Global Magnetic Fields in Turbulent Motion

A large eddy simulation of magnetohydrodynamic (MHD) turbulent channel flow is carried out to investigate the dynamo mechanism. It is shown that the streamwise component of the mean magnetic field is generated and sustained due to the effect of the turbulent electromotive force. The Reynolds-averaged turbulence model for MHD flows is assessed; it is suggested that the cross-helicity dynamo effect contributes to the turbulent electromotive force; that is, the electromotive force parallel to the mean vorticity is generated due to the turbulent cross helicity. To verify the importance of the cross-helicity dynamo, the transport equation for the turbulent electromotive force is evaluated; it is confirmed that the term involving the cross helicity and the mean vorticity is the main production term for the turbulent electromotive force. The transport equations for the turbulent kinetic and magnetic energies are also examined to discuss the dynamo mechanism from the viewpoint of the energy transfer.

Turbulent dynamo modeling in a rotating frame is performed to enable studies of reversed field pinches of fusion plasma and planetary magnetic fields. The Reynolds stresses, turbulent electromotive force, and other important correlation functions, which appear in the equations for the mean velocity and magnetic field, are modeled using the mean fields and four bulk turbulence quantities (the magnetohydrodynamic turbulent energy, its dissipation rate, the cross helicity, and the residual helicity). Four equations for those bulk quantities are combined with the mean-field equations to lead to a self-consistent dynamo model. Specifically, the importance of the cross-helicity effect is pointed out. This model shows that the equilibrium state of reversed field pinches of plasma is a neutral state under the condition of vanishing cross helicity. The relevance to the study of the Earth’s and other planetary magnetic fields is discussed.

Large-scale coherent magnetic fields observed in the nearby galaxies are thought to originate by a mean-field dynamo. This is governed via the turbulent electromotive force (EMF, $\overline{{\boldsymbol {\cal E}} {}}$) generated by the helical turbulence driven by supernova (SN) explosions in the differentially rotating interstellar medium (ISM). In this paper, we aim to investigate the possibility of dynamo action by the virtue of buoyancy due to a cosmic ray (CR) component injected through the SN explosions. We do this by analysing the magnetohydrodynamic simulations of local shearing box of ISM in which the turbulence is driven via random SN explosions and the energy of the explosion is distributed in the CR and/or thermal energy components. We use the magnetic field aligned diffusion prescription for the propagation of CR. We compare the evolution of magnetic fields in the models with the CR component to our previous models that did not involve the CR. We demonstrate that the inclusion of CR component enhances the growth of dynamo slightly. We further compute the underlying dynamo coefficients using the test-field method and argue that the entire evolution of the large-scale mean magnetic field can be reproduced with an α − Ω dynamo model. We also show that the inclusion of CR component leads to an unbalanced turbulent pumping between magnetic field components and additional dynamo action by the Rädler effect.

513 The presence of helicity in correlation characteristics of turbulent flows is one of the observed manifestations of mirror-symmetry violation. Helicity is defined as the scalar product of the flow velocity and vorticity. Along with energy, helicity is a second-order invariant of the motion of an ideal fluid. This phenomenon is observed in both laboratory and natural geo- and astrophysical flows. Helical characteristics of turbulence related to the angular-moment accumulation in smallscale motions are among the main sources of magnetic field generation in rotating objects. Enhanced helicity is observed in many coherent vortex structures over a broad range of scales. This was devoted to the local structure of turbulent helicity. It is shown that the helicity dissipation can be determined from the results of simultaneous measurements of the velocity and vorticity components using the exact relations obtained previously [1] for the helical component of the third-order two-point correlation tensor. Among immediate consequences of these relations are (i) the power-law helicity spectrum with an exponent of ‐5/3, which has been obtained previously only qualitatively [2] and is now observed both under natural conditions and in numerical simulations [3‐5] and (ii) the more hypothetical helicity spectrum with an exponent of ‐4/3 that is typical “exclusively” of a helical cascade [2]. Very few measurements of helicity in turbulent flows are known, since such measurements are related to fairly complicated problems encountered in the measurement of multicomponent velocity-field gradients. The known experiments were carried out for turbulent flows behind a wire grid and in a jet [6, 7]. The existence of a helicity cascade, obeying a ‐5/ 3 power law, along with an energy cascade was confirmed by recent observations [8] of the atmospheric boundary layer at altitudes ~ 50 km [8] using an acoustic circulometer at the Obukhov Institute of Atmospheric Physics (Moscow) capable of measuring velocity and helicity simultaneously. The measured values of helicity were close to theoretical estimates. Without making hypotheses concerning the helicity cascade nature, let us consider correlation characteristics of homogeneous helical turbulence. The pair velocity correlation 〈 v i ( x ) v j ( x + r ) 〉 is described by the following function:

