Interfacial dynamics and energy cascade in immiscible Rayleigh–Taylor turbulence

We investigate interfacial dynamics and multiscale energy transfer in immiscible Rayleigh–Taylor turbulence using numerical simulations with varying surface-tension coefficients

. Capillarity is shown to control characteristic length scales, interfacial area, and global energy and enstrophy budgets. The flow exhibits self-similar evolution with respect to surface tension, with the maximum kinetic energy scaling as

sigma Superscript 1 divided by 2 σ 1 / 2 $\sigma ^{1/2}$

and the flow duration as

sigma Superscript negative 1 divided by 4 σ − 1 / 4 $\sigma ^{-1/4}$

. A scale-by-scale budget shows that surface tension removes kinetic energy at large scales while injecting it at small scales, with the crossover occurring near the Hinze scale. We further recast and verify a local kinematic relationship between surface-tension power and interface stretching, up to conservative transport,

bold italic f Superscript sigma Baseline bold dot bold italic u equals minus sigma script upper S StartAbsoluteValue bold nabla c EndAbsoluteValue plus normal t normal r normal a normal n normal s normal p normal o normal r normal t f σ ⋅ u = − σ S | ∇ c | + t r a n s p o r t $ \boldsymbol{f}^\sigma \boldsymbol{\cdot }\boldsymbol{u} = - \sigma \mathcal{S}\,|\boldsymbol{\nabla }c| + \mathrm{transport}$

, where

bold italic f Superscript sigma f σ $\boldsymbol{f}^{\sigma }$

is the surface-tension force,

bold italic u u $\boldsymbol{u}$

is the velocity,

c c $c$

is the heavy-fluid volume fraction, and

script upper S S $\mathcal{S}$

is the interface stretch rate. This relation links kinetic energy transfer to the scalar-variance cascade, and shows that energy transfer to the interface is governed by local strain. Statistics of individual bubbles and droplets reveal vertically elongated filaments with diameters of approximately three capillary scales, yielding a linear volume–area relation. Their vertical velocities scale with the square root of equivalent diameter, consistent with drag–buoyancy balance. These findings, particularly the direct link between surface-tension power and resolved interface stretching, provide a rigorous physical framework for developing subgrid-scale closures for large-eddy simulations of immiscible turbulent flows.