scholarly journals Instability and transition to turbulence in a free shear layer affected by a parallel magnetic field

2007 ◽  
Vol 574 ◽  
pp. 131-154 ◽  
Author(s):  
A. VOROBEV ◽  
O. ZIKANOV
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Shear Layer ◽  
Three Dimensional ◽  
Magnetic Reynolds Number ◽  
Transition To Turbulence ◽  
Free Shear Layer ◽  
Parallel Magnetic Field ◽  
Oblique Waves ◽  
Electrically Conducting

Instability and transition to turbulence in a temporally evolving free shear layer of an electrically conducting fluid affected by an imposed parallel magnetic field is investigated numerically. The case of low magnetic Reynolds number is considered. It has long been known that the neutral disturbances of the linear problem are three-dimensional at sufficiently strong magnetic fields. We analyse the details of this instability solving the generalized Orr–Sommerfeld equation to determine the wavenumbers, growth rates and spatial shapes of the eigenmodes. The three-dimensional perturbations are identified as oblique waves and their properties are described. In particular, we find that at high hydrodynamic Reynolds number, the effect of the strength of the magnetic field on the fastest growing perturbations is limited to an increase of their oblique angle. The dimensions and spatial shape of the waves remain unchanged. The transition to turbulence triggered by the growing oblique waves is investigated in direct numerical simulations. It is shown that initial perturbations in the form of superposition of two symmetric waves are particularly effective in inducing three-dimensionality and turbulence in the flow.

Hydromagnetic instability of a free shear layer at small magnetic Reynolds numbers

1971 ◽  
Vol 49 (1) ◽  
pp. 21-31 ◽  
Author(s):  
Kanefusa Gotoh
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Shear Layer ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Free Shear Layer ◽  
Electrically Conducting ◽  
The Stability ◽  
The Magnetic Field

The effect of a uniform and parallel magnetic field upon the stability of a free shear layer of an electrically conducting fluid is investigated. The equations of the velocity and the magnetic disturbances are solved numerically and it is shown that the flow is stabilized with increasing magnetic field. When the magnetic field is expressed in terms of the parameter N (= M2/R2), where M is the Hartmann number and R is the Reynolds number, the lowest critical Reynolds number is caused by the two-dimensional disturbances. So long as 0 [les ] N [les ] 0·0092 the flow is unstable at all R. For 0·0092 < N [les ] 0·0233 the flow is unstable at 0 < R < Ruc where Ruc decreases as N increases. For 0·0233 < N < 0·0295 the flow is unstable at Rlc < R < Ruc where Rlc increases with N. Lastly for N > 0·0295 the flow is stable at all R. When the magnetic field is measured by M, the lowest critical Reynolds number is still due to the two-dimensional disturbances provided 0 [les ] M [les ] 0·52, and Rc is given by the corresponding Rlc. For M > 0·52, Rc is expressed as Rc = 5·8M, and the responsible disturbance is the three-dimensional one which propagates at angle cos−1(0·52/M) to the direction of the basic flow.

Development of a three-dimensional free shear layer

1998 ◽  
Vol 369 ◽  
pp. 49-89 ◽  
Author(s):  
A. J. RILEY ◽  
M. V. LOWSON
Keyword(s):  
Shear Layer ◽  
Flow Instability ◽  
Delta Wing ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Transition To Turbulence ◽  
Free Shear Layer ◽  
Velocity Data ◽  
Sweep Angle ◽  
Vortical Structures

Experiments have been undertaken to characterize the flow field over a delta wing, with an 85° sweep angle, at 12.5° incidence. Application of a laser Doppler anemometer has enabled detailed three-dimensional velocity data to be obtained within the free shear layer, revealing a system of steady co-rotating vortical structures. These sub-vortex structures are associated with low-momentum flow pockets in the separated vortex flow. The structures are found to be dependent on local Reynolds number, and undergo transition to turbulence. The structural features disappear as the sub-vortices are wrapped into the main vortex core. A local three-dimensional Kelvin–Helmholtz-type instability is suggested for the formation of these vortical structures in the free shear layer. This instability has parallels with the cross-flow instability that occurs in three-dimensional boundary layers. Velocity data at high Reynolds numbers have shown that the sub-vortical structures continue to form, consistent with flow visualization results over fighter aircraft at flight Reynolds numbers.

