scholarly journals Transport and instability in driven two-dimensional magnetohydrodynamic flows

2016 ◽  
Vol 799 ◽  
pp. 541-578 ◽  
Author(s):  
Sam Durston ◽  
Andrew D. Gilbert
Keyword(s):  
Magnetic Field ◽  
Time Scale ◽  
Large Scale ◽  
Body Force ◽  
Passive Scalar ◽  
Fast Time ◽  
Two Dimensional ◽  
Mean Flow ◽  
The Mean ◽  
Background Shear

This paper concerns the generation of large-scale flows in forced two-dimensional systems. A Kolmogorov flow with a sinusoidal profile in one direction (driven by a body force) is known to become unstable to a large-scale flow in the perpendicular direction at a critical Reynolds number. This can occur in the presence of a ${\it\beta}$-effect and has important implications for flows observed in geophysical and astrophysical systems. It has recently been termed ‘zonostrophic instability’ and studied in a variety of settings, both numerically and analytically. The goal of the present paper is to determine the effect of magnetic field on such instabilities using the quasi-linear approximation, in which the full fluid system is decoupled into a mean flow and waves of one scale. The waves are driven externally by a given random body force and move on a fast time scale, while their stress on the mean flow causes this to evolve on a slow time scale. Spatial scale separation between waves and mean flow is also assumed, to allow analytical progress. The paper first discusses purely hydrodynamic transport of vorticity including zonostrophic instability, the effect of uniform background shear and calculation of equilibrium profiles in which the effective viscosity varies spatially, through the mean flow. After brief consideration of passive scalar transport or equivalently kinematic magnetic field evolution, the paper then proceeds to study the full magnetohydrodynamic system and to determine effective diffusivities and other transport coefficients using a mixture of analytical and numerical methods. This leads to results on the effect of magnetic field, background shear and ${\it\beta}$-effect on zonostrophic instability and magnetically driven instabilities.

scholarly journals WKB theory for rapid distortion of inhomogeneous turbulence

1999 ◽  
Vol 390 ◽  
pp. 325-348 ◽  
Author(s):  
S. NAZARENKO ◽  
N. K.-R. KEVLAHAN ◽  
B. DUBRULLE
Keyword(s):  
Large Scale ◽  
Isotropic Turbulence ◽  
Two Dimensional ◽  
Turbulent Spot ◽  
Mean Flow ◽  
Mean Velocity ◽  
Inhomogeneous Turbulence ◽  
Large Scale Vortex ◽  
The Mean ◽  
Mean Strain

A WKB method is used to extend RDT (rapid distortion theory) to initially inhomogeneous turbulence and unsteady mean flows. The WKB equations describe turbulence wavepackets which are transported by the mean velocity and have wavenumbers which evolve due to the mean strain. The turbulence also modifies the mean flow and generates large-scale vorticity via the averaged Reynolds stress tensor. The theory is applied to Taylor's four-roller flow in order to explain the experimentally observed reduction in the mean strain. The strain reduction occurs due to the formation of a large-scale vortex quadrupole structure from the turbulent spot confined by the four rollers. Both turbulence inhomogeneity and three-dimensionality are shown to be important for this effect. If the initially isotropic turbulence is either homogeneous in space or two-dimensional, it has no effect on the large-scale strain. Furthermore, the turbulent kinetic energy is conserved in the two-dimensional case, which has important consequences for the theory of two-dimensional turbulence. The analytical and numerical results presented here are in good qualitative agreement with experiment.

Structural stability theory of two-dimensional fluid flow under stochastic forcing

2011 ◽  
Vol 682 ◽  
pp. 332-361 ◽  
Author(s):  
NIKOLAOS A. BAKAS ◽  
PETROS J. IOANNOU
Keyword(s):  
Structural Stability ◽  
Stability Theory ◽  
Large Scale ◽  
Random Excitation ◽  
Two Dimensional ◽  
Mean Flow ◽  
Homogeneous Fluid ◽  
Stochastic Forcing ◽  
Random Forcing ◽  
The Mean

Large-scale mean flows often emerge in turbulent fluids. In this work, we formulate a stability theory, the stochastic structural stability theory (SSST), for the emergence of jets under external random excitation. We analytically investigate the structural stability of a two-dimensional homogeneous fluid enclosed in a channel and subjected to homogeneous random forcing. We show that two generic competing mechanisms control the instability that gives rise to the emergence of an infinitesimal jet: advection of the eddy vorticity by the mean flow that is shown to be jet forming and advection of the vorticity gradient of the jet by the eddies that is shown to hinder the formation of the mean flow. We show that stochastic forcing with small streamwise coherence and an amplitude larger than a certain threshold leads to the emergence of jets in the channel through a bifurcation of the non-linear SSST system.

