scholarly journals Condensates in rotating turbulent flows

2018 ◽  
Vol 841 ◽  
pp. 434-462 ◽  
Author(s):  
Kannabiran Seshasayanan ◽  
Alexandros Alexakis
Keyword(s):  
Numerical Simulations ◽  
Turbulent Flows ◽  
Rotation Rate ◽  
Large Scale ◽  
Two Dimensional ◽  
Control Parameters ◽  
Scaling Properties ◽  
Viscous Forces ◽  
Critical Rotation ◽  
Axis Of Rotation

Using a large number of numerical simulations we examine the steady state of rotating turbulent flows in triple periodic domains, varying the Rossby number $Ro$ (that measures the inverse rotation rate) and the Reynolds number $Re$ (that measures the strength of turbulence). The examined flows are sustained by either a helical or a non-helical Roberts force, that is invariant along the axis of rotation. The forcing acts at a wavenumber $k_{f}$ such that $k_{f}L=4$, where $2\unicode[STIX]{x03C0}L$ is the size of the domain. Different flow behaviours were obtained as the parameters are varied. Above a critical rotation rate the flow becomes quasi-two-dimensional and transfers energy to the largest scales of the system, forming large coherent structures known as condensates. We examine the behaviour of these condensates and their scaling properties close to and away from this critical rotation rate. Close to the critical rotation rate the system transitions supercritically to the condensate state, displaying a bimodal behaviour oscillating randomly between an incoherent-turbulent state and a condensate state. Away from the critical rotation rate, it is shown that two distinct mechanisms can saturate the growth of the large-scale energy. The first mechanism is due to viscous forces and is similar to the saturation mechanism observed for the inverse cascade in two-dimensional flows. The second mechanism is independent of viscosity and relies on the breaking of the two-dimensionalization condition of the rotating flow. The two mechanisms predict different scaling with respect to the control parameters of the system (Rossby and Reynolds), which are tested with the present results of the numerical simulations. A phase space diagram in the $Re,Ro$ parameter plane is sketched.

K–ϵ model for rotating homogeneous decaying turbulence

2016 ◽  
Vol 94 (11) ◽  
pp. 1200-1204 ◽  
Author(s):  
Hamed Marzougui
Keyword(s):  
Kinetic Energy ◽  
Numerical Simulations ◽  
Decay Rate ◽  
Rate Equation ◽  
Rotation Rate ◽  
Dissipation Rate ◽  
Direct Numerical Simulations ◽  
Uniform Rotation ◽  
Axis Of Rotation ◽  
Decaying Turbulence

In the present work, we propose a modification to the standard K–ϵ model for simulating homogeneous decaying turbulence subjected to uniform rotation. In this modification, the dissipation rate equation is formulated in terms of the rotation rate Ω, the integral length scales along the axis of rotation [Formula: see text], and its isotropic value [Formula: see text]. The comparison of our results with the corresponding direct numerical simulations proves that the new model reproduces in an excellent way the decay rate of the turbulent kinetic energy.

Simulation of Natural Ventilation of Workshop in Large-Scale Iron and Steel Enterprises Based on CFD

2012 ◽  
Vol 170-173 ◽  
pp. 2478-2483
Author(s):  
Yan Long ◽  
Ke Liu ◽  
Shi Ping Jin ◽  
Yan Fu
Keyword(s):  
Numerical Simulations ◽  
Design Optimization ◽  
Theoretical Basis ◽  
Large Scale ◽  
Natural Ventilation ◽  
Two Dimensional ◽  
Iron And Steel ◽  
To Come ◽  
Flow States

Method of CFD was adopted to carry out two-dimensional numerical simulations for internal natural ventilation process of a standard triple-span workshop in iron and steel enterprises with3 different layouts of heat resources. Flow states and relevant parameters of air-fluid in the workshop were obtained to come up with theoretical basis for design, optimization and process layout of natural ventilation in workshops.

