Quantifying the turbulent mixing driven by the Faraday instability in rotating miscible fluids

Abstract

The effect of the rotation on the turbulent mixing of two miscible fluids of small contrasting density, induced by Faraday instability, is investigated using direct numerical simulations. We quantify the irreversible mixing, which depicts the conversion of the available potential energy (APE) to the background potential energy (BPE) through the irreversible mixing rate M. We demonstrate that at lower forcing amplitudes, the turbulent kinetic energy (t.k.e.) increases with an increase in the Coriolis frequency f till (f/ω)2<0.25, where ω is the forcing frequency, during the sub-harmonic instability phase. This enhancement of t.k.e. is attributed to the excitement of more unstable modes. The irreversible mixing sustains for an extended period with increasing (f/ω)2 till 0.25 owing to the prolonged sub-harmonic instability phase and eventually ceases with instability saturation. When (f/ω)2>0.25, the Coriolis force significantly delays the onset of the sub-harmonic instabilities. The strong rotational effects result in lower turbulence because the bulk of the APE expends to BPE, decreasing APE that converts back to t.k.e. reservoir for (f/ω)2>0.25. Therefore, in the subsequent oscillation, the t.k.e. available to contribute to the external energy input from periodic forcing is small. Since the instability never saturates for (f/ω)2>0.25, the conversion of APE to BPE via M continues, and we find prolonged irreversible mixing. At higher forcing amplitudes, the instability delaying effect of rotation is negligible, and the turbulence is less intense and short-lived. Therefore, the irreversible mixing phenomenon also ends quickly for (f/ω)2<0.25. However, when (f/ω)2>0.25, a continuous irreversible mixing is observed. We also examine the mixing efficiency in terms of M and find that the mixing is efficient at lower forcing amplitudes and rotation rates of (f/ω)2>0.25 because the major portion of APE expends to BPE.