Joint probability density of a passive article with force and magnetic field

TL;DR

This paper analyzes the joint probability density of a passive particle influenced by harmonic, viscous, and magnetic forces using Navier-Stokes and Fokker-Planck equations, providing approximate solutions and numerical results.

Contribution

It introduces an approximate method to solve the joint probability density in a magnetohydrodynamic context using Fourier transforms and moment calculations.

Findings

Derived approximate solutions for the joint probability density.

Numerically calculated kurtosis, correlation coefficient, and moments.

Analyzed the effects of magnetic and force parameters on particle behavior.

Abstract

We firstly study the Navier-Stokes equation for the motion of a passive particle with harmonic, viscous, perturbative forces, subject to an exponentially correlated Gaussian force. Secondly, from the Fokker-Planck equation in an incompressible conducting fluid of magnetic field, we approximately obtain the solution of the joint probability density by using double Fourier transforms in three-time domains. In addition, the kurtosis, the correlation coefficient, and the moment from moment equation are numerically calculated.