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 On the self-sustained nature of large-scale motions in turbulent Couette flow

2015 ◽  
Vol 782 ◽  
pp. 515-540 ◽  
Author(s):  
Subhandu Rawat ◽  
Carlo Cossu ◽  
Yongyun Hwang ◽  
François Rincon
Keyword(s):  
Couette Flow ◽  
Turbulent Flows ◽  
Large Scale ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Buffer Layers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Steady Solutions ◽  
Smagorinsky Constant

Large-scale motions in wall-bounded turbulent flows are frequently interpreted as resulting from an aggregation process of smaller-scale structures. Here, we explore the alternative possibility that such large-scale motions are themselves self-sustained and do not draw their energy from smaller-scale turbulent motions activated in buffer layers. To this end, it is first shown that large-scale motions in turbulent Couette flow at $Re=2150$ self-sustain, even when active processes at smaller scales are artificially quenched by increasing the Smagorinsky constant $C_{s}$ in large-eddy simulations (LES). These results are in agreement with earlier results on pressure-driven turbulent channel flows. We further investigate the nature of the large-scale coherent motions by computing upper- and lower-branch nonlinear steady solutions of the filtered (LES) equations with a Newton–Krylov solver, and find that they are connected by a saddle–node bifurcation at large values of $C_{s}$. Upper-branch solutions for the filtered large-scale motions are computed for Reynolds numbers up to $Re=2187$ using specific paths in the $Re{-}C_{s}$ parameter plane and compared to large-scale coherent motions. Continuation to $C_{s}=0$ reveals that these large-scale steady solutions of the filtered equations are connected to the Nagata–Clever–Busse–Waleffe branch of steady solutions of the Navier–Stokes equations. In contrast, we find it impossible to connect the latter to buffer-layer motions through a continuation to higher Reynolds numbers in minimal flow units.

Numerical Solutions of the Navier-Stokes Equations in Inlet Regions

1972 ◽  
Vol 39 (4) ◽  
pp. 873-878 ◽  
Author(s):  
J. W. McDonald ◽  
V. E. Denny ◽  
A. F. Mills
Keyword(s):  
Reynolds Number ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Improved Method ◽  
Navier Stokes Equations ◽  
Two Dimensional Flow ◽  
Vorticity Equations

Numerical solutions of the Navier-Stokes equations are obtained for steady two-dimensional flow in the inlet region of both a tube and a channel. The entering flow is considered to be either uniform (u = constant, v = 0) or irrotational (u = constant, ω = 0). Values of Reynolds number Re = u0a/ν range from 0.75 to 2 × 106. An improved method for solving the stream function-vorticity equations of hydrodynamics has been developed. The method is stable at all Reynolds numbers and appears to be computationally superior to previous methods.

Flow Past a Forced Oscillating Cylinder: A Three-Dimensional Numerical Study

2019 ◽  
Author(s):  
Huan Ping ◽  
Yan Bao ◽  
Dai Zhou ◽  
Zhaolong Han
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Flow Dynamics ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Flow Past ◽  
Flow Past A Cylinder ◽  
Two Dimensional Flow

Abstract In this paper, we conducted a three-dimensional investigation of flow past a cylinder undergoing forced oscillation. The flow configuration is similar to the work of Blackburn & Henderson (1999) [1], in which Reynolds number equals to 500 and a fixed motion amplitude of A/D = 0.25. The oscillation frequencies are varied in the range near to the natural shedding frequency of a stationary cylinder. The flow dynamics are governed by Navier-Stokes equations and the solutions are obtained by employing high-order spectral/hp element method. It is found that the flow dynamics are significantly distinguished from the study of two-dimensional flow by Blackburn & Henderson (1999) [1]. The values of hydrodynamic forces are smaller compared to that in the two-dimensional study. However, lock-in boundary we identified is broader. In addition, a different type of hysteresis loop of energy transfer coefficient is obtained.

Stability of Hagen-Poiseuille flow with superimposed rigid rotation

1976 ◽  
Vol 73 (1) ◽  
pp. 153-164 ◽  
Author(s):  
P.-A. Mackrodt
Keyword(s):  
Poiseuille Flow ◽  
Pipe Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Neutral Curve ◽  
Rigid Rotation ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Navier Stokes Equations

The linear stability of Hagen-Poiseuille flow (Poiseuille pipe flow) with superimposed rigid rotation against small three-dimensional disturbances is examined at finite and infinite axial Reynolds numbers. The neutral curve, which is obtained by numerical solution of the system of perturbation equations (derived from the Navier-Stokes equations), has been confirmed for finite axial Reynolds numbers by a few simple experiments. The results suggest that, at high axial Reynolds numbers, the amount of rotation required for destabilization could be small enough to have escaped notice in experiments on the transition to turbulence in (nominally) non-rotating pipe flow.

