Related Experiment Video
Updated: Aug 12, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
Published on: July 19, 2016
Scale dependence of the coarse-grained velocity derivative tensor structure in turbulence
1Institut Non Linéaire de Nice (UMR CNRS 6618), Université de Nice Sophia Antipolis, 1361 Route des Lucioles, F-06560 Valbonne, France.
Abstract:
Velocity fluctuations in hydrodynamic turbulence have a nontrivial structure, characterized by correlations of the velocity gradient tensor. In this paper, we consider a phenomenological model, incorporating the main features of hydrodynamic fluid turbulence, aimed at predicting the structure of the velocity gradient tensor coarse grained at a spatial scale r. This model [M. Chertkov, A. Pumir, and B.I. Shraiman, Phys. Fluids 11, 2394 (1999)] is formulated as a set of stochastic ordinary differential equations, with three dimensionless parameters, characterizing the reduction of the nonlinearity induced by the pressure term, the reisotropization effect of the small scale velocity field, and the influence of the small scales on the coarse-grained velocity derivative tensor. Semiclassical solutions of this model are obtained and compared with direct numerical simulations (DNS) data. The DNS data show that the joint probability distribution function of the second and third invariants of M becomes increasingly skewed as the scale r decreases in the inertial range. The model results correctly reproduce this behavior provided the parameter that controls nonlinearity reduction is finely tuned; the influence of the other parameters in the model is much weaker.
More Related Videos
Related Concept Videos
Vector Transformation in Rotating Coordinate Systems
Newtonian Fluid: Problem Solving
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...
Velocity and Acceleration in Steady and Unsteady Flow
The acceleration can be generalized to any point in the flow, and expressed as components along three perpendicular directions, representing changes in velocity over time.
Navier–Stokes Equations
Dimensionless Groups in Fluid Mechanics
Derivatives of Vector Functions

