Log Normal Intermittency and Randomly Stirred Fluids

Abstract

Energy fluctuation is studied in the randomly forced fluid model of De Dominicis andMartin by mode-coupling and renormalization group methods. The universal log normal intermittency exponent is consequently calculated from first principles and found to be in agreement with the accepted value.

Universal properties of three-dimensional magnetohydrodynamic turbulence: do Alfvén waves matter?

“…According to the Kolmogorov's hypothesis for fluid turbulence [4], in the inertial range energy spectrum E(k) = K o ǫ 2/3 k −5/3 , where K o , a universal constant, is the Kolmogorov's constant and ǫ is the energy dissipation rate per unit mass. Various calculations, based on different techniques by different groups [7,30,31,32] show that K o ∼ 1.5 in three dimensions. Having noted that the energy spectra, even in the presence of a mean magnetic field scale as k −5/3 extensions of Kolmogorov's hypothesis for 3dMHD allows one to define Kolmogorov's constants for the Elsässer fields:…”

“…For small δ, δ ≃ 9δ. A standard calculation on the randomly stirred model yields intermittency exponent δ = 0.2 [32] where δ = 9δ, whereas the best possible estimate from experiments is 0.23 [32]. This model, despite having well-known limitations and difficulties [38], serves as a qualitative illustration of multiscaling.…”

Dominance of rare events in some problems in statistical physics

“…Careful experiment revealed the existence of these fluctuations. The fluctuations occurred rarely -these were the rare events of turbulence [12][13][14][15][16][17][18][19]. These rare events constitute one of the most difficult issues to understand in the theory of turbulence.…”

Is Turbulence as Simple as Tossing a Coin?

“…This can be seen in static critical phenomena, critical dynamics, dynamics of interfacial growth, statistics of polymer chain and myriad other problems [3]. However, the Gaussian model fails to be a starting point while discussing intermittency in fluid turbulence [4,5,6,7,8,9,10,11,12,13,14,15,16]. In the large deviation theory, the central role is played by the distribution associated with tossing of a coin.…”

“…This gets related to the exponential of the free energy difference ∆F between initial and final states leading to Jarzynski's equality. Defining w D ≡ w−∆F , the equality can also be cast in the form: e −wD = 1 (10) where w D is the dissipative work along a 'given' path and the fact that average is unity implies that there are paths for which w D < 0 -a case of transient violation of the second law of thermodynamics. These violations can be portrayed as the rare events, which are highlighted by Jarzynski equality.…”