Stability of the poiseuille flow in a longitudinal magnetic field

The stability to small perturbations of a 2D flow of a conducting viscous fluid with large Reynolds numbers in a longitudinal magnetic field is investigated. A complete linearized system of magnetohydrodynamics equations is considered using the method of collocations and the differential sweep method. The dependences of the critical Reynolds numbers on the electrical conductivity are analyzed in detail. A new instability branch for large Reynolds numbers and a jumpwise variation of the critical Reynolds numbers are discovered.     

飞行器低Reynolds数层流分离理论探讨

低Reynolds数流动由于自身特点导致气动特性严重恶化,非定常、非线性效应突出且预测困难,加之相关基础理论研究不足,给以临近空间低速飞行器和高性能微小型飞行器为代表的低Reynolds数飞行器的开发和研制带来了瓶颈和挑战.首先概述了飞行器低Reynolds数的范畴、低Reynolds数空气动力学的主要问题与挑战.随后从低Reynolds数层流分离基础理论出发,依次介绍了低Reynolds数层流分离经典理论、低Reynolds数层流分离非定常流动特性、低Reynolds数后缘层流分离泡.在此基础上,通过对经典长层流分离泡与后缘层流分离泡力学特性的差异以及随攻角和Reynolds数的演化规律的详细分析,逐步揭示了一些低Reynolds数复杂气动效应的本质,如小攻角升力系数的非线性效应,翼型随Reynolds数下降气动特性的二次恶化效应等.最后对低Reynolds数流动基础理论的发展过程进行了总结,并对层流分离诱导转捩及再附效应等复杂流动问题进行了展望.      

Nonlinear current helicity fluxes in turbulent dynamos and alpha quenching

Large scale dynamos produce small scale current helicity as a waste product that quenches the large scale dynamo process (alpha effect). This quenching can be catastrophic (i.e., intensify with magnetic Reynolds number) unless one has fluxes of small scale magnetic (or current) helicity out of the system. We derive the form of helicity fluxes in turbulent dynamos, taking also into account the nonlinear effects of Lorentz forces due to fluctuating fields. We confirm the form of an earlier derived magnetic helicity flux term, and also show that it is not renormalized by the small scale magnetic field, just like turbulent diffusion. Additional nonlinear fluxes are identified, which are driven by the anisotropic and antisymmetric parts of the magnetic correlations. These could provide further ways for turbulent dynamos to transport out small scale magnetic helicity, so as to avoid catastrophic quenching.     

绕圆柱体自由表面磁流体流动和传热的研究

本文对在不同雷诺数下,绕圆柱体的磁流体自由表面流动及传热进行了模拟,分析了磁场对绕流圆柱尾迹和涡分离的影响,获得了两种雷诺数下的电磁力密度、流场和温度场分布。结果表明,磁场不仅影响了流动的形态,而且对湍流有抑制作用,降低了自由表面的更新机制,从而减少了传热能力;在相同的Hartmann数下,相比低雷诺数下的流动换热情况,高雷诺数下的湍流不能被完全抑制,自由表面与尾迹的相互作用也较强,因而自由表面换热也较强。     

Universal nonlinear small-scale dynamo

We consider astrophysically relevant nonlinear MHD dynamo at large Reynolds numbers (Re). We argue that it is universal in a sense that magnetic energy grows at a rate which is a constant fraction C(E) of the total turbulent dissipation rate. On the basis of locality bounds we claim that this "efficiency of the small-scale dynamo", C(E), is a true constant for large Re and is determined only by strongly nonlinear dynamics at the equipartition scale. We measured C(E) in numerical simulations and observed a value around 0.05 in the highest resolution simulations. We address the issue of C(E) being small, unlike the Kolmogorov constant which is of order unity.     

On the nonlinear instability of the solutions of hydrodynamic-type systems

New exact solutions (including periodic) of three-dimensional nonstationary Navier-Stokes equations containing arbitrary functions are described. The problems of the nonlinear stability/instability of the solutions have been analyzed. It has been found that a feature of a wide class of the solutions of hydrodynamic-type systems is their instability. It has been shown that instability can occur not only at sufficiently large Reynolds numbers, but also at arbitrary small Reynolds numbers (and can be independent of the fluid velocity profile). A general physical interpretation of the solution under consideration is given. It is important to note that the instability of the solutions has been proven using a new exact method (without any assumptions and approximations), which can be useful for analyzing other nonlinear physical models and phenomena.     

Turbulence regeneration in pipe flow at moderate Reynolds numbers

We present the results of an experimental investigation into the nature and structure of turbulent pipe flow at moderate Reynolds numbers. A turbulence regeneration mechanism is identified which sustains a symmetric traveling wave within the flow. The periodicity of the mechanism allows comparison to the wavelength of numerically observed exact traveling wave solutions and close agreement is found. The advection speed of the upstream turbulence laminar interface in the experimental flow is observed to form a lower bound on the phase velocities of the exact traveling wave solutions. Overall our observations suggest that the dynamics of the turbulent flow at moderate Reynolds numbers are governed by unstable nonlinear traveling waves.     