An Exact Solution of the Unsteady Navier-Stokes Equations Resulting From a Stretching Surface

1994 ◽  
Vol 61 (3) ◽  
pp. 629-633 ◽  
Author(s):  
S. H. Smith
Keyword(s):  
Exact Solution ◽  
Stokes Equations ◽  
Limited Range ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Stretching Surface ◽  
Navier Stokes Equations ◽  
Short Period ◽  
Two Dimensional Flow ◽  
Surrounding Fluid

When a stretching surface is moved quickly, for a short period of time, a pulse is transmitted to the surrounding fluid. Here we describe an exact solution in terms of a similarity variable for the Navier-Stokes equations which represents the effect of this pulse for two-dimensional flow. The unusual feature is that this solution is only valid for a limited range of the Reynolds number; outside this domain unbounded velocities result.

scholarly journals Nonlinear amplification in hydrodynamic turbulence

2021 ◽  
Vol 930 ◽  
Author(s):  
Kartik P. Iyer ◽  
Katepalli R. Sreenivasan ◽  
P.K. Yeung
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Developed Turbulence ◽  
Advection Term ◽  
Nonlinear Amplification

Using direct numerical simulations performed on periodic cubes of various sizes, the largest being $8192^3$ , we examine the nonlinear advection term in the Navier–Stokes equations generating fully developed turbulence. We find significant dissipation even in flow regions where nonlinearity is locally absent. With increasing Reynolds number, the Navier–Stokes dynamics amplifies the nonlinearity in a global sense. This nonlinear amplification with increasing Reynolds number renders the vortex stretching mechanism more intermittent, with the global suppression of nonlinearity, reported previously, restricted to low Reynolds numbers. In regions where vortex stretching is absent, the angle and the ratio between the convective vorticity and solenoidal advection in three-dimensional isotropic turbulence are statistically similar to those in the two-dimensional case, despite the fundamental differences between them.

scholarly journals Gyrotactic swimmers in turbulence: shape effects and role of the large-scale flow

2018 ◽  
Vol 856 ◽  
Author(s):  
M. Borgnino ◽  
G. Boffetta ◽  
F. De Lillo ◽  
M. Cencini
Keyword(s):  
Large Scale ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Scale ◽  
Navier Stokes Equations ◽  
Preferential Sampling ◽  
Wide Range ◽  
Shape Effects ◽  
Dilute Suspensions ◽  
Large Scale Flow

We study the dynamics and the statistics of dilute suspensions of gyrotactic swimmers, a model for many aquatic motile microorganisms. By means of extensive numerical simulations of the Navier–Stokes equations at different Reynolds numbers, we investigate preferential sampling and small-scale clustering as a function of the swimming (stability and speed) and shape parameters, considering in particular the limits of spherical and rod-like particles. While spherical swimmers preferentially sample local downwelling flow, for elongated swimmers we observe a transition from downwelling to upwelling regions at sufficiently high swimming speed. The spatial distribution of both spherical and elongated swimmers is found to be fractal at small scales in a wide range of swimming parameters. The direct comparison between the different shapes shows that spherical swimmers are more clusterized at small stability and speed numbers, while for large values of the parameters elongated cells concentrate more. The relevance of our results for phytoplankton swimming in the ocean is briefly discussed.

A Quasi-Generalized-Coordinate Approach for Numerical Simulation of Complex Flows

2006 ◽  
Vol 128 (6) ◽  
pp. 1394-1399 ◽  
Author(s):  
Donghyun You ◽  
Meng Wang ◽  
Rajat Mittal ◽  
Parviz Moin
Keyword(s):  
Coordinate System ◽  
Stokes Equations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Cost Effective ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Curvilinear Coordinate ◽  
Generalized Coordinate

A novel structured grid approach which provides an efficient way of treating a class of complex geometries is proposed. The incompressible Navier-Stokes equations are formulated in a two-dimensional, generalized curvilinear coordinate system complemented by a third quasi-curvilinear coordinate. By keeping all two-dimensional planes defined by constant third coordinate values parallel to one another, the proposed approach significantly reduces the memory requirement in fully three-dimensional geometries, and makes the computation more cost effective. The formulation can be easily adapted to an existing flow solver based on a two-dimensional generalized coordinate system coupled with a Cartesian third direction, with only a small increase in computational cost. The feasibility and efficiency of the present method have been assessed in a simulation of flow over a tapered cylinder.

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