The process of star formation in interstellar molecular clouds is believed to be controlled by driven supersonic magnetohydrodynamic turbulence. We suggest that in the inertial range such turbulence obeys the Kolmogorov law, while in the dissipative range it behaves as Burgers turbulence developing shock singularities. On the base of the She–Lévêque analytical model we then predict the velocity...

In a famous calculation of the “large-distance and longtime properties of a randomly stirred fluid,” Forster, Nelson, and Stephen (FNS) analyzed the consequences of various forcing scenarios for the Navier–Stokes equation and, to some extent, Burgers equation. They considered both a conservative forcing (Model A) and a nonconservative one (Model B), and predicted nontrivial properties for the l...

The effect of chemical treatment at fiber–plastic interface and fiber loading level on creep property of bamboo fiber high-density polyethylene (BF/HDPE) composites was investigated. For single modifier systems, the use of maleic anhydride grafted polyethylene (PE-g-MA) as a coupling agent helped reduce the creep and achieved the optimum effect at the 5.7% loading level. The addition of either ...

In this paper, an H-Galerkin mixed finite element method is discussed for the coupled Burgers equations. The optimal error estimates of the semi-discrete and fully discrete schemes of the coupled Burgers equation are derived. Keywords—The coupled Burgers equation; H-Galerkin mixed finite element method; Backward Euler’s method; Optimal error estimates.

Katz and Pavlovic recently proposed a dyadic model of the Euler equations for which they proved finite time blow-up in the H3/2+ǫ Sobolev norm. It is shown that their model can be reduced to the dyadic inviscid Burgers equation where nonlinear interactions are restricted to dyadic wavenumbers. The inviscid Burgers equation exhibits finite time blow-up in Hα, for α ≥ 1/2, but its dyadic restrict...

The creep behavior of bagasse-based composites with virgin and recycled polyvinyl chloride (B/PVC) and high density polyethylene (B/HDPE) as well as a commercial wood and HDPE composite decking material was investigated. The instantaneous deformation and creep rate of all composites at the same loading level increased at higher temperatures. At a constant load level, B/PVC composites had better...

Burgers equation is a simplified form of the Navier-Stokes equation that represents the non-linear features of it. In this paper, the transient two-dimensional non-linear Burgers equation is solved using the Lattice Boltzmann Method (LBM). The results are compared with the Modified Local Crank-Nicolson method (MLCN) and exact solutions. The LBM has been emerged as a new numerical method for sol...

In this letter, a coupled system of viscous Burgers’ equations with zero Dirichlet boundary conditions and appropriate initial data is considered. For the well-known single viscous Burgers’ equation with zero Dirichlet boundary conditions, the zero equilibrium is the unique global exponential point attractor. A similar property is shown for the coupled Burgers’ equations, i.e., trajectories sta...

In this paper we establish rigorously that the family of Burgers vortices of the three-dimensional Navier-Stokes equation is stable for small Reynolds numbers. More precisely, we prove that any solution whose initial condition is a small perturbation of a Burgers vortex will converge toward another Burgers vortex as time goes to infinity, and we give an explicit formula for computing the change...