Buoyancy--Shear--Drag--Scalar Turbulence Modeling for Rayleigh--Taylor Mixing

A buoyancy--shear--drag model [O. Schilling, \textit{Physica D} \textbf{402}, 132238 (2020)] is extended to include scalar variance to describe scalar (i.e., molecular) mixing in addition to mechanical mixing. The two coefficients in the scalar variance equation are calibrated to predict specific values of the scalar variance decay exponent and molecular mixing parameter for Rayleigh--Taylor mixing. An ordinary differential equation for the normalized scalar fluctuation $\Theta(t)=\phi^{\prime}/\overline{\phi}$ with terms representing production and destruction of scalar variance is coupled to the buoyancy--shear--drag equations. Analytic solutions of the resulting coupled equations for Rayleigh--Taylor mixing are obtained, which modify the classical expression $h(t)=\alpha\,At\,g\,t^2$ for the mixing layer width. Applications of the buoyancy--shear--drag--scalar model to Rayleigh--Taylor turbulent mixing are briefly described.