Connection between the Burgers equation with an elastic forcing term and a stochastic process.

0 Aspects of the stochastic Burgers equation and their connection with turbulence

Aspects of the stochastic Burgers equation and their connection with turbulence. Summary. We present results for the 1 dimensional stochastically forced Burgers equation when the spatial range of the forcing varies. As the range of forcing moves from small scales to large scales, the system goes from a chaotic, structureless state to a structured state dominated by shocks. This transition takes...

Invariant measures for Burgers equation with stochastic forcing

2 00 5 A note on the forced Burgers equation

We obtain the exact solution for the Burgers equation with a time dependent forcing, which depends linearly on the spatial coordinate. For the case of a stochastic time dependence an exact expression for the joint probability distribution for the velocity fields at multiple spatial points is obtained. A connection with stretched vortices in hydrodynamic flows is discussed. Burgers equation [1],...

B-spline Collocation Methods for Numerical Solutions of the Burgers’ Equation

The Burgers’ equation first appeared in the paper by Bateman [3], who mentioned two of the essentially steady solutions. Due to extensive works of Burgers [4] involving the Burgers’ equation especially as a mathematical model for the turbulence, it is known as Burgers’ equation. The equation is used as a model in fields as wide as heat conduction [5], gas dynamics [13], shock waves [4], longitu...

Survey of roughness by stochastic oscillations

In this paper, connection between surface roughness and directed polymers in random medium are studied, when the surface is considered as a directed line undergoing stochastic oscillations. This is performed by studying the influence of a stochastic elastic forcing term −κy+η(s), on a particle moving along a rough surface. Two models are proposed and analysed in this way: the random-walk proces...