Interplay of surface geometry and vorticity dynamics in incompressible flows on curved surfaces

doi:10.1007/s10483-017-2238-8

Abstract

Abstract:

Incompressible viscous flows on curved surfaces are considered with respect to the interplay of surface geometry, curvature, and vorticity dynamics. Free flows and cylindrical wakes over a Gaussian bump are numerically solved using a surface vorticitystream function formulation. Numerical simulations show that the Gaussian curvature can generate vorticity, and non-uniformity of the Gaussian curvature is the main cause. In the cylindrical wake, the bump dominated by the positive Gaussian curvature can significantly affect the vortex street by forming velocity depression and changing vorticity transport. The results may provide possibilities for manipulating surface flows through local change in the surface geometry.

Key words: fillet welds, exact solution, theory of elasticity, two-dimensional flow, incompressible viscous, vorticity dynamics, curvature

2010 MSC Number:

76D17

Qian SHI, Yu CHEN, Xilin XIE. Interplay of surface geometry and vorticity dynamics in incompressible flows on curved surfaces. Applied Mathematics and Mechanics (English Edition), 2017, 38(9): 1191-1212.

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