Jochen Cleve

Stochastic energy-cascade model for (1 + 1)-dimensional fully developed turbulence

Geometrical random multiplicative cascade processes are often used to model positive-valued multifractal fields such as the energy dissipation in fully developed turbulence. We propose a dynamical generalization describing the energy dissipation in terms of a continuous and homogeneous stochastic field in one space and one time dimension. In the model, correlations originate in the overlap of the respective spacetime histories of field amplitudes. The theoretical two- and three-point correlation functions are found to be in excellent agreement with their equal-time counterparts extracted from wind tunnel turbulent shear flow data.

Intermittency exponent of the turbulent energy cascade

We consider the turbulent energy dissipation from one-dimensional records in experiments using air and gaseous helium at cryogenic temperatures, and obtain the intermittency exponent via the two-point correlation function of the energy dissipation. The air data are obtained in a number of flows in a wind tunnel and the atmospheric boundary layer at a height of about 35 m above the ground. The helium data correspond to the centerline of a jet exhausting into a container. The air data on the intermittency exponent are consistent with each other and with a trend that increases with the Taylor microscale Reynolds number, R(lambda), of up to about 1000 and saturates thereafter. On the other hand, the helium data cluster around a constant value at nearly all R(lambda), this being about half of the asymptotic value for the air data. Some possible explanation is offered for this anomaly.

The Markovian metamorphosis of a simple turbulent cascade model

Abstract Markovian properties of a discrete random multiplicative cascade model of log-normal type are discussed. After taking small-scale resummation and observational breaking of the ultrametric hierarchy into account, qualitative agreement with Kramers–Moyal coefficients, recently deduced from a fully developed turbulent flow, is achieved.

Stochastic Small-Scale Modelling of Turbulent Wind Time Series

Today’s wind field simulation tools are based on Gaussian statistics and if they resolve the smallest scales they are not concerned about a consistent description of velocity and dissipation. We present a data-driven stochastic model that provides such a consistent description. The model is a multifractal extension of fractional Brownian motion, it also describes the non-Gaussian statistics of turbulent wind fields. In order to further integrate skewness and stationarity an additional small correlation between the multifractal part and the fractional Brownian motion is added.