Optimal Growth and Transition to Turbulence in Magnetohydrodynamic Duct Flow

2010 ◽  
Author(s):  
Dmitry Krasnov ◽  
Oleg Zikanov ◽  
Maurice Rossi ◽  
Thomas Boeck
Keyword(s):  
Magnetic Field ◽  
Optimal Growth ◽  
Transition Process ◽  
Finite Amplitude ◽  
Magnetic Reynolds Number ◽  
Transition To Turbulence ◽  
Duct Flow ◽  
Electrically Conducting ◽  
Nonlinear Mechanism ◽  
The Magnetic Field

We consider the flow of an electrically conducting fluid in a duct in the presence of a constant magnetic field perpendicular to the flow. The technologically relevant approximation of small magnetic Reynolds number is adopted. The focus of investigation is on the nonlinear mechanism of transition consisting of transient growth and subsequent breakdown of finite amplitude perturbations. Numerical analysis demonstrates that the strongest growth is experienced by perturbations localized in the sidewall boundary layers parallel to the imposed magnetic field. This result and the direct numerical simulations of the transition process indicate that the commonly accepted picture of the transition in MHD duct based on the numerical and theoretical analysis of the flow in the Hartmann channel is misleading. The flow may become turbulent within the sidewall layers long before the Hartmann layers on the walls perpendicular to the magnetic field are able to sustain nonlinear transition.

Shear Layer Transition and the Sharp-Edged Orifice

1980 ◽  
Vol 102 (2) ◽  
pp. 219-222 ◽  
Author(s):  
J. A. Clark ◽  
Lam Kit
Keyword(s):  
Shear Layer ◽  
Growth Pattern ◽  
Three Dimensional ◽  
Growth Patterns ◽  
Transition To Turbulence ◽  
Free Shear Layer ◽  
Layer Transition ◽  
Vortex Shedding Frequency ◽  
Vortex Tubes ◽  
Mutual Induction

The present experiments provide information about free shear layer transition to turbulence and the associated three-dimensional behavior patterns of vortex growth and breakdown. The free shear layers of a submerged jet were generated from two-dimensional sharp-edged orifices. Two distinct types of growth patterns, namely, the twisting growth pattern and the interlocking growth pattern were observed. The interaction phenomena of these vortex tubes are hypothesized to be associated with mutual induction. Quantitative data of exit central velocity, pre-coalescent wavelength between consecutive vortices, and vortex shedding frequency were measured and the interrelationships of Strouhal number, Reynolds number and the dimensionless convection velocity of vortices are discussed.

Effects of wavelength and amplitude of a wavy cylinder in cross-flow at low Reynolds numbers

2009 ◽  
Vol 620 ◽  
pp. 195-220 ◽  
Author(s):  
K. LAM ◽  
Y. F. LIN
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Circular Cylinder ◽  
Drag Coefficient ◽  
Shear Layer ◽  
Lift Coefficient ◽  
Three Dimensional ◽  
Spanwise Direction ◽  
Free Shear Layer ◽  
The Mean

Three-dimensional numerical simulations of laminar flow around a circular cylinder with sinusoidal variation of cross-section along the spanwise direction, named ‘wavy cylinder’, are performed. A series of wavy cylinders with different combinations of dimensionless wavelength (λ/Dm) and wave amplitude (a/Dm) are studied in detail at a Reynolds number of Re = U∞Dm/ν = 100, where U∞ is the free-stream velocity and Dm is the mean diameter of a wavy cylinder. The results of variation of mean drag coefficient and root mean square (r.m.s.) lift coefficient with dimensionless wavelength show that significant reduction of mean and fluctuating force coefficients occurs at optimal dimensionless wavelengths λ/Dm of around 2.5 and 6 respectively for the different amplitudes studied. Based on the variation of flow structures and force characteristics, the dimensionless wavelength from λ/Dm = 1 to λ/Dm = 10 is classified into three wavelength regimes corresponding to three types of wake structures. The wake structures at the near wake of different wavy cylinders are captured. For all wavy cylinders, the flow separation line varies along the spanwise direction. This leads to the development of a three-dimensional free shear layer with periodic repetition along the spanwise direction. The three-dimensional free shear layer of the wavy cylinder is larger and more stable than that of the circular cylinder, and in some cases the free shear layer even does not roll up into a mature vortex street behind the cylinder. As a result, the mean drag coefficients of some of the typical wavy cylinders are less than that of a corresponding circular cylinder with a maximum drag coefficient reduction up to 18%. The r.m.s. lift coefficients are greatly reduced to practically zero at optimal wavelengths. In the laminar flow regime (60 ≤ Re ≤ 150), the values of optimal wavelength are Reynolds number dependent.

