Session G43: Turbulence: Buoyancy-Driven and Stratified I

Entrainment at multi-scales: the case of Rayleigh-Taylor turbulence

A partially turbulent flow continuously incorporates irrotational fluid into the turbulent region, a phenomenon known as entrainment. Although locally acting at viscous scales, turbulent entrainment is independent of viscosity from a global point of view: these two apparently contraddictory phenomena are reconciled by taking into account the fractal nature of the turbulent/non-turbulent interface (TNTI), the thin interface separating the turbulent from the irrotational region. In this contribution, we present a new equation for computing the entrainment velocity at multi-scales. This is done by defining the local entrainment velocity as the propagation speed of an iso-surface of filtered enstrophy relative to the coarse-grained velocity field, and using the filtered enstrophy budget to split the total velocity into its individual components, i.e. viscous, inviscid, baroclinic and sub-filter. We test our equation on a dataset of Rayleigh-Taylor turbulence, a temporal mixing layer substained by an unstable buoyancy gradient.   

A Reynolds-averaged Navier–Stokes closure model for natural convection based on Rayleigh–Prandtl scaling theory

A new turbulence model has been developed for Reynolds-averaged Navier-Stokes (RANS) simulations of buoyancy-driven flows to overcome the incapability of existing models for accurately predicting Rayleigh-Bénard convection (RBC). In this study, the behavior of the commonly employed k-ε model for RBC is investigated at very high Rayleigh number (Ra) conditions. The present analysis reveals that the conventional k-ε model incorrectly predicts the turbulent heat flux as an exponentially growing solution, instead of converging to a correct finite value. To deal with this issue, a new model is proposed, aiming to accurately predict a steady-state heat transfer solution for RBC by applying the Grossmann and Lohse theory, which considers the Nusselt and Reynolds dependence on the Ra and Prandtl (Pr) numbers. The new model algebraically modifies the term in the ε equation that is related to buoyancy-induced turbulent kinetic energy production, allowing the new model to be used in conjunction with the k-ε model. The proposed modeling methodology for natural convection based on Ra-Pr scaling and dynamical systems theory, is expected to be applicable to other RANS models that include the buoyancy effect on turbulent kinetic energy.   

Super-ultimate transient of turbulent thermal convection between horizontal porous walls

Turbulent thermal convection between horizontal porous walls heated from below and cooled from above has been investigated numerically and experimentally. It has been found that at low Rayleigh number Ra, the Nusselt number Nu in the bulk region scales with Ra^{1/3} as in the classical state, whereas at high Ra, Nu scales with Ra^{1/2}, implying the ultimate state in which the vertical heat flux is independent of thermal conductivity, i.e., the so-called conduction anomaly. At low Ra, vertical (wall-normal) fluid motion is not excited in the near-wall region despite wall permeability, so that the classical state can be observed. At high Ra, large-scale thermal plumes appear even near the walls from convective instabilities of near-wall thermal conduction layers to significantly intensify the wall heat flux, leading to the ultimate state. In between these two distinct scaling ranges of Ra, we have found super-ultimate transient in which Nu ~ Ra. This super-ultimate scaling is considered to be a consequence of full excitation of large-scale thermal plumes comparable with those in the ultimate state at high Ra and of less energy dissipation in the flow through porous media than in the ultimate state at high Ra.   

Effect of initial conditions on transition in Rayleigh-Taylor and Richtmyer-Meshkov instabilities

Rayleigh-Taylor (RT) instability is a type of flow consisting of a layer of heavy fluid over light fluid. Small perturbations along the interface separating the two layers cause the unstable system to begin mixing and eventually break down into turbulence. Richtmyer-Meshkov (RM) instability, while otherwise similar to RT, has the additional complexity of a shockwave disrupting the interface. These two variable-density flow instabilities are relevant to a variety of applications such as climate and combustion. Existing research suggests that the transition process in both RT and RM is strongly influenced by initial conditions. We explore this dependence using direct numerical simulation and implicit large eddy simulation in a variety of natural transition scenarios initialized with different combinations of perturbation modes and amplitudes. For analysis, we consider various quantities of interest including mixing layer height, mixture fraction, vorticity, turbulent length scale, and turbulent kinetic energy of the flow. Specifically, we use these metrics to track the amount of time required for transition to occur and to describe the state of the resulting turbulence. Lastly, we discuss the results of this sensitivity analysis on initial conditions and its importance for understanding variability in instability-driven turbulence.