Decay Of Grid-generated Turbulence Research Articles

Saturation of decaying counterflow turbulence in helium II

We are concerned with the problem of the decay of a tangle of quantized vortices in He II generated by a heat current. Direct application of Vinen's equation yields the temporal scaling of vortex line density $L\ensuremath{\sim}{t}^{\ensuremath{-}1}$. Schwarz and Rozen [Phys. Rev. Lett. 66, 1898 (1991); Phys. Rev. B 44, 7563 (1991)] observed a faster decay followed by a slower decay. More recently, Skrbek et al. [Phys. Rev. E 67, 047302 (2003)] found an initial transient followed by the same classical ${t}^{\ensuremath{-}3/2}$ scaling as observed in the decay of grid-generated turbulence. We present a simple theoretical model which, we argue, contains the essential physical ingredients, and accounts for these apparently contradictory results.

Decay laws, anisotropy and cyclone–anticyclone asymmetry in decaying rotating turbulence

The effect of a background rotation on the decay of grid-generated turbulence is investigated from experiments using the large-scale ‘Coriolis’ rotating platform. A first transition occurs at 0.4 tank rotation (instantaneous Rossby number Ro ≃ 0.25), characterized by a t−6/5 → t−3/5 transition of the energy-decay law. After this transition, anisotropy develops in the form of vertical layers, where the initial vertical velocity fluctuations remain trapped. The vertical vorticity field develops a cyclone–anticyclone asymmetry, reproducing the growth law of the vorticity skewness, Sω(t) ≃ (Ωt)0.7, reported by Morize, Moisy & Rabaud (Phys. Fluids, vol. 17 (9), 2005, 095105). A second transition is observed at larger time, characterized by a return to vorticity symmetry. In this regime, the layers of nearly constant vertical velocity become thinner as they are advected and stretched by the large-scale horizontal flow, and eventually become unstable. The present results indicate that the shear instability of the vertical layers contributes significantly to the re-symmetrization of the vertical vorticity at large time, by re-injecting vorticity fluctuations of random sign at small scales. These results emphasize the importance of the nature of the initial conditions in the decay of rotating turbulence.

Grid-generated turbulence in two-phase flow: The effect of parameters of the carrier medium and particles

Results are given of an experimental investigation of the initial region of decay of grid-generated turbulence in a downward two-phase flow of the “gas-solid particles” type. Optical diagnostic methods are used to obtain the distributions of the dynamic parameters of two-phase flow, namely, averaged and fluctuation velocities of gas, and the curves of decay of turbulence along the flow axis are constructed for grids with square meshes sized 4.8, 10, and 16 mm. The investigation results demonstrate that solid particles 700 μm in size have varying effect on the degree of decay of turbulence. In the case of grids with small mesh sizes of 4.8 and 10 mm, the presence of such particles leads to additional generation of turbulence; in the case of a grid with mesh size of 16 mm, vice versa, the particles suppress the turbulence. Investigations reveal that these tendencies become still more pronounced with increasing concentration of particles. In addition, the investigation of the effect of velocity phase slip reveals that the generation of turbulence increases with the difference between phase velocities. In so doing, variation of the pattern of the effect of particles on turbulence is observed for a grid with large meshes, namely, the suppression of turbulence at low values of velocity slip and generation of turbulence with increasing slip. Based on the results of analysis of experimental data, a criterional parameter is suggested, which defines the effect of particles on the turbulence of two-phase flow, i.e., the ratio of the Reynolds number of particle to the turbulence Reynolds number for gas.

On leakage of energy from turbulence to internal waves in the oceanic mixed layer

In this paper, we address the question of energy leakage from turbulence to internal waves (IWs) in the oceanic mixed layer (OML). If this leakage is substantial, then not only does this have profound implications as far as the dynamics of the OML is concerned, but it also means that the equation for the turbulence kinetic energy (TKE) used in OML models must include an appropriate sink term, and traditional models must be modified accordingly. Through comparison with the experimental data on grid-generated turbulence in a stably stratified fluid, we show that a conventional two-equation turbulence model without any IW sink term can explain these observations quite well, provided that the fluctuating motions that persist long after the decay of grid-generated turbulence are interpreted as being due to IW motions generated by the initial passage of the grid through the stably stratified fluid and not during turbulence decay. We conclude that there is no need to postulate an IW sink term in the TKE equation, and conventional models suffice to model mixing in the OML.

The decay of turbulence in thermally stratified flow

The decay of grid-generated turbulence in the presence of strong thermal stratification is studied in a continuously stratified, open-loop wind tunnel at Brunt–Väisälä frequencies up to 2.5s−1. The data include one-point statistical measurements through moments of fourth order and associated power- and cross-spectra. Cross-channel phase measurements are used to analyse the scales of correlation of velocity and temperature. The present data are considerably more coherent than previous salt-stratified data, and the structural form of stratified turbulence is thus more clearly manifested. No internal wave effects are observed at any stage of the decay. Stratified turbulence is found to be a two-scale process dominated by buoyancy forces at large scales of motion and dissipative effects at small scales. The two-scale structure is used to develop universal buoyancy scalings for the decay of the vertical heat flux, the scalar variance, and the molecular dissipation rates, and, in particular, for the vertical velocity decay. Velocity and temperature spectra satisfy universal equilibrium scaling at high wavenumbers, but show buoyancy effects at small wavenumbers. The flow remains isotropic at high wavenumbers over the entire range of turbulent decay studied. Cospectral and phase data are used to validate the two-scale model of the turbulence. The flow may show large-scale restratification while active turbulence persists at smaller scales, so that the vanishing of the vertical transport does not represent extinction of turbulent motion. Additionally, an original universal equilibrium scaling is developed for the cross-spectrum. Lengthscale evolution is measured, and the overturning and buoyancy lengthscales (associated with potential and kinetic energy, respectively) are found to characterize flow development. The role of the Prandtl number is assessed by comparison to previous works, and the Prandtl number is found to have a significant influence upon stratified turbulence evolution.