Substructures within a turbulent spot which develops in a slightly heated laminar boundary layer have been identified using arrays of cold wires aligned in either a streamwise direction or in a direction normal to the wall. At any given streamwise distance from the spot origin, histograms of the number of detected substructures exhibit a peak, defining the most probable spot or the spot with the most likely number of substructures. The number of substructures in the most probable spot increases with streamwise distance but all substructures are convected at approximately the same velocity for any given distance from the wall. This velocity is approximately equal to that of the leading edge of the spot and increases slightly with distance from the wall. The increase in the number of substructures accounts for the streamwise growth of the spot. A simple relation is derived for determining the number of substructures at a particular streamwise station and a geometrical construction is proposed for identifying the origin of a new substructure. There is sufficient evidence for suggesting that the new substructures are formed near the trailing edge of the spot. The convection velocity, inclination and lengthscales of the substructures compare favourably with the corresponding characteristics of hairpin vortices.

Substructures in a turbulent spot

In nearly every area of fluid mechanics, our understanding is limited by the onset or presence of turbulence. Although recent years have seen a great increase in our physical understanding, a predictive theory of turbulent flow has not yet been established. Aside from certain results that can be derived through dimensional reasoning, it is still not possible to solve from first principles the simplest turbulent flow with the simplest conceivable boundary conditions. Our continuing inability to make accurate, reliable predictions seriously limits the technological advancement of aircraft design, design of turbomachinery, combustors, mixers, and a wide variety of other devices that depend on fluid motion for their operation. Anyone who is introduced to the subject of turbulence for the first time quickly encounters the decomposition of the unsteady flow first proposed by Osborne Reynolds in 1895. Various flow variables are divided into a mean and fluctuating part, and upon substitution into the Navier-Stokes equations the result is a system of equations identical in form to the original system except for convective stress terms, which arise from averaging products of velocity fluctuations. In order to close the system of equations, a second relation is needed between the convective stresses and the mean velocity field. Until recently, much theoretical and experimental effort was focused on finding relationships that could be applied to larger and larger classes of mean flows with the ultimate hope of finding a universal constitutive relation for "turbulent fluid." There was never any guarantee that such a relation actually exists and the goals of this effort remain largely unrealized. Hope for a universal turbulence model has been slowly replaced by the growing www.annualreviews.org/aronline Annual Reviews

Organized motion in turbulent flow 8184

The main characteristics of the astroclimate (the structure of turbulent fields and conditions for their formation) are studied for several Russian astronomical observatories in southern Siberia and North Caucasus, including Sayan Solar, Baikal Astrophysical, Special Astrophysical, and Kolyvansky Ridge Observatories and the Center for Laser Atmosphere Sensing of Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences. The experimental results have been received from long-term astroclimate observations (expeditions in 2006–2017) with the use of small-size ultrasonic weather stations; and theoretical results, from the numerical solution of different boundary problems for the Navier–Stokes equations. The presence of regions with coherent (non-Kolmogorov) turbulence over the observatories has been ascertained, the formation of which is caused by the topography and the nonuniform heating of the underlying surface. Large-scale coherent vortex structures and coherent turbulence have been detected inside dome rooms. Numerical simulation allows us to analyze the influence of design features and temperature regimes of the telescope components and to test the telescope optical characteristics, including the minimization of the effects of external and under-dome turbulence. The paper includes the review of the history and evolution of the “coherent structure” and “coherent turbulence” concepts based on the world scientific literature and our own researches.

Formation of Turbulence at Astronomical Observatories in Southern Siberia and North Caucasus

Measurement results of main atmospheric parameters are given for different geographical areas and meteorological situations. A mobile ultrasonic meteosystem was used for the measurements. It is shown that turbulence in mountains has non-Kolmogorov character and pronounced features of coherent structure. The authors define coherent structures and specify their main properties. In particular, structure functions and values of the Kolmogorov and Obukhov constants vary for the coherent turbulence in comparison with the Kolmogorov incoherent one. The structure function of temperature fluctuations has been calculated on the base of model three-dimensional spectrum of coherent turbulence; the behavior of its asymptotes has been studied.

Structure function of temperature fluctuations in coherent turbulence

Possible approaches to modeling two-dimensional coherent hydrodynamic structures based on the statistical mechanics of local vortices are considered. The exact definitions of coherent structures are given and the mechanisms of their formation are shown. The bases of the kinetic theory of Onsager vortices are given and the possibility of applying the classical molecular-kinetic theory for the explanation of the origin of vortex meso-structures in the shear flows is considered.

E. W. Teh

Papers

The fabric of turbulence