Nearly incompressible turbulence for different 2D and slab energy ratios

Renormalization for Autonomous Nearly Incompressible Bv Vector Fields in 2d

Given a bounded autonomous vector field b : R2 → R2, we study the uniqueness of bounded solutions to the initial value problem for the related transport equation ∂tu + b · ∇u = 0. Assuming that b is of class BV and it is nearly incompressible, we prove uniqueness of weak solutions to the transport equation. The starting point of the present work is the result which has been obtained in [10] (wh...

Comparison of three different numerical schemes for 2D steady incompressible lid-driven cavity flow

In this study, a numerical solution of 2D steady incompressible lid-driven cavity flow is presented. Three different numerical schemes were employed to make a comparison on the practicality of the methods. An alternating direction implicit scheme for the vorticity-stream function formulation, explicit and implicit schemes for the primitive variable formulation of governing Navier-Stokes equatio...

Turbulence in nearly incompressible fluids: density spectrum, flows, correlations and implication to the interstellar medium

Interstellar scintillation and angular radio wave broadening measurements show that interstellar and solar wind (electron) density fluctuations exhibit a Kolmogorovlike k−5/3 power spectrum extending over many decades in wavenumber space. The ubiquity of the Kolmogorov-like interstellar medium (ISM) density spectrum led to an explanation based on coupling incompressible magnetohydrodynamic (MHD...

Energy cascades in physical scales of 3D incompressible magnetohydrodynamic turbulence

Steady nearly incompressible vector fields in 2D: chain rule and renormalization

Given bounded vector field b : R → R, scalar field u : R → R and a smooth function β : R → R we study the characterisation of the distribution div(β(u)b) in terms of div b and div(ub). In the case of BV vector fields b (and under some further assumptions) such characterisation was obtained by L. Ambrosio, C. De Lellis and J. Malý, up to an error term which is a measure concentrated on so-called...