# Density effects on post-shock turbulence structure and dynamics

## Abstract

Turbulence structure resulting from multi-fluid or multi-species, variable-density isotropic turbulence interaction with a Mach 2 shock is studied using turbulence-resolving shock-capturing simulations and Eulerian (grid) and Lagrangian (particle) methods. The complex roles that density plays in the modification of turbulence by the shock wave are identified. Statistical analyses of the velocity gradient tensor (VGT) show that density variations significantly change the turbulence structure and flow topology. Specifically, a stronger symmetrization of the joint probability density function (PDF) of second and third invariants of the anisotropic VGT, PDF$$(Q^{\ast },R^{\ast })$$, as well as the PDF of the vortex stretching contribution to the enstrophy equation, are observed in the multi-species case. Furthermore, subsequent to the interaction with the shock, turbulent statistics also acquire a differential distribution in regions having different densities. This results in a nearly symmetric PDF$$(Q^{\ast },R^{\ast })$$ in heavy-fluid regions, while the light-fluid regions retain the characteristic tear-drop shape. To understand this behaviour and the return to ‘standard’ turbulence structure as the flow evolves away from the shock, Lagrangian dynamics of the VGT and its invariants is studied by considering particle residence times and conditional particle variables in different flow regions. The pressure Hessian contributions to the VGT invariants transport equations are shown to be not only affected by the shock wave, but also by the density in the multi-fluid case, making them critically important to the flow dynamics and turbulence structure.

- Authors:

- Michigan State Univ., East Lansing, MI (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1573337

- Report Number(s):
- LA-UR-18-31241

Journal ID: ISSN 0022-1120

- Grant/Contract Number:
- 89233218CNA000001

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Fluid Mechanics

- Additional Journal Information:
- Journal Volume: 880; Journal ID: ISSN 0022-1120

- Publisher:
- Cambridge University Press

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; compressible turbulence; shock waves; turbulence simulation

### Citation Formats

```
Tian, Yifeng, Jaberi, Farhad A., and Livescu, Daniel. Density effects on post-shock turbulence structure and dynamics. United States: N. p., 2019.
Web. doi:10.1017/jfm.2019.707.
```

```
Tian, Yifeng, Jaberi, Farhad A., & Livescu, Daniel. Density effects on post-shock turbulence structure and dynamics. United States. doi:10.1017/jfm.2019.707.
```

```
Tian, Yifeng, Jaberi, Farhad A., and Livescu, Daniel. Fri .
"Density effects on post-shock turbulence structure and dynamics". United States. doi:10.1017/jfm.2019.707. https://www.osti.gov/servlets/purl/1573337.
```

```
@article{osti_1573337,
```

title = {Density effects on post-shock turbulence structure and dynamics},

author = {Tian, Yifeng and Jaberi, Farhad A. and Livescu, Daniel},

abstractNote = {Turbulence structure resulting from multi-fluid or multi-species, variable-density isotropic turbulence interaction with a Mach 2 shock is studied using turbulence-resolving shock-capturing simulations and Eulerian (grid) and Lagrangian (particle) methods. The complex roles that density plays in the modification of turbulence by the shock wave are identified. Statistical analyses of the velocity gradient tensor (VGT) show that density variations significantly change the turbulence structure and flow topology. Specifically, a stronger symmetrization of the joint probability density function (PDF) of second and third invariants of the anisotropic VGT, PDF$(Q^{\ast },R^{\ast })$, as well as the PDF of the vortex stretching contribution to the enstrophy equation, are observed in the multi-species case. Furthermore, subsequent to the interaction with the shock, turbulent statistics also acquire a differential distribution in regions having different densities. This results in a nearly symmetric PDF$(Q^{\ast },R^{\ast })$ in heavy-fluid regions, while the light-fluid regions retain the characteristic tear-drop shape. To understand this behaviour and the return to ‘standard’ turbulence structure as the flow evolves away from the shock, Lagrangian dynamics of the VGT and its invariants is studied by considering particle residence times and conditional particle variables in different flow regions. The pressure Hessian contributions to the VGT invariants transport equations are shown to be not only affected by the shock wave, but also by the density in the multi-fluid case, making them critically important to the flow dynamics and turbulence structure.},

doi = {10.1017/jfm.2019.707},

journal = {Journal of Fluid Mechanics},

number = ,

volume = 880,

place = {United States},

year = {2019},

month = {10}

}

Works referenced in this record:

