Journal ArticleDOI
Energy stability theory of decelerating swirl flows
G. P. Neitzel,Stephen H. Davis +1 more
TLDR
In this article, an infinite circular cylinder, filled with viscous, incompressible fluid, is rotating as a solid body and the resulting swirl flow is susceptible to centrifugal instabilities.Abstract:
An infinite circular cylinder, filled with viscous, incompressible fluid, is rotating as a solid body. At time t=0 the angular velocity ω (t) of the cylinder is decreased in a prescribed fashion. The resulting swirl flow is susceptible to centrifugal instabilities. The method of energy is used to determine sufficient conditions, R<RG, where R is a Reynolds number, such that rotationally symmetric disturbances of arbitrary amplitude decay to zero with time. Both impulsive and smooth angular velocity histories of the container are considered. The analysis further provides a lower bound t+ on the onset time before which all disturbances must decay to zero, for R≳RG. If the final state (as t→∞) also corresponds to solid body rotation (e.g., when the cylinder is brought to rest), then the analysis simultaneously provides an upper bound t‡ on the decay time after which all disturbances decay zero, for R≳RG. In this case centrifugal instabilities are confined to times t in the interval t+<t<t‡.read more
Citations
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Journal ArticleDOI
Viscous flows and instabilities near rotating bodies
TL;DR: In this article, a survey of experiments on the flow near rotating bodies is presented, where the flow and the instabilities around, between and within these rotating bodies and combinations of them are investigated.
Journal ArticleDOI
Centrifugal instabilities during spin-down to rest in finite cylinders. Numerical experiments
G. P. Neitzel,Stephen H. Davis +1 more
TL;DR: In this article, the effects of the enhanced mixing due to instability on the spin-down characteristics and torque are discussed, and the results are compared with experiment and the onset time for instability and the spindown time are given.
Journal ArticleDOI
Stability of stationary endwall boundary layers during spin-down
Juan Lopez,Patrick Weidman +1 more
TL;DR: In this article, the impulsive spin-down problem is examined numerically for Savac' (1983, 1987) conditions and good agreement with his experiments is achieved, which include quantitative space-time information regarding the axisymmetric waves.
Journal ArticleDOI
Convective instability of a micropolar fluid layer by the method of energy
Georgy Lebon,C. Perez-Garcia +1 more
TL;DR: In this article, the convective instability of a micropolar incompressible fluid layer heated from below is treated within the framework of Serrin-Joseph's energy method, and the influence of various micropolarity parameters on the onset of convection is also analyzed.
Journal ArticleDOI
Spin-up of stratified rotating flows at large Schmidt number: experiment and theory
TL;DR: In this paper, the authors consider the nonlinear spin-up/down of a rotating stratified fluid in a coni-cal container and show good quantitative agreement for positive changes in the rotation rate of the container (relative to the initial rotation sense).
References
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Journal ArticleDOI
On a time-dependent motion of a rotating fluid
H. P. Greenspan,L. N. Howard +1 more
TL;DR: In this article, the authors consider the way in which the state of rigid rotation of a contained viscous fluid is established, and they find that the motion consists of three distinct phases, namely, the development of the Ekman layer, the inviscid fluid spin-up, and the viscous decay of residual oscillations.
Journal ArticleDOI
The Stability of Time-Periodic Flows
TL;DR: In this article, the authors give a review of three prototypal problems having sinusoidal time variation: parallel shear flows, convective instabilities, and centrifugal instabilities.
Journal ArticleDOI
Global stability of time-dependent flows: impulsively heated or cooled fluid layers
TL;DR: In this article, the stability of time-dependent diffusive temperature profiles in fluid layers subject to impulsive changes in surface temperature is discussed. Butler et al. used the method of energy to discuss the stability and the interpretation of these regions.
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