One of eminent statistical characteristics of homogeneous, isotropic developed turbulence in the three dimensional system is the self-similar energy cascade in the wavenumber space. This results in the power law behavior for the velocity structure function , the -th moment of the velocity difference at two positions separated by . is a universal function of . Several years ago, it was found that even when the turbulence is not fully developed, i.e., the Reynolds number is not extremely high and the the scaling range where the above scaling law holds is not wide enough, scaling behaviors of which has an extended form of that in developed turbulence holds. They are called the extended self-similarity (ESS) and the generalized extended self-similarity (GESS). I will talk about a phenomenological derivation of ESS and GESS, proposing a new scaling hypothesis on the basis of the large deviation theory of probability theory. Furthermore, using numerical and experimental data, I will examine the validity of the present approach.
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Intermittency is a quite ubiquitous phenomenon in nonlinear dynamics. The
intermittency observed when a particular dynamical state undergoes the
instability is called the modulational (often called the on-off)
intermittency. Recently, an experimental confirmation of the on-off
intermittency in the electrohydrodynamic convection in nematics under
dichotomous noise was reported by John et al.. An eminent statistics
of the observation is the intermittent generation of convective pattern.
In my talk, in order to elucidate the experiment I will first propose a phenomenological nonlinear stochastic model which has the structure of the Swift-Hohenberg equation for local convection variable with fluctuating threshold. Then, I will discuss results of numerical integration of the model equation associated with the intermittent emergence of convective pattern. Detailed analysis on the statistics of the intermittent pattern dynamics will be addressed.
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John Th, Behn U and R Stannarius 2002, Phys. Rev. E 65 046229
For the modulational intermittency (on-off intermittency), see the following references:
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