Pressure–Strain Correlation Modeling: Towards Achieving Consistency with Rapid Distortion Theory

Abstract

In turbulence closure modeling, it is widely accepted that the rapid pressure-strain correlation (RPSC) model be consistent with the rapid distortion theory (RDT). It is desirable to achieve this consistency with a closure model that is computationally tractable and satisfies the requisite mathematical constraints of realizability and linearity in the appropriate variables. In this investigation, starting from a detailed modal analysis of two-dimensional mean flows, we identify important flow features to be incorporated into the model. However, the dynamical system analysis shows that the suggested physics cannot be embodied in a model with all desired computational and mathematical attributes. To resolve this conflict, we propose a slight compromise in the physical requirement and ease one of the linearity constraints leading to a "best possible" tractable model. Overall, the present work provides important insight into RPSC closure modeling challenges-arising from the interplay among physical fidelity, computational viability and mathematical constraints-and proposes avenues for future improvement.

Intercomponent energy transfer in incompressible homogeneous turbulence: multi-point physics and amenability to one-point closures

“…With respect to the evolution of the Reynolds stress anisotropies and the turbulent kinetic energy in elliptic flows, the amplitudes of these oscillations are typically small when compared to the overall trend of their evolution. This has been exhibited in RDT-based simulations (Mishra & Girimaji 2010) and DNS . In this light, it may be expedient to focus on capturing the mean of these oscillations.…”

“…In Godeferd, Cambon & Scott (2001), strategies for such an approach were outlined and discussed. Further, newer models seek to conform with the predictions of the RDT, where applicable, as shown in the works of Johansson & Hallback (1994) and Mishra & Girimaji (2010). A notable example in this context is the work of Cambon, Jacquin & Lubrano (1992), who tried to use the information from spectral investigations to develop better closures in physical space, for rotating flows.…”

On the realizability of pressure–strain closures

“…We propose a simple recourse to making the coefficients of the closure expression functions of the mean flow invariants. Lee (1990), Girimaji (2000), Sjogren & Johansson (2000) and Mishra & Girimaji (2010) represent the few investigations that have considered such an approach. This procedure of using the mean gradient tensor in lieu of the wavevector space information is advantageous, not only for predictive fidelity but also for realizability.…”

Toward second-moment closure modelling of compressible shear flows

“…Preliminary steps towards such a calibration applied to two-dimensional incompressible turbulence is outlined in Mishra & Girimaji (2010). Accordingly, the coefficients would also be functions of mean-flow-gradient invariants.…”