Oscillating-grid experiments in water and superfluid helium.

Abstract

Passing a fluid through a grid is a well-known mechanism used to study the properties of turbulence. Oscillating a horizontal grid vertically in a tank has also been used extensively and is considered to be a source of almost homogenous isotropic turbulence. When the oscillating grid is turned on a turbulent flow is induced. A front translates into the experimental tank, behind which the flow is highly turbulent. Long predicted that the growth of such a front would grow diffusively as the square root of time (i.e., d ∼ sqrt[t]) and Dickinson and Long presented experimental evidence for the diffusive result at a low mesh Reynolds number of 555. This paper revisits these experiments and attempts a set of two models for the advancing front in both square and round tanks. We do not observe significant differences between runs in square and round tanks. The experiments in water reach mesh Reynolds numbers of order 30000. Using some data from superfluid helium experiments we are able to explore mesh Reynolds numbers to about 43000. We find the power law for the advancing front decreases weakly with the mesh Reynolds number. Using a very long tank we find that the turbulent front stops completely at a certain depth and attempt a simple explanation for that behavior. We study the propagation of the turbulent front into tubes of different diameters inserted into the main tank. We show that these tubes exclude wavelengths much larger than the tube diameter. We explore the variation of the position of the steady-state boundary H on tube diameter D and find that H = cD with c ∼ 2. We suggest this may be explained by saturation of the energy-containing length scale ℓ(e). We also report on the effect of plugging up just one hole of the grid. Finally, we recall some earlier oscillating grid experiments in superfluid (4)He in the light of the present results.