Fujihiro Hamba

Statistical Analysis of Chemically Reacting Passive Scalars in Turbulent Shear Flows

Diffusion and reaction of chemically reacting passive scalars in turbulent shear flows are investigated. A binary irreversible reaction with no heat release is considered. The binary and triple correlations such as the scalar fIux, the scalar variance, and the squared-scalar flux are calculated by applying a two-scale direct-interaction formalism. The results are simplified by the use of the inertial-range theory to construct two models for the passive scalars: an ensemble-averaged model of k - e type, and a LES model.

EFFECTS OF PRESSURE FLUCTUATIONS ON TURBULENCE GROWTH IN COMPRESSIBLE HOMOGENEOUS SHEAR FLOW

Direct numerical simulation results are used to study compressibility effects on turbulent energy growth in homogeneous shear flow. Normalized amplitude of the pressure fluctuations is shown to decrease as the turbulent Mach number increases. This decrease causes the reduction in the pressure–strain term, changes the anisotropy of the Reynolds stress, and reduces the growth rate of turbulent kinetic energy as is the case of mixing layers. The transport equation for the pressure variance is examined in detail. It is shown that when the turbulent Mach number is high the pressure-variance dissipation term is not negligible and contributes to the reduction in the pressure fluctuations. The pressure-variance dissipation is closely related to the high-wavenumber part of the pressure-variance spectrum. Profile of the spectrum is observed to depend on the turbulent Mach number. A statistical theory called the two-scale direct-interaction approximation is applied to obtain model expressions for pressure-related te...

Turbulent dynamo effect and cross helicity in magnetohydrodynamic flows

A three‐dimensional direct simulation of inhomogeneous magnetohydrodynamic (MHD) turbulence is carried out to investigate the turbulent dynamo effect. The velocity field is driven by an external force so that the velocity and magnetic fields are statistically inhomogeneous in one direction and homogeneous in the other two directions. Several statistical quantities are obtained such as the mean magnetic field, the turbulent energy, and the turbulent electromotive force. The data are used to examine the modeling of the dynamo effect in the four‐equation turbulence model. It is shown that the dynamo term related to the cross helicity is more important than the well‐known α dynamo term. Some model constants in the four‐equation model are estimated using the least‐square method.

A turbulence model for magnetohydrodynamic plasmas

The statistical theory of inhomogeneous turbulence is applied to develop a system of model equations for magnetohydrodynamic (MHD) turbulence. The statistical descriptors of MHD turbulence are taken to be the turbulent MHD energy, its dissipation rate, the turbulent cross helicity (velocity-magnetic field correlation), turbulent MHD residual energy (difference between the kinetic and magnetic energies), and turbulent residual helicity (difference between the kinetic and current helicities). Evolution equations for these statistical quantities are coupled to the mean-field dynamics. The model is applied to two MHD-plasma phenomena: turbulence evolution with prescribed mean velocity and magnetic fields in the solar wind, and mean flow generation in the presence of a mean magnetic field and cross helicity in tokamak plasmas. These applications support the validity of the turbulence model. In the presence of a mean magnetic field, turbulence dynamics should be subject to combined effects of nonlinearity and Alfvén waves; consequences for the dissipation rate of MHD residual energy are discussed.

Analysis of filtered Navier–Stokes equation for hybrid RANS/LES simulation

Hybrid Reynolds-averaged Navier–Stokes/large eddy simulation (RANS/LES) is expected to accurately predict wall-bounded turbulent flows at high Reynolds numbers. It is known that extra terms due to the noncommutivity between the hybrid filter and the spatial derivative appear in the hybrid-filtered equations. In this paper the filtered Navier–Stokes equation is investigated using direct numerical simulation data of turbulent channel flow. In particular, the transport equations for the resolved and modeled energies are evaluated to examine the contribution of the extra terms. The RANS and LES regions are located by setting the width of the hybrid filter varying from the grid spacing to the channel half width. In the first case the RANS region is located near the wall for wall modeling in LES. In the second case the RANS and LES regions are located upstream and downstream, respectively. The extra terms in the Navier–Stokes and continuity equations show fairly large values in the RANS/LES interface region in ...

