Browsing by Author "Yoneda, Tsuyoshi"

Now showing 1 - 3 of 3

An ODE for boundary layer separation on a sphere and a hyperbolic space
(2014-07-15)
Chan, Chi Hin
;
Czubak, Magdalena
;
Yoneda, Tsuyoshi
;
應用數學系
;
Department of Applied Mathematics
Ma and Wang derived an equation linking the separation location and times for the boundary layer separation of incompressible fluid flows. The equation gave a necessary condition for the separation (bifurcation) point. The purpose of this paper is to generalize the equation to other geometries, and to phrase it as a simple ODE. Moreover we consider the Navier-Stokes equation with the Coriolis effect, which is related to the presence of trade winds on Earth. (C) 2014 Elsevier B.V. All rights reserved.
An ODE for boundary layer separation on a sphere and a hyperbolic space
(2014-07-15)
Chan, Chi Hin
;
Czubak, Magdalena
;
Yoneda, Tsuyoshi
;
應用數學系
;
Department of Applied Mathematics
Ma and Wang derived an equation linking the separation location and times for the boundary layer separation of incompressible fluid flows. The equation gave a necessary condition for the separation (bifurcation) point. The purpose of this paper is to generalize the equation to other geometries, and to phrase it as a simple ODE. Moreover we consider the Navier-Stokes equation with the Coriolis effect, which is related to the presence of trade winds on Earth. (C) 2014 Elsevier B.V. All rights reserved.
On the stationary Navier-Stokes flow with isotropic streamlines in all latitudes on a sphere or a 2D hyperbolic space
(2013-09-01)
Chan, Chi Hin
;
Yoneda, Tsuyoshi
;
應用數學系
;
Department of Applied Mathematics
In this paper, we show the existence of real-analytic stationary Navier-Stokes flows with isotropic streamlines in all latitudes in some simply-connected flow region on a rotating round sphere. We also exclude the possibility of having a Poiseuille's flow profile to be one of these stationary Navier-Stokes flows with isotropic streamlines. When the sphere is replaced by a 2-dimensional hyperbolic space, we also give the analog existence result for stationary parallel laminar Navier-Stokes flows along a circular-arc boundary portion of some compact obstacle in the 2-D hyperbolic space. The existence of stationary parallel laminar Navier-Stokes flows along a straight boundary of some obstacle in the 2-D hyperbolic space is also studied. In any one of these cases, we show that a parallel laminar flow with a Poiseuille's flow profile ceases to be a stationary Navier-Stokes flow, due to the curvature of the background manifold.