Spectral analysis of the turbulent mixing of two fluids

Steinkamp, Michael

doi:10.2172/212563

Cited by 4 publications

(5 citation statements)

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“…b(y = 0, τ ) attains the configurational or "no-mix" value at α 1 = α 2 = 0.5 (the configurational b = 0.067 for ρ 1 = 1.0 and ρ 2 = 1.667 as in our case) during late times. Similar spectral turbulence models [15,57] have also observed this same tendency to relax toward the configurational value of b(y = 0, τ ). The MOBILE simulation results are not purely immiscible.…”

Section: Growth and Saturation Of B In The Lwn Modelsupporting

confidence: 61%

“…The current version of the source term is a simple extrapolation from the single-point form which integrates to the latter for consistency. The source term could in principle be made more sophisticated with better spectral characteristics [57,73]. However, this involves a convolution which is not straightforward to compute or implement in a practical model so we leave this for future research.…”

Section: Discussionmentioning

confidence: 99%

“…This particular functional form of b(y = 0, k) was used previously in Ref. [57], so that when k is small, b(y = 0, k) ∼ k m , and when k is large, b(y = 0, k) ∼ k − 5 3 , following the anticipated power-law scaling of the turbulent kinetic energy spectrum within the inertial range. In Figs.…”

Section: A Test Casementioning

confidence: 99%

“…When the spatial diffusion coefficient C d is small, there is a tendency of b(y = 0, τ ) to relax to the "configurational" or the no-mix value of b. The configurational or "no-mix" value of b(y = 0, τ ) is defined as [15,57] FIG. 12.…”

Section: Growth and Saturation Of B In The Lwn Modelmentioning

confidence: 99%

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Local wave-number model for inhomogeneous two-fluid mixing

et al. 2021

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We analyze the local wave-number (LWN) model, a two-point spectral closure model for turbulence, as applied to the Rayleigh-Taylor (RT) instability, the flow induced by the relaxation of a statically-unstable density stratification. Model outcomes are validated against data from 3D simulations of the RT instability. In the first part of the study we consider the minimal model terms required to capture inhomogeneous mixing and show that this version, with suitable model coefficients, is sufficient to capture the evolution of important mean global quantities including mix-width, turbulent mass flux velocity, and Reynolds stress, if the start time is chosen such that the earliest transitions are avoided. However, this simple model does not permit the expected finite asymptote of the density-specific-volume covariance b. In the second part of the study, we investigate two forms for a source term for the evolution of the spectrum of density-specific-volume covariance for the LWN model. The first includes an empirically motivated calibration of the source to achieve the final asymptotic state of constant b. The second form does not require calibration but, in conjunction with enhanced diffusion and drag captures the full evolution of all the dynamical quantities, namely, the mix-layer growth, turbulent mass-flux velocity, Reynolds stress, as well as the desired behavior of b.

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Section: Growth and Saturation Of B In The Lwn Modelsupporting

confidence: 61%

Section: Discussionmentioning

confidence: 99%

Section: A Test Casementioning

confidence: 99%

Section: Growth and Saturation Of B In The Lwn Modelmentioning

confidence: 99%

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Local wave-number model for inhomogeneous two-fluid mixing

et al. 2021

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“…Similar balances for variable-density turbulence lead to analogous approximations, Steinkamp (1996) and Steinkamp, Clark, and Harlow (1995).…”

Section: G the Boussinesq Approximationmentioning

confidence: 86%

Turbulence transport with nonlocal interactions

Linn¹,

Clark²,

Harlow³

et al. 1998

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This preliminary report describes a variety of issues in turbulence transport analysis with particular emphasis on closure procedures that are nonlocal in wave-number and/or physical space. Anomalous behavior of the transport equations for large-scale parts of the turbulence spectrum are resolved by including the physical-space nonlocal interactions. Direct and reverse cascade processes in wavenumber space are given a much richer potential for realistic description by the nonlocal formulations. The discussion also describes issues, many still not resolved, regarding new classes of self-similar form functions.

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