Theoretical analysis of the velocity field, stress field and vortex sheet of generalized second order fluid with fractional anomalous diffusion

Abstract

The velocity field of generalized second order fluid with fractional anomalous diiusion caused by a plate moving impulsively in its own plane is investigated and the anomalous diffusion problems of the stress field and vortex sheet caused by this process are studied. Many previous and classical results can be considered as particular cases of this paper, such as the solutions of the fractional diffusion equations obtained by Wyss; the classical Rayleigh’s time-space similarity solution; the relationship between stress field and velocity field obtained by Bagley and co-worker and Podlubny’s results on the fractional motion equation of a plate. In addition, a lot of significant results also are obtained. For example, the necessary condition for causing the vortex sheet is that the time fractional diffusion index β must be greater than that of generalized second order fluid α; the establiihment of the vorticity distribution function depends on the time history of the velocity profile at a given point, and the time history can be described by the fractional calculus.