scholarly journals LDV Measurements Near a Vortex Shedding Strut Mounted in a Pipe

1983 ◽  
Vol 105 (2) ◽  
pp. 185-196 ◽  
Author(s):  
T. T. Yeh ◽  
Baldwin Robertson ◽  
W. M. Mattar
Keyword(s):  
Vortex Shedding ◽  
Velocity Vector ◽  
Large Scale ◽  
Laser Doppler Velocimeter ◽  
Two Dimensional ◽  
Velocity Vector Field ◽  
Mean Flow ◽  
Narrow Frequency Band ◽  
Random Components ◽  
The Mean

The velocity field around vortex shedding strut mounted in a circular pipe has been in detail with a laser Doppler velocimeter (LDV) at a pipe Reynolds number equal to 90,000. The instantaneous velocity is decomposed into mean, periodic, and random components. Only the first two harmonics are large enough to be detected; the large-scale structure can be characterized by just these two these and the mean. Profiles of the different velocity terms are given upstream of, downstream of, and close to the strut. The two-dimensional velocity vector field of the mean flow on the transverse diametral plane of symmetry is presented along with its streamlines. Finally, for each spatial component, profiles of vortex visibility, the ratio of the energy of a periodic component to the total fluctuating energy in a narrow frequency band, are given.

scholarly journals Generation of Reverse Meniscus Flow by Applying An Electromagnetic Brake

2021 ◽  
Author(s):  
Alexander Vakhrushev ◽  
Abdellah Kharicha ◽  
Ebrahim Karimi-Sibaki ◽  
Menghuai Wu ◽  
Andreas Ludwig ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Lorentz Force ◽  
Applied Magnetic Field ◽  
Numerical Study ◽  
Flow Direction ◽  
Experimental Studies ◽  
Submerged Entry Nozzle ◽  
Mean Flow ◽  
Slab Caster ◽  
The Mean

AbstractA numerical study is presented that deals with the flow in the mold of a continuous slab caster under the influence of a DC magnetic field (electromagnetic brakes (EMBrs)). The arrangement and geometry investigated here is based on a series of previous experimental studies carried out at the mini-LIMMCAST facility at the Helmholtz-Zentrum Dresden-Rossendorf (HZDR). The magnetic field models a ruler-type EMBr and is installed in the region of the ports of the submerged entry nozzle (SEN). The current article considers magnet field strengths up to 441 mT, corresponding to a Hartmann number of about 600, and takes the electrical conductivity of the solidified shell into account. The numerical model of the turbulent flow under the applied magnetic field is implemented using the open-source CFD package OpenFOAM®. Our numerical results reveal that a growing magnitude of the applied magnetic field may cause a reversal of the flow direction at the meniscus surface, which is related the formation of a “multiroll” flow pattern in the mold. This phenomenon can be explained as a classical magnetohydrodynamics (MHD) effect: (1) the closure of the induced electric current results not primarily in a braking Lorentz force inside the jet but in an acceleration in regions of previously weak velocities, which initiates the formation of an opposite vortex (OV) close to the mean jet; (2) this vortex develops in size at the expense of the main vortex until it reaches the meniscus surface, where it becomes clearly visible. We also show that an acceleration of the meniscus flow must be expected when the applied magnetic field is smaller than a critical value. This acceleration is due to the transfer of kinetic energy from smaller turbulent structures into the mean flow. A further increase in the EMBr intensity leads to the expected damping of the mean flow and, consequently, to a reduction in the size of the upper roll. These investigations show that the Lorentz force cannot be reduced to a simple damping effect; depending on the field strength, its action is found to be topologically complex.

scholarly journals Instability wave models for the near-field fluctuations of turbulent jets

2011 ◽  
Vol 689 ◽  
pp. 97-128 ◽  
Author(s):  
K. Gudmundsson ◽  
Tim Colonius
Keyword(s):  
Flow Field ◽  
Large Scale ◽  
Microphone Array ◽  
Near Field ◽  
Turbulent Jets ◽  
Instability Wave ◽  
Mean Flow ◽  
Velocity Fluctuations ◽  
The Mean ◽  
Scale Structures

