:YAG laser. The motion of the tracer particles was then recorded by high-speed Phantom VEO640 cameras. The trajectories of the tracer particles were reconstructed by the particle tracking technique, from which the positions and velocities of the tracers were obtained, which in turn were used to calculated the statistical quantities of interest, such as the velocity structure functions. Theoretically, for forced two-dimensional turbulence at steady-state, there co-exists a double-cascade: energy is transferred from the forcing scale upwards and dissipated by friction or air-drag that dominate at large-scales, while enstrophy is cascaded from the forcing scale downwards and dissipated by viscosity at small scales. When the external forcing is absent and the turbulence is decaying, the situation can be more complicated. If the large-scale friction is linearly proportional to velocity, such as in the case of electro-magnetically driven liquid layer flows, the decay of energy is exponential and the long-time decay has been studied recently [1]. In our soap-film flows, we observed power-law like energy decay, as shown in Figure 1(a). This could be explained by the existence of an air-drag that is nonlinear with fluid velocity, which is consistent with our other measurements. Moreover, we observed that both the second- and third-order Eulerian velocity structure functions show clear power-law scaling and the scaling exponents, which are different from the expected steady-state scaling based on simply cascade argument, remain the same at different downstream locations. This might imply that the cascade process is influenced by the energy-decay, which would results in the change of the length scales defining the different regimes, similar to that observed in two-dimensional liquid layers [1] and to that of three-dimensional turbulences [4, 5]. The change in energy flux could be anaylzed using the filtering technique [2]. 11:15 15 mins #425 Energy flux vector in a shell model of 2-D rotating turbulence Masanori TAKAOKA, Naoto YOKOYAMA, Eiichi SASAKI Abstract: To investigate anisotropic turbulence, it is indispensable to understand its energy flux as a vector field. We here consider to obtain a flow of energy in the Fourier space similar to the energy cascade in isotropic turbulence. To solve the continuity equation for enrgy flow, we have examined two idea: use of the Moore-Penrose inverse matrix and potential flux vector. We have simulated a two-dimensional shell model extended to $\beta$-plane in order to study the Rhines "lazy eight" spectrum. We will report the result that calculating energy changing rate at each wave number, we obtain energy flux vector by using the above-described methods. We will also discuss the appropriateness of the obtained flux vector field. 11:30 15 mins #507 Sudden transition from non-swirling to swirling axisymmetric turbulence Wouter Bos, Zecong Qin, Aurore Naso Abstract: Strictly axisymmetric turbulence, i.e. turbulence governed by the Navier-Stokes equations modified such that the flow is invariant in the azimuthal direction, is a system intermediate between two- and three-dimensional turbulence. We show by simulations the remarkable feature of the system, that the toroidal energy remains zero even when the toroidal forcing is non-zero. Only when the forcing of both components becomes comparable, the flow abrubtly transitions towards a swirling state. We then derive a statistical model for this behaviour, starting from the axisymmetric Navier-Stokes equations, which very accurately reproduces the transition between the two flow states. 11:45 15 mins #490 Mixing efficiency of laminar and turbulent wall-bounded flows Kai Schneider, Benjamin Kadoch, Wouter Bos Abstract: Typically turbulent flows mix more rapidly a passive scalar than laminar flows do. From an energetic point of view, for statistically homogeneous or periodic fields, laminar flows are more efficient. We show by direct numerical simulation how this changes for wall-bounded flows. 12:00 15 mins #235 Do shear layers spontaneously trigger turbulence? Alexei A. Mailybaev, Simon Thalabard, Jeremie Bec Abstract: see PDF file 12:15 15 mins #191 Nonlinear Evolution of a Baroclinic Wave and Imbalanced Dissipation William Riley Casper, Balu Nadiga Abstract: We consider the nonlinear evolution of an unstable baroclinic wave in a regime of rotating stratified flow that is of relevance to interior circulation in the oceans and in the atmosphere---a regime characterized by small large-scale Rossby and Froude numbers, a small vertical to horizontal aspect ratio, and no bounding horizontal surfaces. Using high-resolution simulations of the non-hydrostatic Boussinesq equations and companion integrations of the balanced quasi-geostrophic equations, we present evidence for a local route to dissipation of balanced energy directly through interior turbulent cascades. Analysis of simulations presented in this study suggest that a developing baroclinic instability can lead to secondary instabilities that can cascade a small fraction of the energy forward to unbalanced scales. Mesoscale shear and strain resulting from the hydrostatic geostrophic baroclinic instability drive frontogenesis. The fronts in turn support ageostrophic secondary circulation and instabilities. These two processes acting together lead to a quick rise in dissipation rate which then reaches a peak and begins to fall slowly when frontogenesis slows down; eventually balanced and imbalanced modes decouple. Dissipation of balanced energy by imbalanced processes scales exponentially with Rossby number of the base flow. We expect that this scaling will hold more generally than for the specific setup we consider given the fundamental nature of the dynamics involved. A break is seen in the total energy spectrum at small scales: While a steep −3 geostrophic scaling with the three-dimensional wavenumber is seen at intermediate scales, the smaller scales display a shallower −5/3 scaling, reminiscent of the atmospheric spectra of Nastrom & Gage. At higher Ro, the vertical shear spectrum has a minimum, like in some relevant obervations 12:30 15 mins #145 INERTIAL AND ANISOTROPIC PARTICLES IN 2D TURBULENCE Michael Shats, Nicolas Francois, Hua Xia, Jia Yang, Horst Punzmann Abstract: Two-dimensional (2D) turbulence, at least at modest Reynolds numbers, shows strongly anisotropic Lagrangian structure, dominated by meandering ‘rivers’ of the average widths of about the turbulence forcing scale [1,2]. Such turbulence can be efficiently generated on the liquid-gas interface perturbed by steep nonlinear Faraday waves [3,4]. We present experimental results on the transport of large and small circular disks as well as anisotropic ‘Pacman’ disks.