The vortex stretching process is relevant to energy transport at various scales in turbulent flow and in vortex reconnection. For these, reasons, exact solutions for vortex flow are useful. Robinson and Saffman [1] examined the Burgers vortex solution and found closed form steady solutions for special parameter values. Unsteady 2D Burgers vortex solutions have been used to model the spanwise st...

Almost nothing decisive has been said about collocation methods for solving SPDEs. Among the best of such SPDEs the Burgers equation shows a prototypical model for describing the interaction between the reaction mechanism, convection effect, and diffusion transport. This paper discusses spectral collocation method to reduce stochastic Burgers equation to a system of stochastic ordinary differen...

Burgers’ equation frequently appears in the study of turbulence theory, as well as some other scientific fields. High and low Reynolds numbers play important roles in both modeling and numerical simulation. In this paper, we apply a numerical scheme to solve a two-dimensional time-fractional Burgers equation. The key feature of the proposed method is formed by combining the discontinuous Galerk...

This paper carries out the integration of Burgers equation by the aid of tanh method. This leads to the complex solutions for the Burgers equation, KdV–Burgers equation, coupled Burgers equation and the generalized time-delayed Burgers equation. Finally, the perturbed Burgers equation in (1+1) dimensions is integrated by the ansatz method. 2010 Elsevier Inc. All rights reserved.

Exact solutions and dynamics of globally coupled phase oscillators 2 Abstract. We analyze mean-field models of synchronization of phase oscillators with singular couplings and subject to external random forces. They are related to the Kuramoto-Sakaguchi model. Their probability densities satisfy local partial differential equations similar to the Porous Medium, Burgers and extended Burgers equa...

The “t-model” for dimensional reduction is applied to the estimation of the rate of decay of solutions of the Burgers equation and of the Euler equations in two and three space dimensions. The model was first derived in a statistical mechanics context, but here we analyze it purely as a numerical tool and prove its convergence. In the Burgers case the model captures the rate of decay exactly, a...

We consider the viscous Burgers equation with a fractional nonlinear term as a model involving non-local nonlinearities in conservation laws, which, surprisingly, has an analytical solution obtained by a fractional extension of the Hopf-Cole transformation. We use this model and its inviscid limit to develop stable spectral and discontinuous Galerkin spectral element methods by employing the co...

The "t-model" for dimensional reduction is applied to the estimation of the rate of decay of solutions of the Burgers equation and of the Euler equations in two and three space dimensions. The model was first derived in a statistical mechanics context, but here we analyze it purely as a numerical tool and prove its convergence. In the Burgers case, the model captures the rate of decay exactly, ...

Spatially coarse-grained (or effective) versions of nonlinear partial differential equations must be closed with a model for the unresolved small scales. For systems that are known to display fractal scaling, we propose a model based on synthetically generating a scale-invariant field at small scales using fractal interpolation, and then analytically evaluating its effects on the large, resolve...

in this study, quality characteristics of incorporated burgers containing 25, 50, 75 and 100 common carp (cyprinus carpio) surimi was evaluated. accordingly, proximate composition, texture profile analysis (tpa), color, water holding capacity (whc) and sensory attributes of resulted burgers were determined. based on data, burgers containing surimi showed lower amount of protein, fat and ash com...