Self-similarity of scalar isosurface area density in a temporal mixing layer

Journal Article · Mon Nov 14 00:00:00 EST 2022 · Journal of Fluid Mechanics

DOI:https://doi.org/10.1017/jfm.2022.819· OSTI ID:1898162

Blakeley, Brandon C. ; Olson, Britton J. ; Riley, James J.

Understanding the behaviour of scalar isosurfaces in a turbulent flow is of particular interest for many problems in turbulent mixing that contain sharp interfaces between regions of the flow. Common examples include combustion, where the chemical reactions occur in thin regions within the flow, and the turbulent/non-turbulent interface in shear flows, where a thin region separates the rotational, turbulent motions from the irrotational, non-turbulent background. Recent advances in computing technology allow for in-depth analysis of these interface problems that are difficult to quantify in a laboratory setting. In this paper, the results of a direct numerical simulation of a passive scalar $$\varPhi$$ evolving on a turbulent, temporally developing mixing layer are described. A novel approach has been taken to calculate the surface area of individual scalar isosurfaces, $$A_{iso}$$ , throughout the simulation, as well as the mean isosurface area density, $$\varSigma$$ , as a function of the cross-stream direction and time. A notable finding is that the profiles of $$\varSigma$$ develop in a self-similar manner when scaled by the Taylor scale of the scalar field, $$\lambda _\phi$$ . Remarkably, the scaling appears to hold for a wide range of isovalues. A rough scaling argument based on the formal definition of $$\varSigma$$ and properties of a temporal mixing layer is presented which also exposes a dependence on $$\lambda _\phi$$ . Based on these results, a possible scaling for the isosurface area is presented as $$A_{iso}/A_0 \sim (Re \, Sc)^{1/2}$$ , where $Re$$ and $$Sc$ are local Reynolds and Schmidt numbers, respectively.

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA); US Department of the Navy, Office of Naval Research (ONR)
• Grant/Contract Number: High Energy Density Physics Fellowship; AC52-07NA27344; N00014-19-1-2154
• OSTI ID: 1898162
• Alternate ID(s): OSTI ID: 1959425
• Report Number(s): LLNL-JRNL-830180; A44; PII: S0022112022008199
• Journal Information: Journal of Fluid Mechanics, Journal Name: Journal of Fluid Mechanics Vol. 951; ISSN 0022-1120
• Publisher: Cambridge University Press (CUP)
• Country of Publication: United Kingdom
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
turbulent mixing
shear layer turbulence
turbulence simulation