AbstractPrevious work has shown that aspects of the evolution of large-scale structures, particularly in forced and transitional mixing layers and jets, can be described by linear and nonlinear stability theories. However, questions persist as to the choice of the basic (steady) flow field to perturb, and the extent to which disturbances in natural (unforced), initially turbulent jets may be modelled with the theory. For unforced jets, identification is made difficult by the lack of a phase reference that would permit a portion of the signal associated with the instability wave to be isolated from other, uncorrelated fluctuations. In this paper, we investigate the extent to which pressure and velocity fluctuations in subsonic, turbulent round jets can be described aslinearperturbations to the mean flow field. The disturbances are expanded about the experimentally measured jet mean flow field, and evolved using linear parabolized stability equations (PSE) that account, in an approximate way, for the weakly non-parallel jet mean flow field. We utilize data from an extensive microphone array that measures pressure fluctuations just outside the jet shear layer to show that, up to an unknown initial disturbance spectrum, the phase, wavelength, and amplitude envelope of convecting wavepackets agree well with PSE solutions at frequencies and azimuthal wavenumbers that can be accurately measured with the array. We next apply the proper orthogonal decomposition to near-field velocity fluctuations measured with particle image velocimetry, and show that the structure of the most energetic modes is also similar to eigenfunctions from the linear theory. Importantly, the amplitudes of the modes inferred from the velocity fluctuations are in reasonable agreement with those identified from the microphone array. The results therefore suggest that, to predict, with reasonable accuracy, the evolution of the largest-scale structures that comprise the most energetic portion of the turbulent spectrum of natural jets, nonlinear effects need only be indirectly accounted for by considering perturbations to the mean turbulent flow field, while neglecting any non-zero frequency disturbance interactions.

The structure of a highly decelerated axisymmetric turbulent boundary layer

2021 ◽  
Vol 929 ◽  
Author(s):  
N. Agastya Balantrapu ◽  
Christopher Hickling ◽  
W. Nathan Alexander ◽  
William Devenport
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Shear Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Large Scale ◽  
Convection Velocity ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean

Experiments were performed over a body of revolution at a length-based Reynolds number of 1.9 million. While the lateral curvature parameters are moderate ( $\delta /r_s < 2, r_s^+>500$ , where $\delta$ is the boundary layer thickness and r s is the radius of curvature), the pressure gradient is increasingly adverse ( $\beta _{C} \in [5 \text {--} 18]$ where $\beta_{C}$ is Clauser’s pressure gradient parameter), representative of vehicle-relevant conditions. The mean flow in the outer regions of this fully attached boundary layer displays some properties of a free-shear layer, with the mean-velocity and turbulence intensity profiles attaining self-similarity with the ‘embedded shear layer’ scaling (Schatzman & Thomas, J. Fluid Mech., vol. 815, 2017, pp. 592–642). Spectral analysis of the streamwise turbulence revealed that, as the mean flow decelerates, the large-scale motions energize across the boundary layer, growing proportionally with the boundary layer thickness. When scaled with the shear layer parameters, the distribution of the energy in the low-frequency region is approximately self-similar, emphasizing the role of the embedded shear layer in the large-scale motions. The correlation structure of the boundary layer is discussed at length to supply information towards the development of turbulence and aeroacoustic models. One major finding is that the estimation of integral turbulence length scales from single-point measurements, via Taylor's hypothesis, requires significant corrections to the convection velocity in the inner 50 % of the boundary layer. The apparent convection velocity (estimated from the ratio of integral length scale to the time scale), is approximately 40 % greater than the local mean velocity, suggesting the turbulence is convected much faster than previously thought. Closer to the wall even higher corrections are required.

Analysis of Turbulence in the Tip Region of a Waterjet Pump Rotor

2010 ◽  
Author(s):  
Huixuan Wu ◽  
Rinaldo L. Miorini ◽  
Joseph Katz
Keyword(s):  
Energy Flux ◽  
Large Scale ◽  
Multiple Scales ◽  
Tip Clearance ◽  
Mean Flow ◽  
Production Characteristic ◽  
Pump Rotor ◽  
The Mean ◽  
Turbulence Production ◽  
Waterjet Pump

A series of high resolution planar particle image velocimetry measurements performed in a waterjet pump rotor reveal the inner structure of the tip leakage vortex (TLV) which dominates the entire flow field in the tip region. Turbulence generated by interactions among the TLV, the shear layer that develops as the backward leakage flow emerges from the tip clearance as a “wall jet”, the passage flow, and the endwall is highly inhomogeneous and anisotropic. We examine this turbulence in both RANS and LES modelling contexts. Spatially non-uniform distributions of Reynolds stress components are explained in terms of the local mean strain field and associated turbulence production. Characteristic length scales are also inferred from spectral analysis. Spatial filtering of instantaneous data enables the calculation of subgrid scale (SGS) stresses, along with the SGS energy flux (dissipation). The data show that the SGS energy flux differs from the turbulence production rate both in trends and magnitude. The latter is dominated by energy flux from the mean flow to the large scale turbulence, which is resolved in LES, whereas the former is dominated by energy flux from the mean flow to the SGS turbulence. The SGS dissipation rate is also used for calculating the static and dynamic Smagorinsky coefficients, the latter involving filtering at multiple scales; both vary substantially in the tip region, and neither is equal to values obtained in isotropic turbulence.

