Lagrangian evaluations of viscous models for velocity gradient dynamics in non-stationary turbulence - Parashar, Nishant; Sinha, Sawan S.; Srinivasan, Balaji (The International journal of heat and fluid flow, 2019)
•A novel methodology to evaluate existing models (the linear Lagrangian diffusion model (LLDM) and the recent fluid deformation closure model (RFDM)) of the viscous processes incumbent in the evolution equation of velocity gradients employed.•Unlike previous evaluations, these evaluations are performed following identified fluid particles (Lagrangian evaluations) from direct numerical simulations. Evaluations are performed for both compressible and nearly incompressible non-stationary decaying turbulent flow fields.•LLDM grossly overestimates the magnitude of the viscous process in both incompressible and compressible flows.•Performance of RFDM in nearly incompressible flows and compressible flows at low Mach numbers is found to be good. However, as Mach number increases, the model performance deteriorates.•A plausible alternative approach is suggested to address the shortcomings identified in the LLD and the RFD models for compressible flows. Simple autonomous dynamical models of velocity gradients are found to be useful in understanding the essential physics of non-linear turbulent processes. Such models can also be employed as closure models for the Lagrangian PDF methods of turbulence computations. The pressure Hessian and the viscous processes incumbent in the exact velocity gradient evolution equation are non-local in nature. Several models have been proposed for these processes. In this work, we focus specifically on two models meant for the incumbent viscous process: the linear Lagrangian diffusion model (LLDM) and the recent fluid deformation closure model (RFDM). Performance of both the models have indeed been examined earlier, but most evaluations have been restricted to statistical stationary flow fields. In this work, we subject these models to further scrutiny. Our evaluation procedure (i) uses direct numerical simulation data of decaying isotropic (non-stationary) turbulence, (ii) follows identified fluid particles (the so-called Lagrangian evolution), (iii) uses both compressible and nearly incompressible flow fields. In nearly incompressible regime, the RFD model is found to be satisfactory, while the LLDM model overestimates viscous effects at late times. In the compressible regime, both the models show inadequacies. For compressible flows, we propose an alternative modelling strategy which shows improvement over both LLD and RFD models.