Research of Magnetic Stage Control System Based on DSP

2011 ◽  
Vol 474-476 ◽  
pp. 2058-2063
Author(s):  
Yi Zhang ◽  
Shao Liang Wei ◽  
Hui Zhi Sun
Keyword(s):  
Control System ◽  
Large Scale ◽  
Current Loop ◽  
Two Dimensional ◽  
Control Parameters ◽  
Coordinate Measuring Machines ◽  
Variable Control ◽  
Stage System

Nanometer two-dimensional platform can realize the accurate positioning of X and Y coordinate, and it is the important parts of Nanometer Coordinate Measuring Machines (Nano-CMM),in order to realize the demand of large scale nanometer position , the magnetic stage is adopted, and magnetic stage control system is researched in this paper ,and designed the current loop, velocity loop and position loop controller, and the affection of variable control parameters are researched, and at last the magnetic stage system is realized.

scholarly journals The fate of random initial vorticity distributions for two-dimensional Euler equations on a sphere

2015 ◽  
Vol 786 ◽  
pp. 1-4 ◽  
Author(s):  
Paul K. Newton
Keyword(s):  
Numerical Simulations ◽  
Euler Equations ◽  
Large Scale ◽  
Initial Conditions ◽  
Infinite Family ◽  
Small Scale ◽  
Two Dimensional ◽  
Random Initial Conditions ◽  
Long Time ◽  
Initial Vorticity

The paper by Dritschel et al. (J. Fluid Mech., vol. 783, 2015, pp. 1–22) describes the long-time behaviour of inviscid two-dimensional fluid dynamics on the surface of a sphere. At issue is whether the flow settles down to an equilibrium or whether, for generic (random) initial conditions, the long-time solution is periodic, quasi-periodic or chaotic. While it might be surprising that this issue is not settled in the literature, it is important to keep in mind that the Euler equations form a dissipationless Hamiltonian system, hence the set of equations only redistributes the initial vorticity, generating smaller and smaller scales, while keeping kinetic energy, angular impulse and an infinite family of vorticity moments (Casimirs) intact. While special solutions that never settle down to an equilibrium state can be constructed using point vortices, vortex patches and other distributions, the fate of random initial conditions is a trickier problem. Previous statistical theories indicate that the long-time state should be a stationary large-scale distribution of vorticity. By carrying out careful numerical simulations using two different methods, the authors make a compelling case that the generic long-time state resembles a large-scale oscillating quadrupolar vorticity field, surrounded by persistent small-scale vortices. While numerical simulations can never conclusively settle this issue, the results might help guide future theories that seek to prove the existence of such an interesting dynamical long-time state.

scholarly journals Turbulent 2.5-dimensional dynamos

2016 ◽  
Vol 799 ◽  
pp. 246-264 ◽  
Author(s):  
K. Seshasayanan ◽  
A. Alexakis
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Two Dimensional Flow

We study the linear stage of the dynamo instability of a turbulent two-dimensional flow with three components $(u(x,y,t),v(x,y,t),w(x,y,t))$ that is sometimes referred to as a 2.5-dimensional (2.5-D) flow. The flow evolves based on the two-dimensional Navier–Stokes equations in the presence of a large-scale drag force that leads to the steady state of a turbulent inverse cascade. These flows provide an approximation to very fast rotating flows often observed in nature. The low dimensionality of the system allows for the realization of a large number of numerical simulations and thus the investigation of a wide range of fluid Reynolds numbers $Re$, magnetic Reynolds numbers $Rm$ and forcing length scales. This allows for the examination of dynamo properties at different limits that cannot be achieved with three-dimensional simulations. We examine dynamos for both large and small magnetic Prandtl-number turbulent flows $Pm=Rm/Re$, close to and away from the dynamo onset, as well as dynamos in the presence of scale separation. In particular, we determine the properties of the dynamo onset as a function of $Re$ and the asymptotic behaviour in the large $Rm$ limit. We are thus able to give a complete description of the dynamo properties of these turbulent 2.5-D flows.

scholarly journals Kazantsev model in non-helical 2.5-dimensional flows

2016 ◽  
Vol 806 ◽  
pp. 627-648 ◽  
Author(s):  
K. Seshasayanan ◽  
A. Alexakis
Keyword(s):  
Turbulent Flows ◽  
Three Dimensional ◽  
Analytical Calculation ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Control Parameters ◽  
Governing Equations ◽  
Field Correlation ◽  
Good Agreement

We study the dynamo instability for a Kazantsev–Kraichnan flow with three velocity components that depend only on two dimensions $\boldsymbol{u}=(u(x,y,t),v(x,y,t),w(x,y,t))$ often referred to as 2.5-dimensional (2.5-D) flow. Within the Kazantsev–Kraichnan framework we derive the governing equations for the second-order magnetic field correlation function and examine the growth rate of the dynamo instability as a function of the control parameters of the system. In particular we investigate the dynamo behaviour for large magnetic Reynolds numbers $Rm$ and flows close to being two-dimensional and show that these two limiting procedures do not commute. The energy spectra of the unstable modes are derived analytically and lead to power-law behaviour that differs from the three-dimensional and two-dimensional cases. The results of our analytical calculation are compared with the results of numerical simulations of dynamos driven by prescribed fluctuating flows as well as freely evolving turbulent flows, showing good agreement.

