The First Turbulence and First Fossil Turbulence

A model is proposed connecting turbulence, fossil turbulence and the big-bang origin of the universe. While details are incomplete, the model is consistent with our knowledge of these processes and is supported by observations. Turbulence arises in a hot big-bang quantum gravitational dynamics scenario at Planck scales. Chaotic, eddy-like motions produce an exothermic Planck particle cascade from 10^?35 m at 10³² K to 10⁸ larger, 10⁴ cooler, quark-gluon scales. A Planck-Kerr instability gives high Reynolds number (Re ～ 10⁶) turbulent combustion, space-time-energy-entropy and turbulent mixing. Batchelor-Obukhov-Corrsin turbulent-temperature fluctuations are preserved as the first fossil turbulence by inflation stretching the patterns beyond the horizon ct of causal connection faster than light speed c in time t～ 10^?33 sec. Fossil big-bang temperature turbulence reenters the horizon and imprints nucleosynthesis of H-He densities that seed fragmentation by gravity at 10¹² s in the low Reynolds number plasma before its transition to gas at t～ 10¹³ s and T～ 3000 K. Multiscaling coefficients of the cosmic microwave background (CMB) temperature anisotropies closely match those for high Reynolds number turbulence, Bershadskii, A. and Sreenivasan, K.R., Phys. Lett. A 299 (2002) 149-152; Bershadskii, A. and Sreenivasan, K.R., Phys. Lett. A 319 (2003) 21-23. CMB spectra support the interpretation that big-bang turbulence fossils triggered fragmentation of the viscous plasma at supercluster to galaxy mass scales from 10⁴⁶ to 10⁴² kg, Gibson, C.H., Appl. Mech. Rev. 49 (5) (1996) 299-315; Gibson, C.H., J. Fluids Eng. 122 (2000) 830-835; Gibson, C.H., Combust. Sci. Technol. (2004, to be published).     

Ideal Turbulence

Ideal turbulence is a mathematical phenomenon which occurs in certain infinite-dimensional deterministic dynamical systems and implies that the attractor of a system lies off the phase space and among the attractor points there are fractal or even random functions. A mathematically rigorous definition of ideal turbulence is based on standard notions of dynamical systems theory and chaos theory. Ideal turbulence is observed in various idealized models of real distributed systems of electrodynamics, acoustics, radiophysics, etc. In systems without internal resistance, cascade processes are capable to birth structures of arbitrarily small scale and even to cause stochastization of the systems. Just these phenomena are inherent in ideal turbulence and they help to understand the mathematical scenarios for many features of real turbulence.     

Turbulence Plus

This paper attempts to give a concise overview of the turbulence research performed at the Laboratory for Aero and Hydrodynamics of the Delft University of Technology under the guidance of Frans Nieuwstadt. Frans Nieuwstadt was appointed in 1986 as director of the laboratory, and he held this position until his sudden death in 2005. Frans’ principal interest was to investigate turbulence at a fundamental level, but also to consider turbulence and its role in other processes. He coined a name for this research: turbulence plus.     

颗粒存在对网栅后气相流动湍流特性的影响

应用 L DV测试技术对方管内网栅后的气固两相流动 ,在颗粒平均粒径 Dp =0 .2 1 mm,颗粒质量浓度为 0 .2 4%、0 .36 % ;Dp =0 .35 mm,颗粒质量浓度为 0 .1 2 %、0 .2 1 %、0 .335 % ;Dp =0 .6 mm,颗粒质量浓度为 0 .1 6 %、0 .2 45 %、0 .34 5 % ;Dp =0 .9mm,颗粒质量浓度为 0 .2 0 5 %、0 .30 %多种工况下进行了测量 ,得出各种工况下气流脉动速度、湍动能沿流动方向的衰减规律 ,通过与纯气流条件下的实验结果比较 ,分析了颗粒浓度及颗粒尺寸对网栅后气相流动湍流特性的影响。根据测量结果 ,提出了一个在有固相颗粒存在时 ,关于湍流模型方程中模型常数 C2的修定方法。     

Vertical Motions of Heavy Inertial Particles Smaller than the Smallest Scale of the Turbulence in Strongly Stratified Turbulence