Magnetic induction by coherent vortex motion

We investigate experimentally the advection of a magnetic field by a flow of conducting fluid, at moderate magnetic Reynolds numbers. More specifically, we study the influence of a large scale intense vortex on an externally applied field. We show that at large scales the magnetic field lines are distorted in a way that is consistent with a scenario of magnetic field expulsion by vorticity. Measurements at small scales show that the magnetic fluctuations are also quite sensitive to the large scale vortex motion. Received 27 October 1999 and Received in final form 16 March 2000     

Dynamo in protostars

In this paper, we estimate the magnetic Reynolds number of a typical protostar before and after deuterium burning, and claim for the existence of dynamo process in both the phases, because the magnetic Reynolds number of the protostar far exceeds the critical magnetic Reynolds number for dynamo action. Using the equipartition of kinetic and magnetic energies, we estimate the steady-state magnetic field of the protostar to be of the order of kilogauss, which is in good agreement with observations.     

Magnetic stabilization of nematic turbulence

Under an applied magnetic field, turbulence starts off in a nematic liquid at higher critical Reynolds numbers. Also, the internal scale of turbulence is enlarged.     

Asymmetric, helical, and mirror-symmetric traveling waves in pipe flow

New families of three-dimensional nonlinear traveling waves are discovered in pipe flow. In contrast with known waves [H. Faisst and B. Eckhardt, Phys. Rev. Lett. 91, 224502 (2003); H. Wedin and R. R. Kerswell, J. Fluid Mech. 508, 333 (2004), they possess no discrete rotational symmetry and exist at a significantly lower Reynolds numbers (Re). First to appear is a mirror-symmetric traveling wave which is born in a saddle node bifurcation at Re=773. As Re increases, "asymmetric" modes arise through a symmetry-breaking bifurcation. These look to be a minimal coherent unit consisting of one slow streak sandwiched between two fast streaks located preferentially to one side of the pipe. Helical and nonhelical rotating waves are also found, emphasizing the richness of phase space even at these very low Reynolds numbers.     

Possible localized transport induced by a wave propagating along a vacuum–matter interface

Macroscopic derivation of the entrainment of matter induced by a surface elastic wave propagating along the flexible vacuum–matter interface is conducted by considering the nonlinear coupling between the interface and the rarefaction effect. The critical reflux values associated with the product of the second-order (unit) body forcing and the Reynolds number (representing the viscous dissipations) decrease as the Knudsen number (representing the rarefaction measure) increases from zero to 0.1. We obtained the matter-freezed or zero-volume-flow-rate states for specific Reynolds numbers and wave numbers which might be linked to the evolution of the Universe.     

Flame-acoustic coupling of combustion instability in a non-premixed backward-facing step combustor: the role of acoustic-Reynolds stress

Combustion instability in a laboratory scale backward-facing step combustor is numerically investigated by carrying out an acoustically coupled incompressible large eddy simulation of turbulent reacting flow for various Reynolds numbers with fuel injection at the step. The problem is mathematically formulated as a decomposition of the full compressible Navier–Stokes equations using multi-scale analysis by recognising the small length scale and large time scale of the flow field relative to a longitudinal mode acoustic field for low mean Mach numbers. The equations are decomposed into those for an incompressible flow with temperature-dependent density to zeroth order and linearised Euler equations for acoustics as a first order compressibility correction. Explicit coupling terms between the two equation sets are identified to be the flow dilatation as a source of acoustic energy and the acoustic Reynolds stress (ARS) as a source of flow momentum. The numerical simulations are able to capture the experimentally observed flow–acoustic lock-on that signifies the onset of combustion instability, marked by a shift in the dominant frequency from an acoustic to a hydrodynamic mode and accompanied by a nonlinear variation of pressure amplitude. Attention is devoted to flow conditions at two Reynolds numbers before and after lock-on to show that, after lock-on, the ARS causes large-scale vortical rollup resulting in the evolution of a compact flame. As compared to acoustically uncoupled simulations at these Reynolds numbers that show an elongated flame with no significant roll up and disturbance in the upstream flow field, the ARS is seen to alter the shear layer dynamics by affecting the flow field upstream of the step as well, when acoustically coupled.     

Observation of nonlinear coupling between small-poloidal wave-number potential fluctuations and turbulent potential fluctuations in Ohmically heated plasmas in the JFT-2M tokamak

Two types of electrostatic modes with small-poloidal wave numbers (approximately 1 and 10-15 kHz) are observed in the edge region of Ohmically heated plasmas in the JFT-2M tokamak. The envelope of the higher frequency coherent mode is modulated at the frequency of the lower frequency mode. A bispectral analysis revealed that a significant nonlinear coupling among the two types of fluctuations and the broadband background turbulent potential fluctuations occurs inside the last closed magnetic flux surface, suggesting that a nonlinear process such as the parametric-modulational instability is involved.     

