Diapycnal mixing efficiency in lock-exchange gravity currents

In this report, results of irreversible mixing efficiency, ${\mathrm{Ri}}_f^{*}$, for a slumping gravity current is presented for a range of Reynolds numbers, $\mathrm{Re}=485$–12 270. Simultaneous velocity and density fields from particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) are used to measure the viscous dissipation ($\epsilon$) and scalar gradients ($\mathbf{\nabla }\rho$, $\mathbf{\nabla }{\rho }^{\prime }$) needed to calculate ${\mathrm{Ri}}_f^{*}$. It is observed that ${\mathrm{Ri}}_f^{*}$ plateaus to ${\mathrm{Ri}}_f^{*}\approx 0.12$, for the range of the buoyancy Reynolds number, ${\mathrm{Re}}_b$, and the gradient Richardson number, ${\mathrm{Ri}}_g$, used in our study. Owing to ambiguities in parametrizing ${\mathrm{Ri}}_f^{*}$ as a function of a single flow parameter, like ${\mathrm{Re}}_b$ or ${\mathrm{Ri}}_g$, a multiparameter space is considered using a turbulent Froude number, ${\mathrm{Fr}}_k$, and a turbulent Reynolds number, ${\mathrm{Re}}_L$. New insights are achieved, wherein it is observed that for a given ${\mathrm{Re}}_b$ or ${\mathrm{Ri}}_g$, ${\mathrm{Ri}}_f^{*}$ can assume different values owing to the turbulent regimes set up by ${\mathrm{Fr}}_k$ and ${\mathrm{Re}}_L$ and the effects of the molecular Prandtl number, Pr. It is also seen that the plateauing value of ${\mathrm{Ri}}_f^{*}$ can be greatly influenced by the flow parameters and fluid properties. We document that mixing efficiency can be increased in strongly stratified flow (${\mathrm{Fr}}_k<0.6$), provided ${\mathrm{Re}}_L$ is sufficiently high. Also, for the parameter range in our study, $3\le {\mathrm{Re}}_b\le 48$ and $0.26\le {\mathrm{Ri}}_g\le 0.9$, we did not notice a drop in the value of ${\mathrm{Ri}}_f^{*}$. This is attributed to the fact that our experiments are in the regime of strongly stratified turbulence with sufficiently high ${\mathrm{Re}}_L$ that could sustain turbulence and mixing. Our study suggests a need for a different parametrization of mixing efficiency in the diffusive ($1\le {\mathrm{Re}}_b\le 10$) and intermediate ($10\le {\mathrm{Re}}_b\le 100$) regimes for a gravity current.

Figure 1

The image illustrates a typical lock-exchange gravity current after it is released and is in its slumping phase.

Figure 2

Schematic of the lock-exchange facility.

Figure 3

Diapycnal mixing efficiency ${\mathrm{Ri}}_f^{*}$ as a function of the buoyancy Reynolds number ${\mathrm{Re}}_b$.

Figure 4

Diapycnal mixing efficiency ${\mathrm{Ri}}_f^{*}$ as a function of the gradient Richardson number ${\mathrm{Ri}}_g$.