Effect of rotation on turbulent mixing across a density interface

Abstract

The effect of rotation on mixing across a density interface is studied experimentally in a two-layer stratified fluid. Mixing is caused by turbulence produced in one of the layers by an oscillating grid. The flow depends on the Richardson number Ri=g′l/u2 and the Rossby number Ro=u/2Ωl, where u, l, g′=gΔp/p, and Ω are, respectively, the local rms, velocity and integral length scale of the turbulence, the reduced gravity, and the background rotation rate. The entrainment rate E of the interface is measured as a function of Ri and Ro in two different regions of the tank, namely, in the region closest to the grid, where turbulence is weakly affected by rotation, and far from the grid, where turbulence become quasi-2D under the effect of rotation. The most important result is the observed decrease of the entrainment rate E in the presence of rotation, when compared with nonrotating experiments. A general entrainment law in the form of E=0.5 Ro Ri is established in contrast with the measured entertainment law under nonrotating conditions E=1.6 Ri−3/2. The ranges of Ri and Ro covered are 7<Ri<50 and 0.1<Ro<1.0. At low values of Ri (Ri<10) and as a function of Ro, significant deviations from the law Ro Ri−1 are observed. At high values of Ri, the comparison between the results obtained under rotating and nonrotating conditions show that rotation has no effect on turbulent mixing when Ri>(3.2)2Ro−2. Interface displacement spectra provide additional information on the dynamics of the interface and the mixing process. These spectra were computed from the records of the interface position obtained using a new device based on the measurements of the traveling time of ultrasonic waves. This method gives information similar to the LIF technique used by Hannoun and List,1 except that the thickness of the interface is not determined. For nonrotating conditions, the spectra show maximum oscillations of the interface at the frequency (g′/l)1/2/2π of internal waves, in agreement with Hannoun and List.1 For higher frequencies, the spectrum decreases with increasing frequency like ω−n with 3<n< (11)/(3) . The results are discussed in relation to the model of Phillips2 (n=3) and the model recently proposed by Mory3 (n= (11)/(3) ). Under rotating conditions, the spectra are not modified for frequencies larger than the Coriolis frequency. Significant fluctuations are observed below the Coriolis frequency, which are related to the radiation of energy by inertial waves in the nonstirred layer.