Effect of rotation on turbulent mixing driven by the Faraday instability

Abstract

The effect of the rotation on the turbulent mixing of two miscible fluids of small contrasting density, produced by Faraday instability, is investigated using direct numerical simulations (DNS). We demonstrate that at lower forcing amplitudes, the t.k.e. increases with an increase in f till (f/\omega\right)^2<0.25, where \omega is the forcing frequency, during the sub-harmonic instability phase. The increase in t.k.e. increases B_V, which increases the total potential energy (TPE). A portion of TPE is the APE. Some parts of APE can convert to $t.k.e.$ via B_V, whereas the rest converts to internal energy, increasing BPE through \phi_i. The remaining TPE also converts to BPE through the diapycnal flux \phi_d resulting in irreversible mixing. With the saturation of the instability, irreversible mixing ceases. When (f/\omega\right)^2 > 0.25, the Coriolis force significantly delays the onset of the sub-harmonic instabilities. During this period, the initial concentration profile diffuses to increase TPE, which eventually expends in BPE. The strong rotational effects suppress t.k.e.. Therefore, B_V and APE become small, and the bulk of the TPE expends to BPE. Since the instability never saturates for $\left(f/\omega\right)^2 > 0.25$, the $B_V$ remains non-zero, resulting in a continuous increase in TPE. Conversion of TPE to BPE via $\phi_d$ continues, and we find prolonged irreversible mixing. At higher forcing amplitudes, the stabilizing effect of rotation is negligible, and the turbulence is less intense and short-lived. Therefore, the irreversible mixing phenomenon also ends quickly for $\left(f/\omega\right)^2<0.25$. However, when $\left(f/\omega\right)^2>0.25$ a continuous mixing is observed. We find that the turbulent mixing is efficient at lower forcing amplitudes and rotation rates of (f/\omega)^2 > 0.25.