Tohru Nakano

Velocity field statistics in homogeneous steady turbulence obtained using a high-resolution direct numerical simulation

Velocity field statistics in the inertial to dissipation range of three-dimensional homogeneous steady turbulent flow are studied using a high-resolution DNS with up to N=10243 grid points. The range of the Taylor microscale Reynolds number is between 38 and 460. Isotropy at the small scales of motion is well satisfied from half the integral scale (L) down to the Kolmogorov scale (η). The Kolmogorov constant is 1.64±0.04, which is close to experimentally determined values. The third order moment of the longitudinal velocity difference scales as the separation distance r, and its coefficient is close to 4/5. A clear inertial range is observed for moments of the velocity difference up to the tenth order, between 2λ≈100η and L/2≈300η, where λ is the Taylor microscale. The scaling exponents are measured directly from the structure functions; the transverse scaling exponents are smaller than the longitudinal exponents when the order is greater than four. The crossover length of the longitudinal velocity struct...

Correlation between the Doping Dependences of Superconducting Gap Magnitude 2Δ 0 and Pseudogap Temperature T* in High-T c Cuprates

We report that in La 2- x Sr x CuO 4 (La214) and Bi 2 Sr 2 CaCu 2 O 8+δ (Bi2212), the resistivity ρ and magnetic susceptibility χ decrease more sharply below T * , corresponding to the onset temperature of a spin gap (pseudogap) at least for Bi2212. In each system, T * scales with the superconducting gap magnitude 2Δ 0 ( T * ∼2Δ 0 /4.3 k B ), which increases as the doping level is lowered. We also report that 2Δ 0 is almost proportional to T max (> T * ), where T max is the temperature exhibiting a broad peak of χ and k B T max has been considered to give the measure of effective exchange energy J eff ; the α factors in 2Δ 0 ∼α k B T max ∼α J eff are nearly one and two for La214 and Bi2212, respectively.

Longitudinal Structure Functions in Decaying and Forced Turbulence

In order to reliably compute the longitudinal structure functions in decaying and forced turbulence, local isotropy is examined with the aid of the isotropic expression of the incompressible condit...

Role of Pressure in Turbulence

There is very limited knowledge of the kinematical relations for the velocity structure functions higher than three. Instead, the dynamical equations for the structure functions of the velocity increment are obtained from the Navier–Stokes equation under the assumption of the local homogeneity and isotropy. These equations contain the correlation between the velocity and pressure gradient increments, which is very difficult to know theoretically and experimentally. We have examined these dynamical relations by using direct numerical simulation data at very high resolution at large Reynolds numbers, and found that the contribution of the pressure term is important to the dynamics of the longitudinal velocity with large amplitudes. The pressure term is examined from the view point of the conditional average and the role of the pressure term in the turbulence dynamics is discussed.

Direct interaction approximation of turbulence in the wave packet representation

The wave packet representation of the Navier–Stokes equations is developed. In order to show its feasibility, it is applied to turbulence in the framework of the direct interaction approximation (DIA). The theory is free from a spurious divergence encountered in the usual DIA theory. The effect of convection due to large eddies is successfully eliminated without relying on any ad hoc approximation, but the contribution from their velocity gradient is included. The Kolmogorov spectrum with the Kolmogorov constant 1.67 is predicted if the shell width is set equal to 2. The passive scalar field in turbulence can be treated similarly, yielding the counterpart of the Kolmogorov constant 0.84. Both the constants agree with experiment fairly well, implying that the present wave packet representation is reliable.

IUTAM Symposium on Geometry and Statistics of Turbulence

Preface. A. General and Mathematical. B. Coherent Structures, Intermittency, and Cascade. C. Probability Density Functions and Structure Functions. D. Passive Scalar Advections. E. Vortices, Vorticity, and Strain Dynamics. F. Large Scale Motions, LES, and Closure. G. Thermal Turbulence, and Stratified and Rotating Turbulence. H. Transition Mechanisms. I. Modulation of Turbulence. J. Pipe-Flow and Channel-Flow Turbulence. K. Boundary Layers and Near-Wall Turbulence. Participant List. Index.

Multifractal Analysis of Simulated Two-Dimensional Turbulence

Simulated two-dimensional Navier-Stokes turbulence with the k -4 energy spectrum is considered from a multifractal point of view. The calculations cover the range of Reynolds numbers 55< R L <850. Turbulence has an inertial range in almost one decade of wave number. The generalized dimensions D q are computed for the enstrophy dissipation rate as well as the energy dissipation rate. For the former D ∞ =1.2∼1.3, implying that the intense enstrophy dissipation occurs nearly on a line. For the latter D q is close to two, the geometrical dimension, for positive values of q , which means that the energy dissipation occurs uniformly in space. We do not observe that both D q depend appreciablly on Reynolds number as well as the pattern of the initial large-scale fields. The pictures obtained from the multifractal considerations are consistent with what is known already in two-dimensional turbulence, implying that the multifractal analysis is a good tool for studying turbulence structure.

Energy transfer and intermittency in four-dimensional turbulence

The energy transfer and small scale intermittency in decaying turbulence in four dimensions are studied by direct numerical simulation and by spectral theory. It is found that (1) a 1∕2 law, −(1∕2)e¯r, in four dimensional (4D) for the longitudinal third-order structure function holds, (2) the energy transfer in 4D is more efficient than in three dimensional (3D), (3) the Kolmogorov constant in 4D is K4=1.28 which is smaller than K3=1.72 in 3D, (4) the velocity gradient intermittency is stronger than in 3D, while (5) the total-energy dissipation rate in 4D is less intermittent than in 3D. The conflicting trends in (4) and (5) are explained by the changes in the balance between the convective and pressure terms as the dimension increases.

The Scaling Exponents of Intermittent Fully Developed Turbulence Based on a New Model

2) The Kolmogorov scaling is based on the assumption that the energy dissipation rate c is homogeneous in space and time. The assumption is, however, contrary to the observation. The effects of the fluctuation of the dissipation rate reveal themselves prominently in small scales and higher order moments. The deviation from K4I is expressed in terms of the intermittency exponents YP, fLp, lJp and ap as

Determination of a Dynamical Scaling Function in a Cascade Model of Turbulence

A dynamical scaling function in a cascade model of turbulence is numerically determined. It indicates that there are two time domains in the scaling function. In the first domain fluctuations supplied to the low wavenumber region are transferred to the higher wavenumber region without any significant effect from the molecular viscosity. The scaling is not the Kolmogorov type, but the intermittent one. After reaching a certain maximum wavenumber, the turbulence enters the second domain, where the fluctuations decay due to the viscosity and obey the Kolmogorov scaling. It is, then, derived that the lower order structure functions obey the Kolmogorov scaling, while the higher order ones show the intermittent scaling. Finally, the present model is discussed in relation to the structures in a turoulent flow.