Velocity gradient dynamics in compressible turbulence: Characterization of pressure-Hessian tensor

2013 ◽  
Vol 25 (12) ◽  
pp. 125103 ◽  
Author(s):  
Sawan Suman ◽  
Sharath S. Girimaji
Keyword(s):  
Velocity Gradient ◽  
Compressible Turbulence ◽  
Gradient Dynamics

On velocity gradient dynamics and turbulent structure

2015 ◽  
Vol 780 ◽  
pp. 60-98 ◽  
Author(s):  
J. M. Lawson ◽  
J. R. Dawson
Keyword(s):  
Velocity Gradient ◽  
Local Strain ◽  
Turbulent Structure ◽  
Stochastic Estimation ◽  
Spatially Resolved ◽  
Gradient Dynamics ◽  
Layer Structures ◽  
Non Local ◽  
Conditional Averaging

The statistics of the velocity gradient tensor $\unicode[STIX]{x1D63C}=\boldsymbol{{\rm\nabla}}\boldsymbol{u}$, which embody the fine scales of turbulence, are influenced by turbulent ‘structure’. Whilst velocity gradient statistics and dynamics have been well characterised, the connection between structure and dynamics has largely focused on rotation-dominated flow and relied upon data from numerical simulation alone. Using numerical and spatially resolved experimental datasets of homogeneous turbulence, the role of structure is examined for all local (incompressible) flow topologies characterisable by $\unicode[STIX]{x1D63C}$. Structures are studied through the footprints they leave in conditional averages of the $Q=-\text{Tr}(\unicode[STIX]{x1D63C}^{2})/2$ field, pertinent to non-local strain production, obtained using two complementary conditional averaging techniques. The first, stochastic estimation, approximates the $Q$ field conditioned upon $\unicode[STIX]{x1D63C}$ and educes quantitatively similar structure in both datasets, dissimilar to that of random Gaussian velocity fields. Moreover, it strongly resembles a promising model for velocity gradient dynamics recently proposed by Wilczek & Meneveau (J. Fluid Mech., vol. 756, 2014, pp. 191–225), but is derived under a less restrictive premise, with explicitly determined closure coefficients. The second technique examines true conditional averages of the $Q$ field, which is used to validate the stochastic estimation and provide insights towards the model’s refinement. Jointly, these approaches confirm that vortex tubes are the predominant feature of rotation-dominated regions and additionally show that shear layer structures are active in strain-dominated regions. In both cases, kinematic features of these structures explain alignment statistics of the pressure Hessian eigenvectors and why local and non-local strain production act in opposition to each other.

Lagrangian investigations of velocity gradients in compressible turbulence: lifetime of flow-field topologies

2019 ◽  
Vol 872 ◽  
pp. 492-514 ◽  
Author(s):  
Nishant Parashar ◽  
Sawan Suman Sinha ◽  
Balaji Srinivasan
Keyword(s):  
Mach Number ◽  
Velocity Gradient ◽  
Direct Numerical Simulations ◽  
Compressible Turbulence ◽  
Lagrangian Particle ◽  
Gradient Tensor ◽  
Velocity Gradient Tensor ◽  
Conditional Mean ◽  
Velocity Gradients ◽  
Decaying Turbulence

We perform Lagrangian investigations of the dynamics of velocity gradients in compressible decaying turbulence. Specifically, we examine the evolution of the invariants of the velocity-gradient tensor. We employ well-resolved direct numerical simulations over a range of Mach number along with a Lagrangian particle tracker to examine trajectories of fluid particles in the space of the invariants of the velocity gradient tensor. This allows us to accurately measure the lifetimes of major topologies of compressible turbulence and provide an explanation of why some selective topologies tend to exist longer than the others. Further, the influence of dilatation on the lifetime of various topologies is examined. Finally, we explain why the so-called conditional mean trajectories (CMT) used previously by several researchers fail to predict the lifetime of topologies accurately.

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