##
Simulations of Cellular Detonation Interaction with Turbulent Flows

journal, February 2016

- Jin, Tai; Luo, Kun; Dai, Qi
- AIAA Journal, Vol. 54, Issue 2

##
Turbulence structures of wall-bounded shear flows found using DNS data

journal, February 1998

- Chong, M. S.; Soria, J.; Perry, A. E.
- Journal of Fluid Mechanics, Vol. 357

##
Flow topology in compressible turbulent boundary layer

journal, June 2012

- Wang, Li; Lu, Xi-Yun
- Journal of Fluid Mechanics, Vol. 703

##
The influence of entropy fluctuations on the interaction of turbulence with a shock wave

journal, March 1997

- Mahesh, Krishnan; Lele, Sanjiva K.; Moin, Parviz
- Journal of Fluid Mechanics, Vol. 334

##
Compact finite difference schemes with spectral-like resolution

journal, November 1992

- Lele, Sanjiva K.
- Journal of Computational Physics, Vol. 103, Issue 1

##
Direct numerical simulations of isotropic compressible turbulence: Influence of compressibility on dynamics and structures

journal, December 2004

- Pirozzoli, S.; Grasso, F.
- Physics of Fluids, Vol. 16, Issue 12

##
Thermodynamic fluctuations in canonical shock–turbulence interaction: effect of shock strength

journal, June 2018

- Sethuraman, Yogesh Prasaad M.; Sinha, Krishnendu; Larsson, Johan
- Theoretical and Computational Fluid Dynamics, Vol. 32, Issue 5

##
Effect of compressibility on the small-scale structures in isotropic turbulence

journal, October 2012

- Wang, Jianchun; Shi, Yipeng; Wang, Lian-Ping
- Journal of Fluid Mechanics, Vol. 713

##
Reynolds- and Mach-number effects in canonical shock–turbulence interaction

journal, February 2013

- Larsson, Johan; Bermejo-Moreno, Ivan; Lele, Sanjiva K.
- Journal of Fluid Mechanics, Vol. 717

##
A general classification of three‐dimensional flow fields

journal, May 1990

- Chong, M. S.; Perry, A. E.; Cantwell, B. J.
- Physics of Fluids A: Fluid Dynamics, Vol. 2, Issue 5

##
Topological evolution in compressible turbulent boundary layers

journal, September 2013

- Chu, You-Biao; Lu, Xi-Yun
- Journal of Fluid Mechanics, Vol. 733

##
Direct numerical simulation of isotropic turbulence interacting with a weak shock wave

journal, June 1993

- Lee, Sangsan; Lele, Sanjiva K.; Moin, Parviz
- Journal of Fluid Mechanics, Vol. 251

##
Interaction of isotropic turbulence with shock waves: effect of shock strength

journal, June 1997

- Lee, Sangsan; Lele, Sanjiva K.; Moin, Parviz
- Journal of Fluid Mechanics, Vol. 340

##
Analysis of small-scale scalar mixing processes in highly under-expanded jets

journal, September 2015

- Buttay, R.; Lehnasch, G.; Mura, A.
- Shock Waves, Vol. 26, Issue 2

##
Simulation of spatially evolving turbulence and the applicability of Taylor’s hypothesis in compressible flow

journal, July 1992

- Lee, Sangsan; Lele, Sanjiva K.; Moin, Parviz
- Physics of Fluids A: Fluid Dynamics, Vol. 4, Issue 7