We study the statistics of the vertical motion of inertial particles in strongly stratified turbulence. We use Kinematic Simulation (KS) and Rapid Distortion Theory (RDT) to study the mean position and the root mean square (rms) of the position fluctuation in the vertical direction. We vary the strength of the stratification and the particle inertial characteristic time. The stratification is modelled using the Boussinesq equation and solved in the limit of RDT. The validity of the approximations used here requires that $ \sqrt{{L}/{g}} < {2\pi}/{\mathcal{N}} < \tau_{\eta} $ , where τ _η is the Kolmogorov time scale, g the gravitational acceleration, L the turbulence integral length scale and $\mathcal{N}$ the Brunt–Väisälä frequency. We introduce a drift Froude number $Fr_{d} = \tau_p g / \mathcal{N} L$ . When Fr _d ?<?1, the rms of the inertial particle displacement fluctuation is the same as for fluid elements, i.e. $\langle(\zeta_3 - \langle \zeta_3 \rangle)^2\rangle^{1/2} = 1.22\, u'/\mathcal{N} + \mbox{oscillations}$ . However, when Fr _d ?>?1, $\langle(\zeta_3 - \langle \zeta_3 \rangle)^2\rangle^{1/2} = 267 \, u' \tau_p$ . That is the level of the fluctuation is controlled by the particle inertia τ _p and not by the buoyancy frequency $\mathcal{N}$ . In other words it seems possible for inertial particles to retain the vertical capping while loosing the memory of the Brunt–Väisälä frequency.     

DNS of Fractal-Generated Turbulence

An innovative approach which combines high order compact schemes, Immersed Boundary Method and an efficient domain decomposition method is used to perform high fidelity Direct Numerical Simulations (DNS) of four spatially evolving turbulent flows, one generated by a regular grid and three generated by fractal square grids. The main results which we have been able to obtain from these simulations are the following: the vorticity field appears more clustered when generated by fractal square grids compared to a regular grid; fractal square grids generate higher vorticities and turbulence intensities than a regular grid; the flow holds clear geometrical imprints of the fractal grids far downstream, a property which could be used in the future for flow design, management and passive control; the DNS obtained with fractal grids confirmed the existence of two turbulent regions, one where the turbulence progressively amplifies closer to the grid (the production region) followed by one where the turbulence decays; the energy spectra of fluctuating turbulent velocities at various locations in the production region of the flow provide some information on how the turbulence is generated at the smallest scales first near the grid where the smallest wakes are dominant, followed by progressively smaller turbulent frequencies further downstream where progressively larger wakes interact.     

Stratified Turbulence in the Atmospheric Mesoscales

The first author proposed earlier that the atmospheric energy spectrum in the mesoscale range is controlled by upscale energy transport in stratified and geostrophic turbulence, with the source of the energy probably convective clouds and storms. This hypothesis is reviewed in the light of a variety of theoretical and mechanistic tests, mostly involving numerical simulation. Some conflicting results are noted, with fluid dynamics simulations mostly negative and meteorological simulations positive, including one new set presented here. The rapid increase in larger-scale energy shown in our simulations should, however, be ascribed in part to a different mechanism, involving the rapid growth of the unconstrained outflow and its further spreading by mean shear. Received 23 May 1997 and accepted 21 February 1998     

A Century of Turbulence

A brief, superficial survey of some very personal nominations for highpoints of the last hundred years in turbulence. Some conclusions can be dimly seen. This field does not appear to have a pyramidal structure, like the best of physics. We have very few great hypotheses. Most of our experiments are exploratory experiments. What does this mean? We believe it means that, even after 100 years, turbulence studies are still in their infancy. We are naturalists, observing butterflies in the wild. We are still discovering how turbulence behaves, in many respects. We do have a crude, practical, working understanding of many turbulence phenomena but certainly nothing approaching a comprehensive theory, and nothing that will provide predictions of an accuracy demanded by designers. This revised version was published online in July 2006 with corrections to the Cover Date.     

Turbulence Energy Distribution in the Stokes Layer

Using the method of matched asymptotic expansions, an analytical solution of the balance equation for turbulence energy is constructed for a shallow basin (sea) in which the fluid depth does not exceed the Stokes layer thickness. In this case, a gradient-viscous balance is established with the turbulent viscosity being balanced mainly by the pressure gradient. It is shown that nonlinear boundary layers attributable to turbulence energy diffusion are formed near the bottom and the free surface (or ice). In the neighborhood of the point of maximum flow velocity (if this maximum is attained inside the flow), a nonlinear internal boundary layer also develops. Outside these layers, the turbulence energy generation is in the first approximation balanced by the energy dissipation. Asymptotic solutions for the boundary layers are constructed.