Unified multifractal description of longitudinal and transverse intermittency in fully developed turbulence

TL;DR

This paper introduces a unified multifractal framework for describing both longitudinal and transverse intermittency in fully developed turbulence, linking structure functions to velocity gradients and validated by high-resolution simulations.

Contribution

It develops a comprehensive multifractal model that jointly describes longitudinal and transverse intermittency, extending traditional models to include gradients and mixed structure functions.

Findings

Longitudinal gradient scaling depends only on longitudinal structure functions.

Transverse gradient scaling depends on mixed longitudinal-transverse structure functions.

Model shows excellent agreement with high-resolution turbulence simulations.

Abstract

Small-scale intermittency is a defining feature of fully developed fluid turbulence, marked by rare and extreme fluctuations of velocity increments and gradients that defy mean-field descriptions. Existing multifractal descriptions of intermittency focus primarily on longitudinal increments and gradients, despite mounting evidence that transverse components exhibit distinct and stronger intermittency. Here, we develop a unified multifractal framework that jointly prescribes longitudinal and transverse velocity increments, and extends to gradients. We derive explicit relations linking inertial-range scaling exponents of structure functions to moments of velocity gradients in dissipation range. Our results reveal that longitudinal gradient scaling is solely prescribed by longitudinal structure functions, as traditionally expected; however, transverse gradient scaling is prescribed by mixed longitudinal-transverse structure functions. Validation with high-resolution direct numerical simulations of isotropic turbulence, at Taylor-scale Reynolds number up to $1300$ demonstrates excellent agreement, paving way for a more complete and predictive description of intermittency faithful to the underlying turbulence dynamics.