The inter-relationships between magnetic helicity, magnetic reconnection, and dynamo effects are discussed. In laboratory experiments, where two plasmas are driven to merge, the helicity content of each plasma strongly affects the reconnection rate, as well as the shape of the diffusion region. Conversely, magnetic reconnection events also strongly affect the global helicity, resulting in efficient helicity cancellation (but not dissipation) during counter-helicity reconnection and a finite helicity increase or decrease (but less efficiently than dissipation of magnetic energy) during co-helicity reconnection. Close relationships also exist between magnetic helicity and dynamo effects. The turbulent electromotive force along the mean magnetic field (alpha-effect), due to either electrostatic turbulence or the electron diamagnetic effect, transports mean-field helicity across space without dissipation. This has been supported by direct measurements of helicity flux in a laboratory plasma. When the dynamo effect is driven by electromagnetic turbulence, helicity in the turbulent field is converted to mean-field helicity. In all cases, however, dynamo processes conserve total helicity except for a small battery effect, consistent with the observation that the helicity is approximately conserved during magnetic relaxation.

The inter-relationships between magnetic helicity, magnetic reconnection, and dynamo effects are discussed. In laboratory experiments, where two plasmas are driven to merge, the helicity content of each plasma strongly affects the reconnection rate, as well as the shape of the diffusion region. Conversely, magnetic reconnection events also strongly affect the global helicity, resulting in efficient helicity cancellation (but not dissipation) during counter-helicity reconnection and a finite helicity increase or decrease (but less efficiently than dissipation of magnetic energy) during co-helicity reconnection. Close relationships also exist between magnetic helicity and dynamo effects. The turbulent electromotive force along the mean magnetic field (alpha-effect), due to either electrostatic turbulence or the electron diamagnetic effect, transports mean-field helicity across space without dissipation. This has been supported by direct measurements of helicity flux in a laboratory plasma. When the dynamo effect is driven by electromagnetic turbulence, helicity in the turbulent field is converted to mean-field helicity. In all cases, however, dynamo processes conserve total helicity except for a small battery effect, consistent with the observation that the helicity is approximately conserved during magnetic relaxation.

26a-L-9 Turbulent electromotive force and cross helicity in MHD flows

Chapter 9 The turbulent electromotive force in the case of rotational mean motion

Freestream turbulence in rivers is a key contributor to the flux of dissolved nutrients, carbon, and other ecologically important solutes into porewater. To advance understanding of turbulent hyporheic exchange and porewater transport, we investigate flow over and through a rough bed of spheres using large eddy simulation (LES). We apply double averaging (combined space and time averaging) to the LES results to determine the mean velocity distribution, momentum balance, and drag forces. Our simulations show large‐scale freestream structures interacting strongly with vortices generated at the surfaces of individual spheres to control turbulent momentum fluxes into the bed. The transition between turbulent flow and Darcy flow occurs over the first row of spheres, where turbulence decays rapidly and turbulent kinetic energy, Reynolds stress, and drag forces peak. Below this region, turbulence is only present in the high‐velocity flow in open pore throats. Experimental observations suggest that minimum mean porewater velocity occurs in the first open pore space below the transition region, but our results show that the minimum occurs between the first and second pore spaces. The simulation mean porewater velocities are approximately half those captured in measurements because the model resolves the entire flow continuum while measurements can access high‐velocity fluid in open pores. The high‐resolution dual time‐space averaging of the LES resolves both turbulent and mean flow features that are important to interfacial solute and particle fluxes, providing a means to include turbulent hyporheic exchange in upscaled river models, which has not been achieved to date.

