Under consideration for publication in J. Fluid Mech. 1 New Scaling Laws for Turbulent PoiseuilleFlow with Wall Transpiration A fully developed, turbulent Poiseuille flow with wall transpiration, i.e. uniform blowing and suction on the lower and upper walls correspondingly, is investigated by both direct numerical simulation (DNS) of the three-dimensional, incompressible Navier-Stokes equations and Lie symmetry analysis. The latter is used to find symmetry transformations and in turn to derive invariant solutions of the set of two-and multi-point correlation equations. We show that the transpiration velocity is a symmetry breaking which implies a logarithmic scaling law in the core of the channel. DNS validates this result of Lie symmetry analysis and hence aids establishing a new logarithmic law of deficit-type. The region of validity of the new logarithmic law is very different from the usual near-wall log-law and the slope constant in the core region differs from the von Kármán constant and is equal to 0.3. Further, extended forms of the linear viscous sublayer law and the near-wall log-law are also derived, which, as a particular case, include these laws for the classical non-transpirating case. The viscous sublayer at the suction side has an asymptotic suction profile. The thickness of the sublayer increase at high Reynolds and transpiration numbers. For the near-wall log-law we see an indication that it appears at the moderate transpiration rates (0.05 < v 0 /u τ < 0.1) and only at the blowing wall. Finally, from the DNS data we establish a relation between the friction velocity u τ and the transpiration v 0 which turns out to be linear at moderate transpiration rates.

Under consideration for publication in J. Fluid Mech. 1Turbulent Plane Couette flow at moderately high Reynolds number

There are few observational techniques for measuring the distribution of kinetic energy within the mesosphere with a wide range of spatial and temporal scales. This study describes a method for estimating the three‐dimensional mesospheric wind field correlation function from specular meteor trail echoes. Each radar echo provides a measurement of a one‐dimensional projection of the wind velocity vector at a randomly sampled point in space and time. The method relies on using pairs of such measurements to estimate the correlation function of the wind with different spatial and temporal lags. The method is demonstrated using a multistatic meteor radar data set that includes ≈105 meteor echoes observed during a 24‐hr time period. The new method is found to be in good agreement with the well‐established technique for estimating horizontal mean winds. High‐resolution correlation functions with temporal, horizontal, and vertical lags are also estimated from the data. The temporal correlation function is used to retrieve the kinetic energy spectrum, which includes the semidiurnal mode and a 3‐hr period wave. The horizontal and vertical correlation functions of the wind are then used to derive second‐order structure functions, which are found to be compatible with the Kolmogorov prediction for spectral distribution of kinetic energy in the turbulent inertial range. The presented method can be used to extend the capabilities of specular meteor radars. It is relatively flexible and has a multitude of applications beyond what has been shown in this study.

PrefaceThe special importance of turbulence maybe comprehended by its ubiquity in innumerable natural and technical systems. Examples for natural turbulent flows are the atmospheric flow and the oceanic current which to calculate is a crucial point in climate research. Classical engineering application involving turbulence are the flows around airplanes or cars or turbulence within jet or reciprocating engines. Though supposed for more than hundred years, only with the advent of super computers it became apparent that the Navier-Stokes equations provide an excellent continuum mechanical model for turbulent flows. Still, the exclusive and direct application of the Navier-Stokes equations to practical flow problems at very high Reynolds numbers without invoking any additional assumptions is still several decades away.However, in most applications it is not at all necessary to know all the detailed fluctuations of velocity and pressure present in turbulent flows but for the most part statistical measures are sufficient. This was in fact the key idea of O. Reynolds who was the first to suggest a statistical description of turbulence. The Navier-Stokes equations, however, constitute a non-linear and, due to the pressure Poisson equation, a non-local set of equations. As an immediate consequence of this the equations for the mean or expectation values for velocity and pressure lead to an infinite set of statistical equations, or, if truncated at some level of statistics, an un-closed system is generated. Received 4 March 2015 AbstractThe present article is intended to give a broad overview and present details on the Lie symmetry induced statistical turbulence theory put forward by the authors and various other collaborators over the last twenty years. For this is crucial to understand that our present text-book knowledge proclaims that Lie symmetries such as Galilean transformation lie at the heart of fluid dynamics. These important properties also carry over to the statistical description of turbulence, i.e. to the Reynolds stress transport equations and its generalization, the multi-point correlation equations (MPCE). Interesting enough, the MPCE admit a much larger set of symmetries, in fact infinite dimensional, subsequently named statistical symmetries. Apart from the MPCE also the two other known complete theories of turbulence, the Lundgren-Monin-Novikov (LMN) hierarchy of probability density functions and the Hopf functional theory, share this property of admitting both classical mechanical and statistical Lie symmetries. As the Galilean transformation illuminates fundamental properties of classical mechanics, the new statistical symmetries mirror key properties of turbulence such as intermittency and non-gaussianity. After an introduction to Lie symmetries have been given, these facts will be detailed for all three turbulence approaches i.e. MPCE, LMN and Hopf approach. From a practical point of view, these new symmetries have important consequences for our understanding of turbulent scaling laws. The symmet...