# Vorticity dynamics after the shock–turbulence interaction

## Abstract

In this article, the interaction of a shock wave with quasi-vortical isotropic turbulence (IT) represents a basic problem for studying some of the phenomena associated with high speed flows, such as hypersonic flight, supersonic combustion and Inertial Confinement Fusion (ICF). In general, in practical applications, the shock width is much smaller than the turbulence scales and the upstream turbulent Mach number is modest. In this case, recent high resolution shock-resolved Direct Numerical Simulations (DNS) (Ryu and Livescu, J Fluid Mech 756, R1, 2014) show that the interaction can be described by the Linear Interaction Approximation (LIA). Using LIA to alleviate the need to resolve the shock, DNS post-shock data can be generated at much higher Reynolds numbers than previously possible. Here, such results with Taylor Reynolds number approximately 180 are used to investigate the changes in the vortical structure as a function of the shock Mach number, M _{s}, up to M _{s} = 10. It is shown that, as M _{s} increases, the shock interaction induces a tendency towards a local axisymmetric state perpendicular to the shock front, which has a profound influence on the vortex-stretching mechanism and divergence of the Lamb vector and, ultimately, on the flow evolutionmore »

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Univ. of California, Berkeley, CA (United States)

- Publication Date:

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

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1221371

- Report Number(s):
- LA-UR-15-20842

Journal ID: ISSN 0938-1287

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Shock Waves

- Additional Journal Information:
- Conference: 21. International symposium on shock interaction, Riga (Latvia), 3-8 Aug 2014; Journal ID: ISSN 0938-1287

- Publisher:
- Springer

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY

### Citation Formats

```
Livescu, Daniel, and Ryu, Jaiyoung. Vorticity dynamics after the shock–turbulence interaction. United States: N. p., 2015.
Web. doi:10.1007/s00193-015-0580-5.
```

```
Livescu, Daniel, & Ryu, Jaiyoung. Vorticity dynamics after the shock–turbulence interaction. United States. doi:10.1007/s00193-015-0580-5.
```

```
Livescu, Daniel, and Ryu, Jaiyoung. Thu .
"Vorticity dynamics after the shock–turbulence interaction". United States. doi:10.1007/s00193-015-0580-5. https://www.osti.gov/servlets/purl/1221371.
```

```
@article{osti_1221371,
```

title = {Vorticity dynamics after the shock–turbulence interaction},

author = {Livescu, Daniel and Ryu, Jaiyoung},

abstractNote = {In this article, the interaction of a shock wave with quasi-vortical isotropic turbulence (IT) represents a basic problem for studying some of the phenomena associated with high speed flows, such as hypersonic flight, supersonic combustion and Inertial Confinement Fusion (ICF). In general, in practical applications, the shock width is much smaller than the turbulence scales and the upstream turbulent Mach number is modest. In this case, recent high resolution shock-resolved Direct Numerical Simulations (DNS) (Ryu and Livescu, J Fluid Mech 756, R1, 2014) show that the interaction can be described by the Linear Interaction Approximation (LIA). Using LIA to alleviate the need to resolve the shock, DNS post-shock data can be generated at much higher Reynolds numbers than previously possible. Here, such results with Taylor Reynolds number approximately 180 are used to investigate the changes in the vortical structure as a function of the shock Mach number, Ms, up to Ms = 10. It is shown that, as Ms increases, the shock interaction induces a tendency towards a local axisymmetric state perpendicular to the shock front, which has a profound influence on the vortex-stretching mechanism and divergence of the Lamb vector and, ultimately, on the flow evolution away from the shock.},

doi = {10.1007/s00193-015-0580-5},

journal = {Shock Waves},

number = ,

volume = ,

place = {United States},

year = {2015},

month = {7}

}

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Works referenced in this record:

##
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

##
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

##
Experimental study of a normal shock/homogeneous turbulence interaction

journal, May 1996

- Barre, S.; Alem, D.; Bonnet, J. P.
- AIAA Journal, Vol. 34, Issue 5

##
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

##
Studies of interactions of a propagating shock wave with decaying grid turbulence: velocity and vorticity fields

journal, January 1999

- Agui, Juan H.; Briassulis, George; Andreopoulos, Yiannis
- Journal of Fluid Mechanics, Vol. 524

##
Direct numerical simulation of canonical shock/turbulence interaction

journal, December 2009

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

##
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

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

journal, September 2014

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

##
Forcing for statistically stationary compressible isotropic turbulence

journal, November 2010

- Petersen, Mark R.; Livescu, Daniel
- Physics of Fluids, Vol. 22, Issue 11

##
Turbulence in Supersonic Flow

journal, October 1953

- Kovasznay, Leslie S. G.
- Journal of the Aeronautical Sciences, Vol. 20, Issue 10

##
Compressibility effects on the growth and structure of homogeneous turbulent shear flow

journal, November 1993

- Blaisdell, G. A.; Mansour, N. N.; Reynolds, W. C.
- Journal of Fluid Mechanics, Vol. 256

##
The effects of heat release on the energy exchange in reacting turbulent shear flow

journal, January 2002

- Livescu, D.; Jaberi, F. A.; Madnia, C. K.
- Journal of Fluid Mechanics, Vol. 450

##
The mixing transition in turbulent flows

journal, April 2000

- Dimotakis, Paul E.
- Journal of Fluid Mechanics, Vol. 409

##
Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves

journal, February 2010

- Johnsen, Eric; Larsson, Johan; Bhagatwala, Ankit V.
- Journal of Computational Physics, Vol. 229, Issue 4

##
On the alignment of strain, vorticity and scalar gradient in turbulent, buoyant, nonpremixed flames

journal, September 1998

- Boratav, O. N.; Elghobashi, S. E.; Zhong, R.
- Physics of Fluids, Vol. 10, Issue 9

##
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

##
Alignment of vorticity and scalar gradient with strain rate in simulated Navier–Stokes turbulence

journal, January 1987

- Ashurst, Wm. T.; Kerstein, A. R.; Kerr, R. M.
- Physics of Fluids, Vol. 30, Issue 8

##
The structure and dynamics of vorticity and rate of strain in incompressible homogeneous turbulence

journal, December 1998

- Nomura, Keiko K.; Post, Gary K.
- Journal of Fluid Mechanics, Vol. 377

##
The structure of inhomogeneous turbulence in variable density nonpremixed flames

journal, November 1993

- Nomura, K. K.; Elghobashi, S. E.
- Theoretical and Computational Fluid Dynamics, Vol. 5-5, Issue 4-5

##
Evolution of enstrophy in shock/homogeneous turbulence interaction

journal, August 2012

- Sinha, Krishnendu
- Journal of Fluid Mechanics, Vol. 707

##
On the Lamb vector divergence in Navier–Stokes flows

journal, August 2008

- Hamman, Curtis W.; Klewicki, Joseph C.; Kirby, Robert M.
- Journal of Fluid Mechanics, Vol. 610

##
A dynamic counterpart of Lamb vector in viscous compressible aerodynamics

journal, October 2014

- Liu, L. Q.; Wu, J. Z.; Shi, Y. P.
- Fluid Dynamics Research, Vol. 46, Issue 6

Works referencing / citing this record:

##
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