In the present investigation, the LES WALE method along with the Zwart cavitation model is utilised to predict the cavitating flow around a Delft Twist-11 hydrofoil and the numerical results show a reasonable agreement with the experimental data. A novel elucidation is provided to the formation of the U-type structure and the Lumley method is introduced into the numerical simulation which can offer a validation of the simulation. The evolution of the cavity structure, especially the formation and development of U-type structures, was investigated thoroughly with the assistant of the Ω method, the Lamb vector, and the vorticity transport equation (VTE). As a third-generation vortex identification, Ω = 0.52 captures the vortex structure during the cavity evolution exhaustively. The cavitation-vortex interaction impacts the cavity evolution profoundly. The primary weak vortex and the secondary weak vortex both have a significant effect on the cavity shedding and the formation of the U-type structure. Moreover, the stretching action and the vorticity bearing motion described by the Lamb vector divergence clarify the formation of the special cavity structure in depth. In virtue of the mean velocity, Reynolds stresses, Lumley triangle, and Lumley distance, the turbulence characteristics were also investigated carefully. The cavitating motion plays a significant role in the turbulence velocity fluctuation and turbulence anisotropy around a twisted hydrofoil.

Three-dimensional (3D) corner separation in a linear highly loaded compressor cascade is studied by using delayed detached-eddy simulation (DDES) method. This paper studies the flow mechanism of corner separation, including vortical structures and turbulence characteristics. The vortical structures are analyzed and the distributions of Reynolds stresses and turbulent anisotropy are also discussed in detail. The results show that there exist different kinds of vortical structures, such as horseshoe vortex, passage vortex, wake shedding vortex, and “corner vortex.” Before the corner separation forms, the passage vortex becomes the main secondary vortex and obviously enhances the corner separation. At approximate 35% chord position, the corner vortex begins to form, enlarges rapidly, and dominates the secondary flow in the cascade. The corner vortex is a compound vortex with its vortex core composed of multiple vortices. Streamwise normal Reynolds stress contributes greatest to the turbulence fluctuation in the corner region. The turbulence develops from two-dimensional (2D) turbulence in the near-wall region to one-component type turbulence in the corner region. The turbulence tends to be more anisotropic when the flow is close to the endwall within the corner separation region.

For the first time, we have directly measured the transport of a vector magnetic field by isotropic turbulence in a high Reynolds number liquid metal flow. In analogy with direct measurements of the turbulent Reynolds stress (turbulent viscosity) that governs momentum transport, we have measured the turbulent electromotive force (emf) by simultaneously measuring three components of velocity and magnetic fields, and computed the correlations that lead to mean-field current generation. Furthermore, we show that this turbulent emf tends to oppose and cancel out the local current, acting to increase the effective resistivity of the medium, i.e., it acts as an enhanced magnetic diffusivity. This has important implications for turbulent transport in astrophysical objects, particularly in dynamos and accretion disks.

Measurements of the mean and turbulence characteristics in nonuniform open-channel flows were carried out using a 3D acoustic Doppler velocimeter. Both accelerating and decelerating flows were investigated. Analyses based on the Reynolds equation and the continuity equation of 2D open-channel flow show that a flow will be in equilibrium if the pressure-gradient parameter β is a constant at different sections along the flow direction. The experimental data show that all the flows investigated are in equilibrium. The effect of the flow nonuniformity on the mean velocity and turbulence profiles was also examined. The study shows that (1) the log law is still valid for both accelerating and decelerating flows in the inner region. The Coles law can be used for the entire region, but the wake-strength parameter Π depends on the β-value; and (2) the turbulence intensities and the Reynolds stress decrease in accelerating flow and increase in decelerating flow, when compared with those in uniform flow. Finally, using the Reynolds equation and the continuity equation of 2D open-channel flow, the theoretical expressions for the distribution of vertical velocity and the Reynolds stress have been developed. The measured vertical velocity and the Reynolds stress profile compare well with the derived expressions.

Numerical and experimental investigation of the near zone flow field in an array of confluent round jets

Physical and logistical considerations of using ultrasonic anemometers in aeolian sediment transport research