Turbulence without pressure in d dimensions
S. Boldyrev
TL;DR
This paper investigates a pressureless Navier-Stokes model in d-dimensional space as a simplified approach to strong turbulence in compressible fluids, deriving key statistical properties and solutions.
Contribution
It introduces a closed-form equation for the velocity-gradient PDF and analyzes its asymptotics, providing numerical solutions for 2D turbulence.
Findings
Derived a closed equation for the velocity-gradient probability density function.
Analyzed asymptotics for Burgers turbulence in the gradient velocity field.
Provided numerical solutions for the two-dimensional case.
Abstract
The randomly driven Navier-Stokes equation without pressure in d-dimensional space is considered as a model of strong turbulence in a compressible fluid. We derive a closed equation for the velocity-gradient probability density function. We find the asymptotics of this function for the case of the gradient velocity field (Burgers turbulence), and provide a numerical solution for the two-dimensional case. Application of these results to the velocity-difference probability density function is discussed.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHydrocarbon exploration and reservoir analysis · Geometric Analysis and Curvature Flows · Hydraulic Fracturing and Reservoir Analysis