Optimal system and exact solutions for the generalized system of 2-dimensional Burgers equations with infinite Reynolds number

Abstract

One of the equations used for studying fluid turbulence is the 2D Burgers equations. Researchers have used various numerical methods to compute the values of the velocity components at different Reynolds number and other parameters of choice. Reynolds number is important in analyzing any type of flow when there is substantial velocity gradient. It indicates the relative significance of the viscous effect compared to the inertia effect. Results available in the literature for the 2D Burgers equations are either for laminar flow which occurs at low Reynolds numbers or for turbulent flow which occurs at high Reynolds numbers. These results cannot be used for superfluidity, the hallmark property of quantum fluids, where Reynolds number is infinite. Although Reynolds number may not be infinite in some superfluid turbulence (Barenghi, 2008; Vinen, 2005) [1,2], it is definitely the case at zero-temperature limit (Sasa and Machida, 2011) [3]. Based on this assumption, we analyse the 2D Burgers equation at infinite Reynolds number using Lie group method. Optimal system of one-dimensional subalgebras is derived and used to obtain generalized distinct exact solutions of the velocity components.