Quasi-Two-Dimensional Turbulence in MHD Shear Flows : The “MATUR” Experiment and Simulations

1999 ◽  
pp. 93-106 ◽  
Author(s):  
Y. Delannoy ◽  
B. Pascal ◽  
T. Alboussiere ◽  
V. Uspenski ◽  
R. Moreau
Keyword(s):  
Shear Flows ◽  
Two Dimensional

Reynolds stresses and mean fields generated by pure waves: applications to shear flows and convection in a rotating shell

2008 ◽  
Vol 602 ◽  
pp. 303-326 ◽  
Author(s):  
E. PLAUT ◽  
Y. LEBRANCHU ◽  
R. SIMITEV ◽  
F. H. BUSSE
Keyword(s):  
Shear Flows ◽  
Rossby Waves ◽  
Zonal Flow ◽  
Quantitative Agreement ◽  
Model Systems ◽  
Geometrical Factor ◽  
Wave Flow ◽  
Nonlinear Frequency ◽  
Two Dimensional ◽  
Reynolds Stresses

A general reformulation of the Reynolds stresses created by two-dimensional waves breaking a translational or a rotational invariance is described. This reformulation emphasizes the importance of a geometrical factor: the slope of the separatrices of the wave flow. Its physical relevance is illustrated by two model systems: waves destabilizing open shear flows; and thermal Rossby waves in spherical shell convection with rotation. In the case of shear-flow waves, a new expression of the Reynolds–Orr amplification mechanism is obtained, and a good understanding of the form of the mean pressure and velocity fields created by weakly nonlinear waves is gained. In the case of thermal Rossby waves, results of a three-dimensional code using no-slip boundary conditions are presented in the nonlinear regime, and compared with those of a two-dimensional quasi-geostrophic model. A semi-quantitative agreement is obtained on the flow amplitudes, but discrepancies are observed concerning the nonlinear frequency shifts. With the quasi-geostrophic model we also revisit a geometrical formula proposed by Zhang to interpret the form of the zonal flow created by the waves, and explore the very low Ekman-number regime. A change in the nature of the wave bifurcation, from supercritical to subcritical, is found.

Three-dimensional vortex formation from an oscillating, non-uniform cylinder

1992 ◽  
Vol 238 ◽  
pp. 31-54 ◽  
Author(s):  
F. Nuzzi ◽  
C. Magness ◽  
D. Rockwell
Keyword(s):  
Flow Structure ◽  
Phase Plane ◽  
Shear Flows ◽  
Vortex Formation ◽  
Excitation Frequency ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Near Wake ◽  
Shedding Frequency

A cylinder having mild variations in diameter along its span is subjected to controlled excitation at frequencies above and below the inherent shedding frequency from the corresponding two-dimensional cylinder. The response of the near wake is characterized in terms of timeline visualization and velocity traces, spectra, and phase plane representations. It is possible to generate several types of vortex formation, depending upon the excitation frequency. Globally locked-in, three-dimensional vortex formation can occur along the entire span of the flow. Regions of locally locked-in and period-doubled vortex formation can exist along different portions of the span provided the excitation frequency is properly tuned. Unlike the classical subharmonic instability in free shear flows, the occurrence of period-doubled vortex formation does not involve vortex coalescence; instead, the flow structure alternates between two different states.

Shear Flows in Two Dimensional Strongly Coupled Yukawa Liquids: A Large Scale Molecular Dynamics Study

2011 ◽  
Author(s):  
R. Ganesh ◽  
J. Ashwin ◽  
Vladimir Yu. Nosenko ◽  
Padma K. Shukla ◽  
Markus H. Thoma ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Large Scale ◽  
Shear Flows ◽  
Two Dimensional ◽  
Strongly Coupled

scholarly journals Eigenvalues in trailing edge flows

1975 ◽  
Vol 19 (2) ◽  
pp. 210-221
Author(s):  
K. Capell
Keyword(s):  
Asymptotic Formula ◽  
Flat Plate ◽  
Similarity Solution ◽  
Shear Flows ◽  
Two Dimensional ◽  
Trailing Edge ◽  
Uniform Shear

Abstract A wake similarity solution for symmetric uniform shear flows merging at the trailing edge of a flat plate has associated with it an eigenfunction problem which was overlooked by Hakkinen and O'Neil (1967). An asymptotic formula for large eigenvalues is obtained and compared with another such formula related to both the Goldstein (1930) inner wake solution and Tillett's (1968) similarity solution for a jet emerging from a two-dimensional channel.

