Experiments on turbulence in a rotating fluid

Abstract

Experiments have been carried out to investigate the effect of rotation of the whole system on decaying turbulence, generally similar to grid turbulence, generated in air in an annular container on a rotating table. Measurements to determine the structure of the turbulence were made during its decay, mean quantities being determined by a mixture of time and ensemble averaging. Quantities measured (as functions of time after the turbulence generation) were turbulence intensities perpendicular to and parallel to the rotation axis, spectra of these two components with respect to a wavenumber perpendicular to the rotation axis, and some correlation coefficients, selected to detect differences in length scales perpendicular and parallel to the rotation axis. The intensity measurements were made for a wide range of rotation rates; the other measurements were made at a single rotation rate (selected to give a Rossby number varying during the decay from about 1 to small values) and, for comparison, at zero rotation. Subsidiary experiments were carried out to measure the spin-up time of the system, and to determine whether the turbulence produced any mean flow relative to the container.

A principal result is that increasing the rotation rate produces faster decay of the turbulence; the nature of the additional energy sink is an important part of the interpretation. Other features of the results are as follows: the measurements with-outrotation can be satisfactorily related to wind-tunnel measurements; even with rotation, the ratio of the intensities in the two directions remains substantially constant; the normalized spectra for the rotating and the non-rotating cases show surprising similarity but do contain slight systematic differences, consistent with the length scales indicated by the correlations; rotation produces a large increase in the length scale parallel to the rotation axis and a smaller increase in that perpendicular to it; the turbulence produces no measurable mean flow.

A model for the interpretation of the results is developed in terms of the action of inertial waves in carrying energy to the boundaries of the enclosure, where it is dissipated in viscous boundary layers. The model provides satisfactory explanations of the overall decay of the turbulence and of the decay of individual spectral components. Transfer of energy between wavenumbers plays a much less significant role in the dynamics of decay than in a non-rotating fluid. The relationship of the model to the interpretation of the length-scale difference in terms of the Taylor-Proudman theorem is discussed.

The model implies that the overall dimensions of the system enter in an important way into the dynamics. This imposes a serious limitation on the application of the results to the geophysical situations at which experiments of this type are aimed.

The paper includes some discussion of the possibility of energy transfer from the turbulence to a mean motion (the ‘vorticity expulsion’ hypothesis). It is possible, on the basis of the observations, to exclude this process as the additional turbulence energy sink. But this does not provide any evidence either for or against the hypothesis in the conditions for which it has been postulated.