Large-scale refractive turbulent interfaces and aero-optical interactions in high Reynolds number compressible separated shear layers

Numerical simulations of the large amplitude stage of the Kelvin-Helmholtz instability of a relatively thin vorticity layer are discussed. At high Reynolds number, the effect of viscosity is commonly neglected and the thin layer is modeled as a vortex sheet separating one potential flow region from another. Since such vortex sheets are susceptible to a short wavelength instability, as well as singularity formation, it is necessary to provide an artificial “regularization” for long time calculations. We examine the effect of this regularization by comparing vortex sheet calculations with fully viscous finite difference calculations of the Navier-Stokes equations. In particular, we compare the limiting behavior of the viscous simulations for high Reynolds numbers and small initial layer thickness with the limiting solution for the roll-up of an inviscid vortex sheet. Results show that the inviscid regularization effectively reproduces many of the features associated with the thickness of viscous vorticity layers with increasing Reynolds number, though the simplified dynamics of the inviscid model allows it to accurately simulate only the large scale features of the vorticity field. Our results also show that the limiting solution of zero regularization for the inviscid model and high Reynolds number and zero initial thickness for the viscous simulations appear to be the same.

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Thin Shear Layers in High Reynolds Number Turbulence—DNS Results

Flow Turbulence and Combustion ◽

10.1007/s10494-013-9499-z ◽

2013 ◽

Vol 91 (4) ◽

pp. 895-929 ◽

Cited By ~ 43

Author(s):

Takashi Ishihara ◽

Yukio Kaneda ◽

Julian C. R. Hunt

Keyword(s):

Reynolds Number ◽

High Reynolds Number ◽

Shear Layers ◽

High Reynolds

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Reynolds number trend of hierarchies and scale interactions in turbulent boundary layers

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2016.0077 ◽

2017 ◽

Vol 375 (2089) ◽

pp. 20160077 ◽

Cited By ~ 20

Author(s):

W. J. Baars ◽

N. Hutchins ◽

I. Marusic

Keyword(s):

Reynolds Number ◽

Large Scale ◽

Reynolds Numbers ◽

Shear Layers ◽

Wall Turbulence ◽

Small Scale ◽

Velocity Fluctuations ◽

Scale Interaction ◽

High Reynolds ◽

Near Wall

Small-scale velocity fluctuations in turbulent boundary layers are often coupled with the larger-scale motions. Studying the nature and extent of this scale interaction allows for a statistically representative description of the small scales over a time scale of the larger, coherent scales. In this study, we consider temporal data from hot-wire anemometry at Reynolds numbers ranging from Re τ ≈2800 to 22 800, in order to reveal how the scale interaction varies with Reynolds number. Large-scale conditional views of the representative amplitude and frequency of the small-scale turbulence, relative to the large-scale features, complement the existing consensus on large-scale modulation of the small-scale dynamics in the near-wall region. Modulation is a type of scale interaction, where the amplitude of the small-scale fluctuations is continuously proportional to the near-wall footprint of the large-scale velocity fluctuations. Aside from this amplitude modulation phenomenon, we reveal the influence of the large-scale motions on the characteristic frequency of the small scales, known as frequency modulation. From the wall-normal trends in the conditional averages of the small-scale properties, it is revealed how the near-wall modulation transitions to an intermittent-type scale arrangement in the log-region. On average, the amplitude of the small-scale velocity fluctuations only deviates from its mean value in a confined temporal domain, the duration of which is fixed in terms of the local Taylor time scale. These concentrated temporal regions are centred on the internal shear layers of the large-scale uniform momentum zones, which exhibit regions of positive and negative streamwise velocity fluctuations. With an increasing scale separation at high Reynolds numbers, this interaction pattern encompasses the features found in studies on internal shear layers and concentrated vorticity fluctuations in high-Reynolds-number wall turbulence. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

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