Quantitative three-dimensional imaging and the structure of passive scalar fields in fully turbulent flows

1990 ◽  
Vol 216 ◽  
pp. 1-34 ◽  
Author(s):  
Rahul R. Prasad ◽  
K. R. Sreenivasan
Keyword(s):  
Turbulent Flows ◽  
Three Dimensional ◽  
Scalar Fields ◽  
Passive Scalar ◽  
Working Fluid ◽  
Small Scale ◽  
Main Body ◽  
Two Dimensional ◽  
Scaling Properties ◽  
Two Dimensional Images

The three-dimensional turbulent field of a passive scalar has been mapped quantitatively by obtaining, effectively instantaneously, several closely spaced parallel two-dimensional images; the two-dimensional images themselves have been obtained by laser-induced fluorescence. Turbulent jets and wakes at moderate Reynolds numbers are used as examples. The working fluid is water. The spatial resolution of the measurements is about four Kolmogorov scales. The first contribution of this work concerns the three-dimensional nature of the boundary of the scalar-marked regions (the ‘scalar interface’). It is concluded that interface regions detached from the main body are exceptional occurrences (if at all), and that in spite of the large structure, the randomness associated with small-scale convolutions of the interface are strong enough that any two intersections of it by parallel planes are essentially uncorrelated even if the separation distances are no more than a few Kolmogorov scales. The fractal dimension of the interface is determined directly by box-counting in three dimensions, and the value of 2.35 ± 0.04 is shown to be in good agreement with that previously inferred from two-dimensional sections. This justifies the use of the method of intersections. The second contribution involves the joint statistics of the scalar field and the quantity χ* (or its components), χ* being the appropriate approximation to the scalar ‘dissipation’ field in the inertial–convective range of scales. The third aspect relates to the multifractal scaling properties of the spatial intermittency of χ*; since all three components of χ* have been obtained effectively simultaneously, inferences concerning the scaling properties of the individual components and their sum have been possible. The usefulness of the multifractal approach for describing highly intermittent distributions of χ* and its components is explored by measuring the so-called singularity spectrum (or the f(α)-curve) which quantifies the spatial distribution of various strengths of χ*. Also obtained is a time sequence of two-dimensional images with the temporal resolution on the order of a few Batchelor timescales; this enables us to infer features of temporal intermittency in turbulent flows, and qualitatively the propagation speeds of the scalar interface. Finally, a few issues relating to the resolution effects have been addressed briefly by making point measurements with the spatial and temporal resolutions comparable with the Batchelor lengthscale and the corresponding timescale.

SYMMETRIC LARGE-SCALE VELOCITY FIELDS IN TWO-DIMENSIONAL THERMAL CONVECTION

1994 ◽  
Vol 04 (05) ◽  
pp. 1369-1374 ◽  
Author(s):  
J. PRAT ◽  
I. MERCADER ◽  
J.M. MASSAGUER
Keyword(s):  
Stability Analysis ◽  
Velocity Field ◽  
Velocity Profile ◽  
Numerical Simulations ◽  
Linear Stability Analysis ◽  
Thermal Convection ◽  
Vertical Profile ◽  
Large Scale ◽  
Velocity Fields ◽  
Two Dimensional

Recent experiments on thermal convection in finite containers [Krishnamurti & Howard, 1981; Howard & Krishnamurti, 1986] show the presence of flows spanning the largest dimension of the container. Numerical simulations of 2D thermal convection showing large-scale flows of this kind have been presented elsewhere [Prat et al., 1993a, 1993b]. In every known example the large scale velocity field has been found to display a vertical profile either antisymmetric or showing rather small departures from antisymmetry. In contrast, theoretical group arguments support the existence of symmetric velocity profiles. In the present paper it will be shown that large-scale velocity fields with vertically symmetric velocity profile do exist. In spite of these flows not being dominant in the range of parameters explored, their geometry and dynamics will be discussed on the basis of a linear stability analysis.

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