Oscillating-grid turbulence including effects of rotation

Abstract

Experiments were performed to investigate some aspects of turbulence in rotating and non-rotating fluid systems where the turbulence was induced by a horizontal grid oscillating vertically. An earlier theory by the second author made use of a planar source of energy, which appeared to be similar to the energy source of the grid, in determining the characteristics of the turbulence at points some distance away. The simplicity of the theory was in the parameterization of the grid ‘action’ by a single quantity K, with dimensions and characteristics of eddy viscosity.The experimental results provide additional confirmation of the theory in the non-rotating case, and indicate the usefulness of the idealized energy source in the rotating case. In the latter, we measured the propagation of the front separating disturbed and undisturbed fluid, moving along the axis of rotation. The thickness d(t) of the disturbed region increases at first as (Kt)½, as in a non-rotating fluid, until the Rossby number K/Ωd2k becomes of order unity.Beyond this the disturbances are wavelike and rotationally dominated, and the thickness now increases linearly with time, yielding a speed of propagation for the front proportional to the wave speed (KΩ)½. Finally, the disturbances reach the bottom and the vessel is in statistical steady state. Then a region of thickness dk independent of time is found, and it contains motion that resembles ordinary, three-dimensional turbulence. dk ∼ (K/Ω)½ is analogous to the depth of the turbulent Ekman layer H ∼ (K/Ω)½, where K is taken as an eddy viscosity.McEwan constructed a similar rotating experiment, although with a different energy source, and observed vortices parallel to the axis of rotation, provided that the Rossby number was less than a critical value. Our observations and theory indicate that the disappearance of the vortices corresponds to h < dk, where h is the total depth of the fluid. At that point, the whole tank is filled with three-dimensional turbulence.