An application of the turbulent magnetohydrodynamic residual-energy equation model to the solar wind

A magnetohydrodynamic (MHD) turbulence model incorporating the turbulent MHD residual energy (difference between the kinetic and magnetic energies) is applied to solar-wind turbulence. In the model, the dynamics of the turbulent cross-helicity (cross-correlation between the velocity and magnetic field) and the turbulent MHD residual energy, which are considered to describe the degree of Alfvenicity of the MHD turbulence, are solved simultaneously with the dynamics of the turbulent MHD energy and its dissipation rate. The transition of solar-wind turbulence from the Alfven-wave-like fluctuations near the Sun in the inner heliosphere to the fully developed MHD turbulence in the outer heliosphere is discussed. Magnetic dominance in the solar-wind fluctuations is addressed from the dynamics of the evolution equation of the residual energy. An interpretation of the observed Alfven ratio (ratio of the kinetic to magnetic energies) of ∼0.5 is proposed from the viewpoint of a stationary solution of the turbulence...

A turbulent dynamo model for the reversed field pinches of plasma

A dynamo model for reversed field pinches (RFP’s) is proposed from the viewpoint of magnetohydrodynamic (MHD) turbulence. This model aims at investigating the sustainment phase of RFP’s, and consists of the mean magnetic induction equation and three equations for the bulk properties of MHD fluctuations, namely, the MHD turbulent energy, its dissipation rate, and the MHD helicity. In particular, the alpha dynamo effect is composed of the familiar alpha term and a new alpha term closely related to inhomogeneity of the field. This model paves the way for explaining the generation and sustainment of alpha and beta effects. Moreover, it can treat finite plasma pressure gradients and fulfill the vanishing of plasma currents at the plasma edge. This model can also be extended to the Earth’s magnetic dynamo model where the mean motion of a fluid plays an important role.

The mechanism of zero mean absolute vorticity state in rotating channel flow

In the core region of spanwise rotating channel flows, the mean velocity profile is approximately linear with a slope of twice the system rotation rate. The mechanism of this zero mean absolute vorticity state is investigated from the turbulence modeling point of view. The mean velocity profile is calculated using three simple nonlinear eddy-viscosity models. It is shown that two models, the curvature-corrected type of explicit algebraic Reynolds stress model and the model with the corotational derivative of the second-order nonlinear term, reproduce well the zero mean absolute vorticity profile. Both models are derived by taking into account the effect of the advection of the Reynolds stress in the rotating frame. In particular, the latter model reflects the memory effect of the second-order nonlinear term. This effect means that a nonzero absolute vorticity creates a difference between the normal stresses, leading to a large shear stress in a rapidly rotating system. Since the actual value of the shear ...

Euclidean invariance and weak-equilibrium condition for the algebraic Reynolds stress model

Taking into account the frame-invariance of a model expression under arbitrarily rotating transformations, Weis & Hutter (J. Fluid Mech. vol. 476, 2003, p. 63) proposed a Euclidean-objective weak-equilibrium condition for the algebraic Reynolds stress model (ARSM). However, Gatski & Wallin (J. Fluid Mech. vol. 518, 2004, p. 147) pointed out that the weak-equilibrium condition proposed is not correct in actual rotating flows such as a rotating channel flow and showed that a non-objective weak-equilibrium condition extended to curved and rotating flows should be assumed. The frame-invariance is an important issue not only for the ARSM but also for general nonlinear eddy-viscosity models. By introducing the corotational derivative of the Reynolds stress, the transport equation for the Reynolds stress can be written to be frame-invariant. It is shown that a frame-invariant expression is desirable as a general model by comparing the error of model expressions in different rotating frames. The extended weak-equilibrium condition of Gatski & Wallin is examined to show that it is in reality objective and it does not contradict a frame-invariant model expression for the Reynolds stress.

Nonlocal analysis of the Reynolds stress in turbulent shear flow

An exact expression for the Reynolds stress is derived using the response function for the velocity fluctuation. The nonlocal eddy viscosity in the expression represents a contribution to the Reynolds stress by the mean velocity gradient at remote points in space and time. A direct numerical simulation of channel flow is conducted to validate the nonlocal expression. The transport equations for the velocity and the response function are numerically solved to evaluate the nonlocal eddy viscosity; it is shown that the nonlocal expression is accurate for both normal and shear stresses. A local expression for the Reynolds stress is also evaluated and reveals that the local approximation is not accurate enough near the wall. Analysis using the nonlocal expression is shown to be useful for obtaining a better understanding of turbulent shear flow.