A causal continuous-time stochastic model for the turbulent energy cascade in a helium jet flow

TL;DR

This paper introduces a continuous-time stochastic model using Lévý bases to accurately simulate energy dissipation in turbulent helium jet flows, outperforming other models in distribution and self-scaling reproduction.

Contribution

It proposes a novel normal inverse Gaussian cascade model that better captures turbulence properties and predicts self-scaling exponents from one-point distributions.

Findings

Normal inverse Gaussian model outperforms others in energy dissipation distribution

Model accurately reproduces self-scaling exponents of turbulence

Distribution shapes are Reynolds number independent

Abstract

We discuss continuous cascade models and their potential for modelling the energy dissipation in a turbulent flow. Continuous cascade processes, expressed in terms of stochastic integrals with respect to L\'evy bases, are examples of ambit processes. These models are known to reproduce experimentally observed properties of turbulence: The scaling and self-scaling of the correlators of the energy dissipation and of the moments of the coarse-grained energy dissipation. We compare three models: a normal model, a normal inverse Gaussian model and a stable model. We show that the normal inverse Gaussian model is superior to both, the normal and the stable model, in terms of reproducing the distribution of the energy dissipation; and that the normal inverse Gaussian model is superior to the normal model and competitive with the stable model in terms of reproducing the self-scaling exponents. Furthermore, we show that the presented analysis is parsimonious in the sense that the self-scaling exponents are predicted from the one-point distribution of the energy dissipation, and that the shape of these distributions is independent of the Reynolds number.