Statistics of a passive scalar in homogeneous turbulence

The buoyancy subrange of stably stratified turbulence is defined as an intermediate range of scales larger than those in the inertial subrange. This subrange encompasses the crossover from internal gravity waves (IGWs) to small-scale turbulence. The energy exchange between the waves and small-scale turbulence is communicated across this subrange. At the same time, it features progressive anisotropization of flow characteristics on increasing spatial scales. Despite many observational and computational studies of the buoyancy subrange, its theoretical understanding has been lagging. This article presents an investigation of the buoyancy subrange using the quasi-normal scale elimination (QNSE) theory of turbulence. This spectral theory uses a recursive procedure of small-scale modes elimination based upon a quasi-normal mapping of the velocity and temperature fields using the Langevin equations. In the limit of weak stable stratification, the theory becomes completely analytical and yields simple expressions for horizontal and vertical eddy viscosities and eddy diffusivities. In addition, the theory provides expressions for various one-dimensional spectra that quantify turbulence anisotropization. The theory reveals how the dispersion relation for IGWs is modified by turbulence, thus alleviating many unique waves' features. Predictions of the QNSE theory for the buoyancy subrange are shown to agree well with various data.

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“…The value of this constant is in fair agreement with laboratory measurements and DNSs that show some spread but point to C CO 1 [139,140].…”

Section: (C) Vertical Spectrum Of the Potential Energysupporting

confidence: 85%

An analytical theory of the buoyancy–Kolmogorov subrange transition in turbulent flows with stable stratification

Sukoriansky

Galperin

2013

Phil. Trans. R. Soc. A.

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“…This can be explained because the maximum principle precludes excitations at large amplitudes. Similar observations were made, for example, in [27] in a different context. We note that the PDFs of the velocity gradients distinguish the two equations more clearly; the Burgers equations are more intermittent than those of the Navier-Stokes equations (not shown here).…”

Section: Probability Density Function (Pdf) Of Velocitysupporting

confidence: 85%

“…This indicates that the maximum principle breaks down in the vicinity of near-singular structure associated with large enstrophy. See also [27,29]. …”

Section: Passive Scalar As Quasi-4d Navier-stokes Flowmentioning

confidence: 99%

Numerical study on comparison of Navier-Stokes and Burgers equations

Ohkitani

Dowker

2012

Physics of Fluids

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We compare freely decaying evolution of the Navier-Stokes equations with that of the 3D Burgers equations with the same kinematic viscosity and the same incompressible initial data by using direct numerical simulations. The Burgers equations are well-known to be regular by a maximum principle [Kiselev and Ladyzenskaya (1957)] unlike the Navier-Stokes equations.It is found in the Burgers equations that the potential part of velocity becomes large in comparison with the solenoidal part which decays more quickly. The probability distribution of the nonlocal term −u · ∇p, which spoils the maximum principle, in the local energy budget is studied in detail. It is basically symmetric, i.e. it can be either positive or negative with fluctuations.Its joint probability density functions with 1 2 |u| 2 and with 1 2 |ω| 2 are also found to be symmetric, fluctuating at the same times as the probability density function of −u · ∇p.A power-law relationship is found in the mathematical bound for enstrophy dQ dt + 2νP ∝ Q a P b α , where Q and P denote the enstrophy and the palinstrophy, respectively and the exponents a and b are determined by calculus inequalities. We propose to quantify nonlinearity depletion by the exponent α on this basis.

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“…latter two papers it is shown that scaling exponents of isotropic longitudinal velocity structure functions are indistinguishable from those of Navier-Stokes turbulence at comparable Reynolds number (see, e.g., Warhaft (2000) and Watanabe & Gotoh (2004)), a result in support of the universality of turbulence with respect to the forcing mechanism. A similar conclusion was drawn by Antonelli et al (2007) for buoyancy-dominated turbulent flows in the atmospheric convective boundary layer.…”

Section: Spatial and Temporal Scaling Laws Of Structure Functions Andmentioning

confidence: 90%

Incompressible Rayleigh–Taylor Turbulence

Boffetta

Mazzino

2017

Annu. Rev. Fluid Mech.

149

130

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Basic fluid equations are the main ingredient to develop theories of the Rayleigh-Taylor buoyancy-induced instability. Turbulence arises in the late stage of the instability evolution as a result of the proliferation of active scales of motion. Fluctuations are maintained by the unceasing conversion of potential energy into kinetic energy. Although the dynamics of turbulent fluctuations is ruled by the same equations controlling the Rayleigh-Taylor instability, here only phenomenological theories are currently available. The main purpose of the present review is to provide an overview of the most relevant (and often contrasting) theoretical approaches to Rayleigh-Taylor turbulence together with numerical and experimental evidences for their support. Although the focus will be mainly on the classical Boussinesq Rayleigh-Taylor turbulence of miscible fluids, the review extends to other fluid systems having viscoelastic behavior, being a↵ect by rotation of the reference frame and, finally, in the presence of reactions.

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Statistics of a passive scalar in homogeneous turbulence

Cited by 140 publications

References 61 publications

An analytical theory of the buoyancy–Kolmogorov subrange transition in turbulent flows with stable stratification

An analytical theory of the buoyancy–Kolmogorov subrange transition in turbulent flows with stable stratification

Numerical study on comparison of Navier-Stokes and Burgers equations

Incompressible Rayleigh–Taylor Turbulence

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