A Corrsin type approximation for Lagrangian fluid Turbulence

TL;DR

This paper introduces a Corrsin-type approximation to better understand Lagrangian turbulence, revealing a new structure function with an extended inertial range and linking it to Eulerian transversal structure functions.

Contribution

It proposes a novel Corrsin-type approximation for Lagrangian turbulence, connecting Eulerian and Lagrangian statistics and identifying a new Lagrangian structure function with an extended inertial range.

Findings

Identification of a new Lagrangian structure function with an extended inertial range

Connection established between Eulerian transversal structure functions and Lagrangian PDFs

Insights into the transition from Eulerian to Lagrangian turbulence statistics

Abstract

In Lagrangian turbulence one is faced with the puzzle that 2D Navier-Stokes flows are nearly as intermittent as in three dimensions although no intermittency is present in the inverse cascade in 2D Eulerian turbulence. In addition, an inertial range is very difficult to detect and it is questionable whether it exists at all. Here, we investigate the transition of Eulerian to Lagrangian probability density functions (PDFs) which leads to a new type of Lagrangian structure function. This possesses an extended inertial range similar to the case of tracer particles in a frozen turbulent velocity field. This allows a connection to the scaling of Eulerian transversal structure functions.