scholarly journals Magnetoconvection in a horizontal duct flow at very high Hartmann and Grashof numbers

2021 ◽  
Vol 931 ◽  
Author(s):  
R. Akhmedagaev ◽  
O. Zikanov ◽  
Y. Listratov
Keyword(s):  
Magnetic Field ◽  
Magnetic Field Effect ◽  
Dimensional Structure ◽  
Two Dimensional ◽  
Duct Flow ◽  
Mean Flow ◽  
Horizontal Magnetic Field ◽  
Nuclear Fusion Reactor ◽  
Dimensional Approximation ◽  
Very High

Direct numerical simulations and linear stability analysis are carried out to study mixed convection in a horizontal duct with constant-rate heating applied at the bottom and an imposed transverse horizontal magnetic field. A two-dimensional approximation corresponding to the asymptotic limit of a very strong magnetic field effect is validated and applied, together with full three-dimensional analysis, to investigate the flow's behaviour in the previously unexplored range of control parameters corresponding to typical conditions of a liquid metal blanket of a nuclear fusion reactor (Hartmann numbers up to $10^4$ and Grashof numbers up to $10^{10}$ ). It is found that the instability to quasi-two-dimensional rolls parallel to the magnetic field discovered at smaller Hartmann and Grashof numbers in earlier studies also occurs in this parameter range. Transport of the rolls by the mean flow leads to magnetoconvective temperature fluctuations of exceptionally high amplitudes. It is also demonstrated that quasi-two-dimensional structure of flows at very high Hartmann numbers does not guarantee accuracy of the classical two-dimensional approximation. The accuracy deteriorates at the highest Grashof numbers considered in the study.

Unsteady disturbances of streaming motions around bodies

1989 ◽  
Vol 209 ◽  
pp. 385-403 ◽  
Author(s):  
H. M. Atassi ◽  
J. Grzedzinski
Keyword(s):  
Wave Equation ◽  
Body Surface ◽  
Source Term ◽  
The Body ◽  
Entire Body ◽  
Two Dimensional ◽  
Mean Flow ◽  
Inhomogeneous Wave ◽  
Inhomogeneous Wave Equation ◽  
The Mean

For small-amplitude vortical and entropic unsteady disturbances of potential flows, Goldstein proposed a partial splitting of the velocity field into a vortical part u(I) that is a known function of the imposed upstream disturbance and a potential part ∇ϕ satisfying a linear inhomogeneous wave equation with a dipole-type source term. The present paper deals with flows around bodies with a stagnation point. It is shown that for such flows u(I) becomes singular along the entire body surface and its wake and as a result ∇ϕ will also be singular along the entire body surface. The paper proposes a modified splitting of the velocity field into a vortical part u(R) that has zero streamwise and normal components along the body surface, an entropy-dependent part and a regular part ∇ϕ* that satisfies a linear inhomogeneous wave equation with a modified source term.For periodic disturbances, explicit expressions for u(R) are given for three-dimensional flows past a single obstacle and for two-dimensional mean flows past a linear cascade. For weakly sheared flows, it is shown that if the mean flow has only a finite number of isolated stagnation points, u(R) will be finite along the body surface. On the other hand, if the mean flow has a stagnation line along the body surface such as in two-dimensional flows then the component of u(R) in this direction will have a logarithmic singularity.For incompressible flows, the boundary-value problem for ϕ* is formulated in terms of an integral equation of the Fredholm type. The theory is applied to a typical bluff body. Detailed calculations are carried out to show the velocity and pressure fields in response to incident harmonic disturbances.

Turbulent Thermal Diffusion Over a Locally-Heated Two-Dimensional Hill

2010 ◽  
Author(s):  
T. Houra ◽  
Y. Nagano ◽  
M. Tagawa
Keyword(s):  
Thermal Diffusion ◽  
Passive Scalar ◽  
Heated Wall ◽  
Windward Side ◽  
Two Dimensional ◽  
Hill Model ◽  
Mean Temperature ◽  
The Mean ◽  
The Hill ◽  
Heated Case

We measure flow and thermal fields over a locally heated two-dimensional hill. The heated sections on the wall are divided into upstream and downstream portions of the hill model. These sections are heated independently, yielding various thermal boundary conditions in contrast to the uniformly heated case. In the separated region formed behind the hill, it is found that the mean temperature profiles in the uniformly heated case are well decomposed into the separately heated cases. This is because the velocity fluctuation produced by the shear layer formed behind the hill is large, so the superposition of a passive scalar in the thermal field can be successfully realized. The rapid increase in the mean temperature near the uniformly heated wall should be due to the heat transfer near the leeward slope of the hill. On the other hand, the mean temperature distributions away from the wall are strongly affected by the turbulent thermal diffusion on the windward side of the hill.

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