It is shown how a complete set of hydrodynamic equations describing an unsteady three-dimensional viscous flow nearby a solid body, can be reduced to a closed system of surface equations using the method of dimension reduction of over-determined systems of differential equations. These systems of equations allow determining the surface distribution of the resulting stresses on the surface of this body as well as all other quantities characterizing the hydrodynamic flow around it.
We identify incompressible planar linear flows that are generalizations of the well known one-parameter family characterized by the ratio of in-plane extension to (out-of-plane) vorticity. The latter `canonical' family is classified into elliptic and hyperbolic linear flows with closed and open streamlines, respectively, corresponding to the extension-to-vorticity ratio being less or greater than unity; unity being the marginal case of simple shear flow. The novel flows possess an out-of-plane extension, but the streamlines may nevertheless be closed or open, allowing for an organization, in a…
Resonant spectral cascade in Womersley flow triggered by arterial geometry
Mechanical Engineering Department, College of Engineering and Technology Arab Academy for Science, Technology and Maritime Transport（阿拉伯科学、技术和海运学院工程学院与技术学院机械工程系）
We present a series of analytically solvable axisymmetric flows on the torus geometry. For the single-component flows, we describe the propagation of sound waves for perfect fluids, as well as the viscous damping of shear and longitudinal waves for isothermal and thermal fluids. Unlike the case of planar geometry, the non-uniform curvature on a torus necessitates a distinct spectrum of eigenfrequencies and their corresponding basis functions. This has several interesting consequences, including breaking the degeneracy between even and odd modes, a lack of periodicity even in the flows of perfe…
Generative prediction of flow fields around an obstacle using the diffusion model
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China（湍流与复杂系统国家重点实验室，工程学院，北京大学，北京100871，中国）；HEDPS-CAPT, Peking University, Beijing 100871, China（HEDPS-CAPT，北京大学，北京100871，中国）
