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

Abstract

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 good agreement with their equal-time counterparts extracted from wind tunnel turbulent shear flow data.

References in corpus (7)

• The multifractal nature of turbulent energy dissipation
• Modelling fluctuations of financial time series: from cascade process to stochastic volatility model
• Multifractal stationary random measures and multifractal random walks with log-infinitely divisible scaling laws
• Stochastic equations generating continuous multiplicative cascades
• Multiplier phenomenology in random multiplicative cascade processes
• The Markovian metamorphosis of a simple turbulent cascade model
• Translationally invariant cumulants in energy cascade models of turbulence

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• A class of spatio-temporal and causal stochastic processes, with application to multiscaling and multifractality
• Data-driven derivation of the turbulent energy cascade generator
• A causal continuous-time stochastic model for the turbulent energy cascade in a helium jet flow