Statistical Theory of Turbulence.

On the Statistical Theory of Turbulence.

The expression for ci is in agreement with the conclusions arrived at above. It shows that the form (14) of the equation of diffusion is a good guide to the physicist as it brings in evidence the quantities significant from his point of view. On the other hand, Kolmogoroff's equations (3) and (4) are more general since they include the case of transition probabilities which are inhomogeneous in...

Statistical theories of turbulence

Statistical properties of turbulence

It is now convenient to reexamine some questions of fundamental nature with the purpose of analyzing the possible consequences of Ruelle’s principle introduced in §5.7. We shall make frequently reference to the general description of motions given in Chap. 5 in a context in which we imagine that the considered motions are attracted by some attracting set in phase space, which will have zero vol...

Determination of Statistical Characteristics of Isotropic Turbulence

Ultrasonic flow measurement technology has the potential to significantly improve flow measurement accuracy beyond that presently achieved. However, current applications fail to achieve theoretical accuracies because of turbulence effects on ultrasonic wave transit time. Herein, the ultrasonic flowmeter equation is reconsidered, where the effects of turbulent velocity and sound speed fluctuatio...

Spectral reduction: a statistical description of turbulence

A method is described for predicting statistical properties of turbulence. Collections of Fourier amplitudes are represented by nonuniformly spaced modes with enhanced coupling coefficients. The statistics of the full dynamics can be recovered from the time-averaged predictions of the reduced model. A Liouville theorem leads to inviscid equipartition solutions. Excellent agreement is obtained w...