Corrections to fully developed turbulent spectra due to compressibility of the fluid

Volchenckov, D Yu; Nalimov, M. Yu.

doi:10.1007/bf02071475

Cited by 15 publications

(2 citation statements)

References 6 publications

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“…In the context of our study, it is especially important that the Kazantzev-Kraichnan ensemble allows one to easily model compressibility, which appears rather difficult if the velocity field is described by Navier-Stokes equations; see e.g. [40,41]. For a compressible fluid (∂ i v i = 0), the covariant derivative can also be introduced in an alternative way, namely, ∇ t h ≡ ∂ t h + ∂ i (v i h), which is obligatory if the field h has the meaning of the density of some conserved quantity.…”

Section: Introduction and Description Of The Modelmentioning

confidence: 99%

Random interface growth in a random environment: Renormalization group analysis of a simple model

Antonov

Kakin

2015

Theor Math Phys

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Abstract. We study effects of turbulent mixing on the random growth of an interface in the problem of the deposition of a substance on a substrate. The growth is modelled by the well-known Kardar-Parisi-Zhang model. The turbulent advecting velocity field is modelled by the Kraichnan's rapid-change ensemble: Gaussian statistics with the correlation function vv ∝ δ(t − twhere k is the wave number and 0 < ξ < 2 is a free parameter. Effects of compressibility of the fluid are studied. Using the field theoretic renormalization group we show that, depending on the relation between the exponent ξ and the spatial dimension d, the system reveals different types of largescale, long-time asymptotic behaviour, associated with four possible fixed points of the renormalization group equations. In addition to known regimes (ordinary diffusion, ordinary growth process, and passively advected scalar field), existence of a new nonequilibrium universality class is established. Practical calculations of the fixed point coordinates, their regions of stability and critical dimensions are calculated to the first order of the double expansion in ξ and ε = 2 − d (one-loop approximation). It turns out that for incompressible fluid, the most realistic values ξ = 4/3 or 2 and d = 1 or 2 correspond to the case of passive scalar field, when the nonlinearity of the KPZ model is irrelevant and the interface growth is completely determined by the turbulent transfer. If the compressibility becomes strong enough, the crossover in the critical behaviour occurs, and these values of d and ξ fall into the region of stability of the new regime, where the advection and the nonlinearity are both important. However, for this regime the coordinates of the fixed point lie in the unphysical region, so its physical interpretation remains an open problem.

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Section: Introduction and Description Of The Modelmentioning

confidence: 99%

Random interface growth in a random environment: Renormalization group analysis of a simple model

Antonov

Kakin

2015

Theor Math Phys

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“…The model for compressible turbulence based on compressible NS equation was firstly proposed in [51]. However, as mentioned in [56,57] authors did not pay attention to the multiplicatively renormalization and the model they obtained was not multiplicatively renormalizable as well as the term proportional to ṽ was missing.…”

Section: B Turbulent Advectionmentioning

confidence: 99%

Influence of turbulent mixing on critical behavior of directed percolation process: Effect of compressibility

2018

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Universal behavior is a typical emergent feature of critical systems. A paramount model of the nonequilibrium critical behavior is the directed bond percolation process that exhibits an active-to-absorbing state phase transition in the vicinity of a percolation threshold. Fluctuations of the ambient environment might affect or destroy the universality properties completely. In this work, we assume that the random environment can be described by means of compressible velocity fluctuations. Using field-theoretic models and renormalization group methods, we investigate large-scale and long-time behavior. Altogether, 11 universality classes are found, out of which 4 are stable in the infrared limit and thus macroscopically accessible. In contrast to the model without velocity fluctuations, a possible candidate for a realistic three-dimensional case, a regime with relevant short-range noise, is identified. Depending on the dimensionality of space and the structure of the turbulent flow, we calculate critical exponents of the directed percolation process. In the limit of the purely transversal random force, critical exponents comply with the incompressible results obtained by previous authors. We have found intriguing nonuniversal behavior related to the mutual effect of compressibility and advection.

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Stochastic Navier-Stokes Equation for a Compressible Fluid: Two-Loop Approximation

Hnatič

Gulitskiy

Lučivjanský

et al. 2019

11th Chaotic Modeling and Simulation International Conference

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A model of fully developed turbulence of a compressible fluid is briefly reviewed. It is assumed that fluid dynamics is governed by a stochastic version of Navier-Stokes equation. We show how corresponding field theoretic-model can be obtained and further analyzed by means of the perturbative renormalization group. Two fixed points of the RG equations are found. The perturbation theory is constructed within formal expansion scheme in parameter y, which describes scaling behavior of random force fluctuations. Actual calculations for fixed points' coordinates are performed to two-loop order.

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Corrections to fully developed turbulent spectra due to compressibility of the fluid

Cited by 15 publications

References 6 publications

Random interface growth in a random environment: Renormalization group analysis of a simple model

Random interface growth in a random environment: Renormalization group analysis of a simple model

Influence of turbulent mixing on critical behavior of directed percolation process: Effect of compressibility

Stochastic Navier-Stokes Equation for a Compressible Fluid: Two-Loop Approximation

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