A new set of numerical simulations of turbulent plane Couette flow in a large box of dimension ( $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}20\pi h,\, 2h,\, 6\pi h$ ) at Reynolds number $(\mathit{Re}_{\tau }) =125$ , 180, 250 and 550 is described and compared with simulations at lower Reynolds numbers, Poiseuille flows and experiments. The simulations present a logarithmic near-wall layer and are used to verify and revise previously known results. It is confirmed that the fluctuation intensities in the streamwise and spanwise directions do not scale well in wall units. The scaling failure occurs both near to and away from the wall. On the contrary, the wall-normal intensity scales in inner units in the near-wall region and in outer units in the core region. The spectral ridge found by Hoyas & Jiménez (Phys. Fluids, vol. 18, 2003, 011702) for the turbulent Poiseuille flow can also be seen in the present flow. Away from the wall, very large-scale motions are found spanning through all the length of the channel. The statistics of these simulations can be downloaded from the webpage of the Chair of Fluid Dynamics.

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-transpiring 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 ( $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}0.05<v_0/u_{\tau }<0.1$ ) and only at the blowing wall. Finally, from the DNS data we establish a relation between the friction velocity $u_{\tau }$ and the transpiration $v_0$ which turns out to be linear at moderate transpiration rates.

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.

We present and characterize in time and three spatial dimensions a Kelvin‐Helmholtz Instability (KHI) event from polar mesospheric summer echoes (PMSE) observed with the Middle Atmosphere Alomar Radar System. We use a newly developed radar imaging mode, which observed PMSE intensity and line of sight velocity with high temporal and angular resolution. The identified KHI event occurs in a narrow layer of 2.4 km thickness centered at 85 km altitude, is elongated along North‐South direction, presents separation between billows of ~8 km in the East‐West direction, and its billow width is~3 km. The accompanying vertical gradients of the horizontal wind are between 35 and 45 m/s/km and vertical velocities inside the billows are +/‐ 12 m/s. Based on the estimated Richardson (< 0.25), horizontal Froude (~0.8), and buoyancy Reynolds (~2.5 ×10⁴) numbers, the observed event is a KHI that occurs under weak stratification and generates strong turbulence.

Measurements of kinetic energy in vortical and divergent fluctuations in the mesosphere and lower thermosphere can be used to study stratified turbulence (ST) and gravity waves. This can be done using horizontal correlation functions of the fluctuating component of velocity. This study introduces a novel method for estimating these correlation functions using radars that observe Doppler shifts of ionized specular meteor trails. The technique solves the correlation functions directly on a longitudinal‐transverse‐up coordinate system, assuming axial symmetry. This procedure is more efficient and leads to smaller uncertainties than a previous approach. The new technique is applied to a year‐long data set from a multistatic specular meteor radar network in Germany, to study the annual variability of kinetic energy within turbulent fluctuations at 87–93 km of altitude. In monthly averages, the kinetic energy is found to be nearly equipartitioned between vortical and divergent modes. Turbulent fluctuations maximize during the winter months with approximately 25% more energy in these months than at other times. The horizontal correlation functions are in agreement with the inertial subrange of ST, exhibiting a 2/3 power law in the horizontal lag direction, with an outermost scale of ST to be about 380 km. This suggests that horizontal correlation functions could be used to estimate turbulent energy transfer rates.

This study is motivated by the importance of the stratified turbulence in geophysical flows. We present a theoretical analysis of the buoyancy subrange based on the theory of strongly stratified turbulence. Some important turbulent scales and their relations are explored. Scaling constants of the buoyancy subrange scaling laws for both kinetic and potential energy spectra are derived and analyzed. It is found that these constants are functions of the horizontal Froude number $F{r}_h$ . For the potential energy spectrum, the scaling constant also depends on the turbulent flux coefficient of $\Gamma$ .