##
Turbulent energy flux generated by shock/homogeneous-turbulence interaction

journal, April 2016

- Quadros, Russell; Sinha, Krishnendu; Larsson, Johan
- Journal of Fluid Mechanics, Vol. 796

##
A Description of Eddying Motions and Flow Patterns Using Critical-Point Concepts

journal, January 1987

- Perry, A. E.; Chong, M. S.
- Annual Review of Fluid Mechanics, Vol. 19, Issue 1

##
The interaction of an isotropic field of acoustic waves with a shock wave

journal, October 1995

- Mahesh, Krishnan; Lee, Sangsan; Lele, Sanjiva K.
- Journal of Fluid Mechanics, Vol. 300

##
Evolution of the velocity gradient tensor invariant dynamics in a turbulent boundary layer

journal, February 2017

- Bechlars, P.; Sandberg, R. D.
- Journal of Fluid Mechanics, Vol. 815

##
Direct numerical simulation of canonical shock/turbulence interaction

journal, December 2009

- Larsson, Johan; Lele, Sanjiva K.
- Physics of Fluids, Vol. 21, Issue 12

##
A study of the evolution and characteristics of the invariants of the velocity-gradient tensor in isotropic turbulence

journal, February 1999

- Ooi, Andrew; Martin, Jesus; Soria, Julio
- Journal of Fluid Mechanics, Vol. 381

##
Numerical study of variable density turbulence interaction with a normal shock wave

journal, September 2017

- Tian, Yifeng; Jaberi, Farhad A.; Li, Zhaorui
- Journal of Fluid Mechanics, Vol. 829

##
An algorithm for tracking fluid particles in numerical simulations of homogeneous turbulence

journal, December 1988

- Yeung, P. K.; Pope, S. B.
- Journal of Computational Physics, Vol. 79, Issue 2

##
Local flow topology and velocity gradient invariants in compressible turbulent mixing layer

journal, June 2015

- Vaghefi, Navid S.; Madnia, Cyrus K.
- Journal of Fluid Mechanics, Vol. 774

##
L AGRANGIAN I NVESTIGATIONS OF T URBULENCE

journal, January 2002

- Yeung, P. K.
- Annual Review of Fluid Mechanics, Vol. 34, Issue 1

##
Evolution of scalar and velocity dynamics in planar shock-turbulence interaction

journal, January 2018

- Boukharfane, R.; Bouali, Z.; Mura, A.
- Shock Waves, Vol. 28, Issue 6

##
Characteristics of chemically reacting compressible homogeneous turbulence

journal, May 2000

- Jaberi, F. A.; Livescu, D.; Madnia, C. K.
- Physics of Fluids, Vol. 12, Issue 5

##
Lagrangian Dynamics and Models of the Velocity Gradient Tensor in Turbulent Flows

journal, January 2011

- Meneveau, Charles
- Annual Review of Fluid Mechanics, Vol. 43, Issue 1

##
A high-order finite difference method for numerical simulations of supersonic turbulent flows

journal, January 2011

- Li, Zhaorui; Jaberi, Farhad A.
- International Journal for Numerical Methods in Fluids, Vol. 68, Issue 6

##
Turbulence structure behind the shock in canonical shock–vortical turbulence interaction

journal, September 2014

- Ryu, Jaiyoung; Livescu, Daniel
- Journal of Fluid Mechanics, Vol. 756

##
Vorticity dynamics after the shock–turbulence interaction

journal, July 2015

- Livescu, D.; Ryu, J.
- Shock Waves, Vol. 26, Issue 3

##
Velocity gradient invariants and local flow-field topology in compressible turbulence

journal, January 2010

- Suman, Sawan; Girimaji, Sharath S.
- Journal of Turbulence, Vol. 11

##
Direct Numerical Simulation of a Mach 2 shock interacting with isotropic turbulence

journal, April 1995

- Hannappel, R.; Friedrich, R.
- Applied Scientific Research, Vol. 54, Issue 3