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Motivated by recent theoretical and experimental work, we numerically investigate spherical Couette flow with a view to obtaining for the first time Taylor vortices at large aspect ratios such as 0.38, 0.42, and 0.48. It is found that Taylor vortices can exist, stable or time-dependent, in a range of Reynolds numbers ͓Re 1 , Re 2 ] and their formation depends on the aspect ratio, on the imposition of various rotationary conditions on the boundaries, on the history of the flow and on the rate at which energy is transferred into the fluid to its final value. With increasing the range ͓Re 1 , Re 2 ] manifests a clear tendency to shorten.Couette flow in a spherical annulus is induced when the outer sphere is held stationary and the inner rotates. Such flows are of importance in classical fluid dynamics owing to their association to a nonlinear behavior and their relation to hydrodynamic instabilities of different kinds. One of the features of spherical Couette flow is the formation of Taylor vortices depending on the aspect ratio ϭ(r o Ϫr i )/r i , where r o and r i is the radius of the outer and of the inner sphere, respectively, and on the Reynolds number of the flow Re ϭr i 2 /, where is the angular velocity of the rotating sphere and is the coefficient of the kinematic viscosity. A survey of previous experimental studies in annular spherical flow, see for example Refs. 1-5, and references therein, reveals that stable Taylor vortices have not been so far observed for spherical gaps with aspect ratio Ͼ0.33. In particular, Liu et al. 2 by counterrotating the outer sphere or using special initial conditions were able to produce Taylor vortices at ϭ0.33. For larger gaps the flow undergoes to nonaxisymmetric secondary waves with spiral arms as the first instability. 2,4,5 The same instability appears in the form of an unstable bifurcation at ϭ0.154, 6 whereas for ϭ0.336 time-dependence manifests itself in a sequence of stable Hopf bifurcations characterized by a fluctuation in the strength of the smaller of the two vortices. 7 These features imply a set of questions. Are there any Taylor vortices at large aspect ratios and up to where? What is the range ͓Re 1 , Re 2 ] of existence of the Taylor vortices and how does it vary with increasing aspect ratio? What is the behavior of the bifurcation appearing with increasing ?In the present study we find stable Taylor vortices at aspect ratios ϭ0.38, 0.42, and 0.48 by modifying the boundary conditions applied in Ref. 2. Actually, by counterrotating the outer sphere and then reducing its angular velocity to zero, we were able to numerically simulate the 1-Taylor vortex state either symmetric or asymmetric with respect to the equator at these aspect ratios. We also show that the range ͓Re 1 , Re 2 ] within which Taylor vortices occur becomes smaller when increases. Furthermore, we were able to detect time dependence of the evolving flow, but the character of the bifurcation we found was different from that described in Refs. 6 and 7. For ϭ0.42 and 0.48 time dependence was follo...

Mixed convection flow in a heated pipe with a heated inner core is examined. Analytic solutions are derived in power series of the Dean number and the product of Reynolds and Rayleigh numbers. The results are compared with flows in the absence of an axial core. The core modifies the flow and the fluid temperature distribution.

When a catheter is inserted through an artery, the wall shear stress increases and the secondary flow exhibits an increased number of instantaneous vortices. These effects become more evident when the annular gap between the catheter and the artery becomes more narrow. Accordingly it is suggested that these factors may affect the preferential distribution of the atheromatous plaques at the sites of the wall with an increased permeability.