Understanding and modeling turbulent fluxes and entrainment in a gravity current

International audienceWe present an experimental study of the mixing processes in a gravity current flowing on an inclined plane. The turbulent transport of momentum and density can be described in a very direct and compact form by a Prandtl mixing length model: the turbulent vertical fluxes of momentum and density are found to scale quadratically with the vertical mean gradients of velocity and density. The scaling coefficient, the square of the mixing length, is approximately constant over the mixing zone of the stratified shear layer. We show how, in different flow configurations, this length can be related to the shear length of the flow (ε/∂ z u^3)^1/2. We also study the fluctuations of the momentum and density turbulent fluxes, showing how they relate to mixing and to the entrainment/detrainment balance. We suggest a quantitative measure of local entrainment and detrainment derived from observed conditional correlations of density flux and density or vertical velocity fluctuations

Boundary Zonal Flow in Rotating Turbulent Rayleigh-Bénard Convection

For rapidly rotating turbulent Rayleigh–Bénard convection in a slender cylindrical cell, experiments and direct numerical simulations reveal a boundary zonal flow (BZF) that replaces the classical large-scale circulation. The BZF is located near the vertical side wall and enables enhanced heat transport there. Although the azimuthal velocity of the BZF is cyclonic (in the rotating frame), the temperature is an anticyclonic traveling wave of mode one, whose signature is a bimodal temperature distribution near the radial boundary. The BZF width is found to scale like Ra1/4Ek2/3 where the Ekman number Ek decreases with increasing rotation rate

Fragility and hysteretic creep in frictional granular jamming

The granular jamming transition is experimentally investigated in a two-dimensional system of frictional, bi-dispersed disks subject to quasi-static, uniaxial compression at zero granular temperature. Currently accepted results show the jamming transition occurs at a critical packing fraction $\phi_c$. In contrast, we observe the first compression cycle exhibits {\it fragility} - metastable configuration with simultaneous jammed and un-jammed clusters - over a small interval in packing fraction ($\phi_1 < \phi < \phi_2$). The fragile state separates the two conditions that define $\phi_c$ with an exponential rise in pressure starting at $\phi_1$ and an exponential fall in disk displacements ending at $\phi_2$. The results are explained through a percolation mechanism of stressed contacts where cluster growth exhibits strong spatial correlation with disk displacements. Measurements with several disk materials of varying elastic moduli $E$ and friction coefficients $\mu$, show friction directly controls the start of the fragile state, but indirectly controls the exponential slope. Additionally, we experimentally confirm recent predictions relating the dependence of $\phi_c$ on $\mu$. Under repetitive loading (compression), the system exhibits hysteresis in pressure, and the onset $\phi_c$ increases slowly with repetition number. This friction induced hysteretic creep is interpreted as the granular pack's evolution from a metastable to an eventual structurally stable configuration. It is shown to depend upon the quasi-static step size $\Delta \phi$ which provides the only perturbative mechanism in the experimental protocol, and the friction coefficient $\mu$ which acts to stabilize the pack.Comment: 12 pages, 10 figure

Stretching fields and mixing near the transition to nonperiodic two-dimensional flow

Although time-periodic fluid flows sometimes produce mixing via Lagrangian chaos, the additional contribution to mixing caused by nonperiodicity has not been quantified experimentally. Here, we do so for a quasi-two-dimensional flow generated by electromagnetic forcing. Several distinct measures of mixing are found to vary continuously with the Reynolds number, with no evident change in magnitude or slope at the onset of nonperiodicity. Furthermore, the scaled probability distributions of the mean Lyapunov exponent have the same form in the periodic and nonperiodic flow states

Knots and Random Walks in Vibrated Granular Chains

We study experimentally statistical properties of the opening times of knots in vertically vibrated granular chains. Our measurements are in good qualitative and quantitative agreement with a theoretical model involving three random walks interacting via hard core exclusion in one spatial dimension. In particular, the knot survival probability follows a universal scaling function which is independent of the chain length, with a corresponding diffusive characteristic time scale. Both the large-exit-time and the small-exit-time tails of the distribution are suppressed exponentially, and the corresponding decay coefficients are in excellent agreement with the theoretical values.Comment: 4 pages, 5 figure

A model for interacting instabilities and texture dynamics of patterns

A simple model to study interacting instabilities and textures of resulting patterns for thermal convection is presented. The model consisting of twelve-mode dynamical system derived for periodic square lattice describes convective patterns in the form of stripes and patchwork quilt. The interaction between stationary zig-zag stripes and standing patchwork quilt pattern leads to spatiotemporal patterns of twisted patchwork quilt. Textures of these patterns, which depend strongly on Prandtl number, are investigated numerically using the model. The model also shows an interesting possibility of a multicritical point, where stability boundaries of four different structures meet.Comment: 4 pages including 4 figures, page width revise

Universal criterion for the breakup of invariant tori in dissipative systems

The transition from quasiperiodicity to chaos is studied in a two-dimensional dissipative map with the inverse golden mean rotation number. On the basis of a decimation scheme, it is argued that the (minimal) slope of the critical iterated circle map is proportional to the effective Jacobian determinant. Approaching the zero-Jacobian-determinant limit, the factor of proportion becomes a universal constant. Numerical investigation on the dissipative standard map suggests that this universal number could become observable in experiments. The decimation technique introduced in this paper is readily applicable also to the discrete quasiperiodic Schrodinger equation.Comment: 13 page

Rotating Convection in an Anisotropic System

We study the stability of patterns arising in rotating convection in weakly anisotropic systems using a modified Swift-Hohenberg equation. The anisotropy, either an endogenous characteristic of the system or induced by external forcing, can stabilize periodic rolls in the K\"uppers-Lortz chaotic regime. For the particular case of rotating convection with time-modulated rotation where recently, in experiment, chiral patterns have been observed in otherwise K\"uppers-Lortz-unstable regimes, we show how the underlying base-flow breaks the isotropy, thereby affecting the linear growth-rate of convection rolls in such a way as to stabilize spirals and targets. Throughout we compare analytical results to numerical simulations of the Swift-Hohenberg equation