scholarly journals Stability of plane Couette flow for high Reynolds number

1983 ◽  
Vol 24 (3) ◽  
pp. 350-357 ◽  
Author(s):  
G. B. Davis ◽  
A. G. Morris
Keyword(s):  
Reynolds Number ◽  
Experimental Evidence ◽  
Linear Stability ◽  
Couette Flow ◽  
Stability Theory ◽  
High Reynolds Number ◽  
Numerical Technique ◽  
Linear Stability Theory ◽  
Plane Couette Flow ◽  
High Reynolds

AbstractExperimental evidence shows that plane Couette flow becomes unstable when the Reynolds number R reaches certain critical values. Linear stability theory does not predict these observations and has been unable to locate these instabilities. A Chebyshev/QR numerical technique is used to investigate much higher values of R than those previously tested. In particular, values of R up to 108 are confidently tested, whereas previously values of R up to only 2 × 104 have been considered.

The high-Reynolds-number asymptotic development of nonlinear equilibrium states in plane Couette flow

2014 ◽  
Vol 750 ◽  
pp. 99-112 ◽  
Author(s):  
Kengo Deguchi ◽  
Philip Hall
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
High Reynolds Number ◽  
Shear Flows ◽  
Stokes Equations ◽  
Entangled States ◽  
Plane Couette Flow ◽  
Long Wavelength ◽  
Nonlinear Equilibrium ◽  
High Reynolds

AbstractThe relationship between nonlinear equilibrium solutions of the full Navier–Stokes equations and the high-Reynolds-number asymptotic vortex–wave interaction (VWI) theory developed for general shear flows by Hall & Smith (J. Fluid Mech., vol. 227, 1991, pp. 641–666) is investigated. Using plane Couette flow as a prototype shear flow, we show that all solutions having $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}O(1)$ wavenumbers converge to VWI states with increasing Reynolds number. The converged results here uncover an upper branch of VWI solutions missing from the calculations of Hall & Sherwin (J. Fluid Mech., vol. 661, 2010, pp. 178–205). For small values of the streamwise wavenumber, the converged lower-branch solutions take on the long-wavelength state of Deguchi, Hall & Walton (J. Fluid Mech., vol. 721, 2013, pp. 58–85) while the upper-branch solutions are found to be quite distinct, with new states associated with instabilities of jet-like structures playing the dominant role. Between these long-wavelength states, a complex ‘snaking’ behaviour of solution branches is observed. The snaking behaviour leads to complex ‘entangled’ states involving the long-wavelength states and the VWI states. The entangled states exhibit different-scale fluid motions typical of those found in shear flows.

scholarly journals Catastrophic Phase Inversion in High-Reynolds-Number Turbulent Taylor-Couette Flow

2021 ◽  
Vol 126 (6) ◽  
Author(s):  
Dennis Bakhuis ◽  
Rodrigo Ezeta ◽  
Pim A. Bullee ◽  
Alvaro Marin ◽  
Detlef Lohse ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
Phase Inversion ◽  
High Reynolds Number ◽  
Taylor Couette ◽  
High Reynolds ◽  
Taylor Couette Flow

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.

Fine Scale Structure of High Reynolds Number Taylor-Couette Flow

2007 ◽  
Author(s):  
W. He ◽  
M. Tanahashi ◽  
T. Miyauchi
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
High Reynolds Number ◽  
Flow Fields ◽  
Fine Scale ◽  
Azimuthal Direction ◽  
Taylor Vortices ◽  
Taylor Couette ◽  
High Reynolds ◽  
Taylor Couette Flow