The magneto-hydrodynamic boundary layer in the two-dimensional steady flow past a semi-infinite flat plate. I. Uniform conditions at infinity

1963 ◽  
Vol 273 (1355) ◽  
pp. 496-508 ◽  
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Drag Coefficient ◽  
Flat Plate ◽  
Magnetic Reynolds Number ◽  
Linear Ordinary Differential Equations ◽  
Electrically Conducting ◽  
The Magnetic Field ◽  
Conditions At Infinity

The problem investigated is the flow of a viscous, electrically conducting liquid past a fixed, semi-infinite, unmagnetized but conducting flat plate. The liquid flow U and also the magnetic field H 0 at a distance from the plate are both assumed to be uniform and parallel to the plate. It is assumed that the Reynolds number R and magnetic Reynolds number R m are large enough for momentum and magnetic boundary layers to have developed. The standard boundary-layer techniques as used in the Blasius solution then apply and the problem reduces to the solution of two simultaneous non-linear ordinary differential equations. These are examined by the use of an iteration method suggested in the non ­ magnetic problem by Weyl and a solution of reasonable accuracy has been obtained for the drag coefficient. This confirms a similar result obtained in a different way by Carrier & Greenspan. The principal result of the paper is that the boundary layer thickens and drag coefficient diminishes steadily as the parameter S = µH 2 0 / 4πρU 2 increases. When S attains the finite value of unity the drag coefficient obtained here actually vanishes with the flow having been reduced to rest by the action of the magnetic field. This result might be inferred qualitatively since a finite amount of work has to be done in conveying liquid particles across the lines of magnetic force.

scholarly journals Exact two-dimensionalization of low-magnetic-Reynolds-number flows subject to a strong magnetic field

2015 ◽  
Vol 773 ◽  
pp. 154-177 ◽  
Author(s):  
Basile Gallet ◽  
Charles R. Doering
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Turbulent Flows ◽  
Three Dimensional ◽  
Vertical Direction ◽  
Threshold Value ◽  
Magnetic Reynolds Number ◽  
Mhd Equations ◽  
Static Approximation ◽  
Long Time

We investigate the behaviour of flows, including turbulent flows, driven by a horizontal body force and subject to a vertical magnetic field, with the following question in mind: for a very strong applied magnetic field, is the flow mostly two-dimensional, with remaining weak three-dimensional fluctuations, or does it become exactly 2-D, with no dependence along the vertical direction? We first focus on the quasi-static approximation, i.e. the asymptotic limit of vanishing magnetic Reynolds number, $\mathit{Rm}\ll 1$: we prove that the flow becomes exactly 2-D asymptotically in time, regardless of the initial condition and provided that the interaction parameter $N$ is larger than a threshold value. We call this property absolute two-dimensionalization: the attractor of the system is necessarily a (possibly turbulent) 2-D flow. We then consider the full magnetohydrodynamic (MHD) equations and prove that, for low enough $\mathit{Rm}$ and large enough $N$, the flow becomes exactly 2-D in the long-time limit provided the initial vertically dependent perturbations are infinitesimal. We call this phenomenon linear two-dimensionalization: the (possibly turbulent) 2-D flow is an attractor of the dynamics, but it is not necessarily the only attractor of the system. Some 3-D attractors may also exist and be attained for strong enough initial 3-D perturbations. These results shed some light on the existence of a dissipation anomaly for MHD flows subject to a strong external magnetic field.

scholarly journals Hall Effect on MHD Transient Flow Past an Impulsively Started Infinite Horizontal Porous Plate in a Rotating System

2018 ◽  
Vol 23 (2) ◽  
pp. 471-483 ◽  
Author(s):  
B. Prabhakar Reddy
Keyword(s):  
Magnetic Field ◽  
Transient Flow ◽  
Porous Plate ◽  
Three Dimensional ◽  
Magnetic Reynolds Number ◽  
Physical Parameters ◽  
Rotating System ◽  
Electrically Conducting ◽  
Secondary Velocity ◽  
Horizontal Porous Plate

Abstract In this paper, the effect of Hall current on an unsteady MHD transient three dimensional flow of an electrically conducting viscous incompressible fluid past an impulsively started infinite horizontal porous plate relative to a rotating system has been studied. It is assumed that the entire system rotates with a constant angular velocity about the normal to the plate and a uniform magnetic field is applied along the normal to the plate and directed into the fluid region. The magnetic Reynolds number is assumed to be so small that the induced magnetic field can be neglected. The expressions for the primary and secondary fields and shearing stress at the plate due to primary and secondary velocity fields are obtained in a non-dimensional form. The non-dimensional governing equations of the flow are solved by using the Galerkin FEM. The effects of the physical parameters, such as the Hartmann number (M), rotation parameter (Ω), porosity parameter (K) and Hall parameter (m) on primary and secondary velocities and shearing stresses τx and τy due to primary and secondary velocities are discussed through graphs and tables, and results are physically interpreted.

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