Observation of a free-Shercliff-layer instability in cylindrical geometry

We report on observations of a free-Shercliff-layer instability in a Taylor-Couette experiment using a liquid metal over a wide range of Reynolds numbers, Re～10(3)-10(6). The free Shercliff layer is formed by imposing a sufficiently strong axial magnetic field across a pair of differentially rotating axial end cap rings. This layer is destabilized by a hydrodynamic Kelvin-Helmholtz-type instability, characterized by velocity fluctuations in the r-θ plane. The instability appears with an Elsasser number above unity, and saturates with an azimuthal mode number m which increases with the Elsasser number. Measurements of the structure agree well with 2D global linear mode analyses and 3D global nonlinear simulations. These observations have implications for a range of rotating MHD systems in which similar shear layers may be produced.     

含铝炸药爆轰产物导电式爆磁压缩发生器

根据爆磁压缩发生器中导电体工作条件,对比了电枢和含铝炸药爆轰产物作为导电体的异同,得出几种高电导率含铝炸药爆轰产物对应的磁雷诺数,分析了含铝炸药爆轰产物代替电枢压缩磁场的可能性。设计了一种含铝炸药爆轰产物导电式螺线型爆磁压缩发生器,分析其运行过程,得出等效电路模型。数值模拟结果表明:相比于电枢作为导电体的传统螺线型爆磁压缩发生器,同体积条件下高电导率含铝炸药爆轰产物导电式爆磁压缩发生器具有更好的输出性能;该设计可以有效地抑制跳匝、电枢与定子线圈短路点接触不良等容易引起磁通损失的问题。     

Rheology of the Cu-H2O nanofluid in porous channel with heat transfer: Multiple solutions

Dynamics of nanofluid comprising a base fluid (water) with copper (Cu) nanoparticles have been considered in channel with porous walls under magnetic field influence. The channel walls are considered to be permeable in order to analyze the wall mass transfer phenomenon. Relevant mathematical modelling has been performed and the derived PDEs are converted into coupled nonlinear ODEs by using suitable transformations. Computations have been made numerically by employing the shooting technique. It is noted that multiple solutions occur for the variation of suction Reynolds number, solid volume fraction and magnetic parameters which are interpreted in detail.     

An approximation of the analytical solution of the Jeffery-Hamel flow by decomposition method

Many researchers have been interested in application of mathematical methods to find analytical solutions of nonlinear equations and for this purpose, new methods have been developed. Since most of fluid mechanics problems due to boundary layer are strongly nonlinear, so analytical solution of them is confronted with some difficulty. In this Letter, the Jeffery-Hamel flow—a nonlinear equation of 3rd order—is studied by Adomian decomposition method. After introducing Adomian decomposition method and the way of obtaining Adomian's polynomial, we solved the problem for divergent and convergent channels. Finally, velocity distribution and shear stress constant is depicted at various Reynolds numbers and comparing our results with some earlier works illustrated their excellent accuracy.     

Numerical demonstration of fluctuation dynamo at low magnetic Prandtl numbers

Direct numerical simulations of incompressible nonhelical randomly forced MHD turbulence are used to demonstrate for the first time that the fluctuation dynamo exists in the limit of large magnetic Reynolds number Rm>1 and small magnetic Prandtl number Pm<1. The dependence of the critical Rmc for dynamo on the hydrodynamic Reynolds number Re is obtained for 1 less than or similar Re less than or similar 6700. In the limit Pm<1, Rmc is about 3 times larger than for the previously well-established dynamo at large and moderate Prandtl numbers: Rmc less than or similar 200 for Re greater than or similar 6000 compared to Rmc approximately 60 for Pm>or=1. It is not yet possible to determine numerically whether the growth rate of the magnetic energy is proportional, Rm1/2 in the limit Rm-->infinity, as it should be if the dynamo is driven by the inertial-range motions at the resistive scale.     

A Reynolds stress model for turbulent flows of viscoelastic fluids

A second-order closure is developed for predicting turbulent flows of viscoelastic fluids described by a modified generalised Newtonian fluid model incorporating a nonlinear viscosity that depends on a strain-hardening Trouton ratio as a means to handle some of the effects of viscoelasticity upon turbulent flows. Its performance is assessed by comparing its predictions for fully developed turbulent pipe flow with experimental data for four different dilute polymeric solutions and also with two sets of direct numerical simulation data for fluids theoretically described by the finitely extensible nonlinear elastic – Peterlin model. The model is based on a Newtonian Reynolds stress closure to predict Newtonian fluid flows, which incorporates low Reynolds number damping functions to properly deal with wall effects and to provide the capability to handle fluid viscoelasticity more effectively. This new turbulence model was able to capture well the drag reduction of various viscoelastic fluids over a wide range of Reynolds numbers and performed better than previously developed models for the same type of constitutive equation, even if the streamwise and wall-normal turbulence intensities were underpredicted.