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• W302200178 abstract "We describe a method for finding the non-Gaussian tails of probability distribution function (PDF) for solutions of stochastic differential equations, such as convection equation for a passive scalar, random driven Navier-Stokes equation etc. Existence of such tails is generally regarded as a manifestation of intermittency phenomenon. Our formalism is based on the WKB approximation in the functional integral for the conditional probability of a large fluctuation. Then the main contribution to the functional integral is given by a coupled field-force configuration — instanton. We argue that the tails of the single-point velocity probability distribution function (PDF) are generally non-Gaussian in developed turbulence. By using instanton formalism for the Navier-Stokes equation, we establish the relation between the PDF tails of the velocity and those of the external forcing. In particular, we show that a Gaussian random force having correlation scale L and correlation time τ produces velocity PDF tails ln (P(upsilon )alpha - {upsilon ^4}atupsilon gg {upsilon _{rms,}}L/tau ). For a short-correlated forcing when (tau ll L/{upsilon _{rms}}) there is an intermediate asymptotics ln (P(upsilon )alpha - {upsilon ^3}atL/tau gg upsilon gg {upsilon _{rms}}). We consider the tails of probability density function (PDF) for the velocity that satisfies Burgers equation driven by a Gaussian large-scale force. The instantonic calculations show that for the PDFs of velocity and its derivatives ({u^{(k)}} = partial _x^ku), the general formula is found: ln (P(|{u^{(k)}}|)alpha - {(|{u^{(k)}}|/{{mathop{rm Re}nolimits} ^k})^{3/(k + 1)}}). We consider high-order correlation functions of the passive scalar in the Kraichnan model. Using the instanton formalism we find the exponents ζn of the structure functions S n for (n gg ) 1 at the condition (d{zeta _2} gg 1) (where d is the dimensionality of space). At (n n c they are n-independent: ({zeta _n} = {zeta _2}{n_c}/4). Besides ζ n , we also estimate n-dependent factors in S n and critical behavior of S n at n close to n c" @default.
• W302200178 created "2016-06-24" @default.
• W302200178 creator A5005404492 @default.
• W302200178 date "1999-01-01" @default.
• W302200178 modified "2023-09-27" @default.
• W302200178 title "Instantons in the theory of turbulence" @default.
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• W302200178 doi "https://doi.org/10.1007/978-3-0348-8689-5_28" @default.
• W302200178 hasPublicationYear "1999" @default.
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