Direct numerical simulation (DNS) has been conducted to investigate turbulence transition process and fine scale structures in Taylor-Couette flow. Fourier-Chebyshev spectral methods have been used for spatial discretization and DNS are conducted up to Re = 12000. With the increase of Reynolds number, fine scale eddies are formed in a stepwise fashion. In relatively weak turbulent Taylor-Couette flow, fine scale eddies elongated in the azimuthal direction appear near the outflow and inflow boundaries between Taylor vortices. These fine scale eddies in the outflow and inflow boundaries are inclined at about −45/135 degree with respect to the azimuthal direction. With the increase of Reynolds number, the number of fine scale eddies increases and fine scale eddies appear in whole flow fields. The Taylor vortices in high Reynolds number organize lots of fine scale eddies. In high Reynolds number Taylor-Couette flow, fine scale eddies parallel to the axial direction are formed in sweep regions between large scale Taylor vortices. The most expected diameter and maximum azimuthal velocity of coherent fine scale eddies are 8 times of Kolmogorov scale and 1.7 times of Kolmogorov velocity respectively for high Reynolds Taylor-Couette flow. This scaling law coincides with that in other turbulent flow fields.

Curvature- and rotation-induced instabilities in channel flow

1990 ◽  
Vol 210 ◽  
pp. 537-563 ◽  
Author(s):  
O. John E. Matsson ◽  
P. Henrik Alfredsson
Keyword(s):  
Reynolds Number ◽  
Linear Stability ◽  
Channel Flow ◽  
Stability Theory ◽  
Critical Reynolds Number ◽  
Secondary Instability ◽  
Linear Stability Theory ◽  
Curved Channel ◽  
Dean Vortices ◽  
Coriolis Effects

In a curved channel streamwise vortices, often called Dean vortices, may develop above a critical Reynolds number owing to centrifugal effects. Similar vortices can occur in a rotating plane channel due to Coriolis effects if the axis of rotation is normal to the mean flow velocity and parallel to the walls. In this paper the flow in a curved rotating channel is considered. It is shown from linear stability theory that there is a region for which centrifugal effects and Coriolis effects almost cancel each other, which increases the critical Reynolds number substantially. The flow visualization experiments carried out show that a complete cancellation of Dean vortices can be obtained for low Reynolds number. The rotation rate for which this occurs is in close agreement with predictions from linear stability theory. For curved channel flow a secondary instability of travelling wave type is found at a Reynolds number about three times higher than the critical one for the primary instability. It is shown that rotation can completely cancel the secondary instability.

The development of a two-dimensional wavepacket in a growing boundary layer

1982 ◽  
Vol 384 (1787) ◽  
pp. 317-332 ◽  
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Linear Stability ◽  
Stability Theory ◽  
Linear Stability Theory ◽  
Two Dimensional ◽  
Displacement Thickness ◽  
Power Comparisons ◽  
The One ◽  
Half Power

The evolution of a two-dimensional wavepacket in a growing boundary layer is discussed in terms of linear stability theory. The wavepacket is represented by an integral of periodic wavetrains, each of which is defined as a series in terms of the inverse of the local displacement thickness Reynolds number to the one half power. Comparisons are made between the waveforms computed directly from the integral, a steepest-descent expansion of the integral, and a global expansion about the peak of the wavepacket.

scholarly journals RANS study of very high Reynolds-number plane turbulent Couette flow

2020 ◽  
Vol 14 (2) ◽  
pp. 6663-6678
Author(s):  
Akshay Sherikar ◽  
P. J. Disimile
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
High Reynolds Number ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Shear Stresses ◽  
Sensitivity Testing ◽  
Wall Functions ◽  
High Reynolds ◽  
Very High

The objective of this study is to expound on the deliverables of a steady-state RANS (Reynolds Averaged Navier Stokes) simulation in one of the simplest flows, Couette flow, at a very high Reynolds number. To that end, a process to perform better grid sensitivity testing is introduced. Three two-equation turbulence models ( , , and ) are compared against each other as well as pitted against formal literature on the subject and core flow velocities, slopes, wall-bounded velocities, shear stresses and kinetic energies are analyzed.  applied with enhanced wall functions is consistently found to be in better agreement with previous studies. Finally, plane turbulent Couette flow at  51,099, the range at which it has not been studied experimentally, numerically or analytically in former studies, is simulated. The results are found to be consistent with the trends asserted by literature and preliminary computations of this study.

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