Optimal perturbations in time-dependent variable-density Kelvin–Helmholtz billows

2016 ◽  
Vol 803 ◽  
pp. 466-501 ◽  
Author(s):  
Adriana Lopez-Zazueta ◽  
Jérôme Fontane ◽  
Laurent Joly
Keyword(s):  
Saddle Point ◽  
Shear Flows ◽  
Longitudinal Velocity ◽  
Three Dimensional ◽  
Variable Density ◽  
Energy Gain ◽  
Time Dependent ◽  
Two Dimensional ◽  
Energy Growth ◽  
Atwood Number

We analyse the influence of the specific features of time-dependent variable-density Kelvin–Helmholtz (VDKH) roll-ups on the development of three-dimensional secondary instabilities. Due to inertial (high Froude number) baroclinic sources of spanwise vorticity at high Atwood number (up to 0.5 here), temporally evolving mixing layers exhibit a layered structure associated with a strain field radically different from their homogeneous counterpart. We use a direct-adjoint non-modal linear approach to determine the fastest growing perturbations over a single period of the time-evolving two-dimensional base flow during a given time interval $[t_{0},T]$. When perturbations are seeded at the initial time of the primary KH mode growth, i.e. $t_{0}=0$, it is found that additional mechanisms of energy growth are onset around a bifurcation time $t_{b}$, a little before the saturation of the primary two-dimensional instability. The evolution of optimal perturbations is thus observed to develop in two distinct stages. Whatever the Atwood number, the first period $[t_{0},t_{b}]$ is characterised by a unique route for optimal energy growth resulting from a combination of the Orr and lift-up transient mechanisms. In the second period $[t_{b},T]$, the growing influence of mass inhomogeneities raises the energy gain over the whole range of spanwise wavenumbers. As the Atwood number increases, the short spanwise wavelength perturbations tend to benefit more from the onset of variable-density effects than large wavelength ones. The extra energy gain due to increasing Atwood numbers relies on contributions from spanwise baroclinic sources. The resulting vorticity field is structured into two elongated dipoles localised along the braid on either side of the saddle point. In return they yield two longitudinal velocity streaks of opposite sign which account for most of the energy growth. This transition towards three-dimensional motions is in marked contrast with the classic streamwise rib vortices, so far accepted as the paradigm for the transition of free shear flows, either homogeneous or not. It is argued that the emergence of these longitudinal velocity streaks is generic of the transition in variable-density shear flows. Among them, the light round jet is known to display striking side ejections as a result of the loss of axisymmetry. The present analysis helps to renew the question of the underlying flow structure behind side jets, otherwise based on radial induction between pairs of counter-rotating longitudinal vortices (Monkewitz & Pfizenmaier, Phys. Fluids A, vol. 3 (5), 1991, pp. 1356–1361). Instead, it is more likely that side ejections would result from the convergence of the longitudinal velocity streaks near the braid saddle point. When the injection time is delayed so as to suppress the initial stage of energy growth, a new class of perturbations arises at low wavenumber with energy gains far larger than those observed so far. They correspond to the two-dimensional Kelvin–Helmholtz secondary instability of the baroclinically enhanced vorticity braid discovered by Reinaud et al. (Phys. Fluids, vol. 12 (10), pp. 2489–2505), leading potentially to another route to turbulence through a two-dimensional fractal cascade.

Re-examination of vorticity transfer theory

1977 ◽  
Vol 354 (1676) ◽  
pp. 1-8 ◽  
Keyword(s):  
Momentum Transfer ◽  
Turbulent Diffusion ◽  
Constant Coefficient ◽  
Shear Flows ◽  
Turbulent Shear ◽  
System Of Equations ◽  
Two Dimensional ◽  
Exchange Coefficient ◽  
Loss Of Information ◽  
Transfer Theory

The averaging procedure required to generate the Reynolds equations for turbulent shear flows results in a loss of information. The system of equations is no longer closed, and additional assumptions are required. The classical closure assumptions are based on Taylor’s (1915, 1932) vorticity transfer theory and Prandtl’s (1925, 1942) momentum transfer theory. In this paper we show that the former is in a very fundamental sense incorrect in that only for very special forms of the eddy exchange coefficient (including a constant coefficient) does turbulent ‘diffusion’ of vorticity also conserve momentum. For expository purposes much of the discussion is centred on an idealized simple two dimensional wake in which momentum and vorticity are conserved transferable properties.

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