On the linear stability of cellular spiral Couette flow

1993 ◽  
Vol 5 (5) ◽  
pp. 1188-1200 ◽  
Author(s):  
Mohamed E. Ali ◽  
P. D. Weidman
Keyword(s):  
Linear Stability ◽  
Couette Flow

scholarly journals On the linear stability of compressible plane Couette flow

1994 ◽  
Vol 258 ◽  
pp. 131-165 ◽  
Author(s):  
Peter W. Duck ◽  
Gordon Erlebacher ◽  
M. Yousuff Hussaini
Keyword(s):  
Linear Stability ◽  
Couette Flow ◽  
Small Amplitude ◽  
Reynolds Numbers ◽  
Inviscid Limit ◽  
Plane Couette Flow ◽  
Moving Wall ◽  
Type Boundary ◽  
The Stability ◽  
Radiation Type

The linear stability of compressible plane Couette flow is investigated. The appropriate basic velocity and temperature distributions are perturbed by a small-amplitude normal-mode disturbance. The full small-amplitude disturbance equations are solved numerically at finite Reynolds numbers, and the inviscid limit of these equations is then investigated in some detail. It is found that instabilities can occur, although the corresponding growth rates are often quite small; the stability characteristics of the flow are quite different from unbounded flows. The effects of viscosity are also calculated, asymptotically, and shown to have a stabilizing role in all the cases investigated. Exceptional regimes to the problem occur when the wave speed of the disturbances approaches the velocity of either of the walls, and these regimes are also analysed in some detail. Finally, the effect of imposing radiation-type boundary conditions on the upper (moving) wall (in place of impermeability) is investigated, and shown to yield results common to both bounded and unbounded flows.

Nonlinear dynamics of viscoelastic Taylor–Couette flow: effect of elasticity on pattern selection, molecular conformation and drag

2009 ◽  
Vol 620 ◽  
pp. 353-382 ◽  
Author(s):  
D. G. THOMAS ◽  
B. KHOMAMI ◽  
R. SURESHKUMAR
Keyword(s):  
Shear Rate ◽  
Linear Stability ◽  
Couette Flow ◽  
Drag Force ◽  
Molecular Conformation ◽  
Vortex Structures ◽  
Time Dependent ◽  
Pattern Selection ◽  
Stability Threshold ◽  
Flow Transitions

Three-dimensional and time-dependent simulations of viscoelastic Taylor–Couette flow of dilute polymer solutions are performed using a fully implicit parallel spectral time-splitting algorithm to discover flow patterns with various spatio-temporal symmetries, namely rotating standing waves (RSWs), disordered oscillations (DOs) and solitary vortex structures referred to as oscillatory strips (OSs) and diwhirls (DWs). A detailed account of the impact of flow transitions on molecular conformation and viscoelastic stress, velocity profiles, hydrodynamic drag force and energy spectra of time-dependent flow states is presented. Overall, predicted pattern selection and flow features compare very favourably with experimental observations. For elasticity number E, that signifies the ratio of elastic to viscous forces, >0.1, and when the shear rate (cylinder rotation speed) is increased above the linear stability threshold, the circular Couette flow (CCF) becomes unstable to RSWs which are characterized by a checkerboard-like pattern in the space–time plot of radial velocity, implying symmetry between inflow/outflow (I/O) regions. As the shear rate is further increased, perturbations that break the I/O symmetry are amplified leading to DOs and/or flame-like patterns with spectral mechanical energy transfer reminiscent of elastically induced low-Reynolds-number turbulence. However, when the shear rate is decreased from those at which such chaotic states are observed, the radially inward acting polymer body force created by flow-induced molecular stretching causes the development of narrow inflow regions surrounded by much broader weak outflow domains. This promotes the formation of solitary vortex structures, which can be stationary and axisymmetric (DWs) or time-dependent (OSs). The dynamics of the formation of these structures by merging and coalescence of vortex pairs and the implication of such events on instantaneous hydrodynamic force are studied. For O(1) values of E, OSs and DWs appear approximately at constant values of the We, defined as the ratio of polymer relaxation time to the inverse shear rate in the gap. As shear rate is decreased further, DWs decay to CCF although at We values less than the linear stability threshold. The flow transitions are hysteretic with respect to We, as evidenced by a plot of drag force versus We.

scholarly journals Decomposition of the temporal growth rate in linear instability of compressible gas flows

2015 ◽  
Vol 778 ◽  
pp. 120-132 ◽  
Author(s):  
Mario Weder ◽  
Michael Gloor ◽  
Leonhard Kleiser
Keyword(s):  
Growth Rate ◽  
Energy Balance ◽  
Linear Stability ◽  
Couette Flow ◽  
Stability Theory ◽  
Compressible Flows ◽  
Linear Instability ◽  
Linear Stability Theory ◽  
Gas Flows ◽  
Temporal Growth Rate

We present a decomposition of the temporal growth rate ${\it\omega}_{i}$ which characterises the evolution of wave-like disturbances in linear stability theory for compressible flows. The decomposition is based on the disturbance energy balance by Chu (Acta Mech., vol. 1 (3), 1965, pp. 215–234) and provides terms for production, dissipation and flux of energy as components of ${\it\omega}_{i}$. The inclusion of flux terms makes our formulation applicable to unconfined flows and flows with permeable or vibrating boundaries. The decomposition sheds light on the fundamental mechanisms determining temporal growth or decay of disturbances. The additional insights gained by the proposed approach are demonstrated by an investigation of two model flows, namely compressible Couette flow and a plane compressible jet.

The influence of initial condition on the linear stability of time-dependent circular Couette flow

1985 ◽  
Vol 28 (2) ◽  
pp. 749 ◽  
Author(s):  
J.-C. Chen ◽  
G. P. Neitzel ◽  
D. F. Jankowski
Keyword(s):  
Linear Stability ◽  
Couette Flow ◽  
Time Dependent ◽  
Initial Condition ◽  
Circular Couette Flow

Linear stability of Couette flow of vibrationally non-equilibrium gas

2016 ◽  
Author(s):  
Yurii N. Grigor’ev ◽  
Igor’ V. Ershov
Keyword(s):  
Linear Stability ◽  
Couette Flow ◽  
Non Equilibrium

Linear stability of cylindrical Couette flow in the convection regime

2005 ◽  
Vol 17 (5) ◽  
pp. 054112 ◽  
Author(s):  
Mohamed E. Ali ◽  
G. B. McFadden
Keyword(s):  
Linear Stability ◽  
Couette Flow ◽  
Convection Regime ◽  
Cylindrical Couette Flow
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