Spectrally condensed turbulence in thin layers

Abstract

We present experimental results on the properties of bounded turbulence in thin fluid layers. In contrast with the theory of two-dimensional ͑2D͒ turbulence, the effects of the bottom friction and of the spectral condensation of the turbulence energy are important in our experiment. Here we investigate how these two factors affect statistical moments of turbulent fluctuations. The inverse energy cascade in a bounded turbulent quasi-2D flow leads to the formation of a large coherent vortex ͑condensate͒ fed by turbulence. This vortex, depending on its strength, can substantially affect the turbulence statistics, even at small scales. Up to the intermediate strength of the condensate, the velocity moments similar to those in isotropic 2D turbulence are recovered by subtracting the coherent component from the velocity fields. A strong condensate leaves a footprint on the underlying turbulence; it generates stronger non-Gaussianity and reduces the efficiency of the inverse energy cascade. Remarkably, the energy flux in the cascade derived from the third-order structure function using the Kolmogorov flux relation gives physically meaningful values in a broad range of experimental parameters regardless of the condensate strength. This result has important implications for the analysis of the atmospheric wind data in upper troposphere and lower stratosphere.

Lagrangian scale of particle dispersion in turbulence

“…In fact, spectra in Fig. 1d,f are steeper, E k $ k À 4 , due to higher damping at large wave numbers 16,18 ; however, when turbulence is forced at lower wave numbers, for example, at f 0 ¼ 30 Hz in FWT, a theoretically predicted k À 3 spectrum is observed in the enstrophy cascade range. The kink in the spectrum marks the forcing scale…”

“…Here turbulence is generated using two methods. In the first, EMT is produced in layers of electrolytes (here in Na 2 SO 4 water solution, specific gravity of SG ¼ 1.03) by running electric current J across the fluid cell 18 . A matrix of magnetic dipoles placed underneath the cell produces spatially varying magnetic field B.…”

Turbulence on Hyperbolic Plane: The Fate of Inverse Cascade

“…The correlation functions F w (X 1 , X 2 ) (either v w (X 1 ) p(X 2 ) or v w (X 1 ) (v w v w + vwvw)(X 2 ) ) and their complex conjugates Fw(X 1 , X 2 ) also possess the symmetry properties (9.12), (9.13) and (9.14). Hence F w (X 1 , X 2 ) may be represented as in (9.18) with a real function G. We also have the relation 26) due to the incompressibility of v. It implies that G satisfies the homogeneous version of Eq. (9.20) whose general solution is proportional to (x 2 −1) −1 .…”

“…This is what happens on a sphere of radius R where there are no points with distances > πR. After reaching the largest distance, the cascade starts feeding energy into largest-scale flow that eventually changes the spectrum for k ≫ R −1 as well [26]. In the hyperbolic plane, however, there is more and more space available at distances ≫ R (the circumference of a circle of radius δ is equal to 2πR sinh(δ/R) increasing exponentially with the radius for δ ≫ R).…”

Structure Formation in Spectrally Condensed Turbulence

“…After the condensate vortex is formed, it exists in steady state. The energy is still supplied to it via the inverse energy cascade from the forcing scale 6 .…”