Session R7: Turbulent Boundary Layers VIII: Geophysical

Disruption of bottom log-layer in LES of Langmuir circulation in shallow seas

We report on disruption of the log-layer in the resolved bottom boundary layer in large- eddy simulations (LES) of full-depth Langmuir circulation (LC) in a wind-driven shear current in neutrally-stratified shallow water. LC consists of parallel counter rotating vortices that are aligned roughly in the direction of the wind and are generated by the interaction of the wind-driven shear with the Stokes drift velocity induced by surface gravity waves. The disruption is analyzed in terms of mean velocity, budgets of turbulent kinetic energy (TKE) and budgets of TKE components. For example, in terms of mean velocity, the mixing due to LC induces a large wake region eroding the classical log- law profile within the range 90 $<$ z+ $<$ 200. The dependence of this disruption on wind and wave forcing conditions is investigated. Results indicate that the amount of disruption is primarily determined by the wavelength of the surface waves generating LC. These results have important implications on turbulence parameterizations for Reynolds-averaged Navier-Stokes simulations (RANSS) of the coastal ocean. Preliminary simulations highlight the need for turbulence models taking into account log-layer disruption by LC, as RANSS with the k-epsilon model is unable to capture this disruption.   

Dispersion length scales within the urban canopy

We discuss the results of lab experiments on three model urban canopies with small, medium and large building aspect ratios to examine the physics of dispersion within the urban canopy from a near-ground continuous point source of passive scalar. The model urban canopies had aspect ratios of building height to width (H/w) = 0.25, 1, 3. Measurements were taken of the turbulent velocity and scalar fields. Plume spreads, concentrations and distance from the source were non-dimensionalized using urban canopy length, time and velocity scales based on the geometry of the buildings. The scaling collapses the data for all three aspect ratios. A model to describe the results is developed. The model is based on a simple Gaussian formulation where the diffusion coefficients are determined by the theories of Taylor (1921) in the horizontal plane, and Hunt and Weber (1979) to account for the vertically inhomogeneous turbulence.   

Scale separation effects in turbulent boundary layers

The velocity and vorticity field interactions that underlie the mean mechanism of turbulent inertia and the wall-normal variation of turbulence kinetic energy are investigated over a wide variation in Reynolds number. Existing well-resolved laboratory data, $\delta^+=375$, $970$ \& $1500$, and data from the atmospheric surface layer over Utah's west desert, $\delta^+=890,000$, are used to establish the relevant statistical and spectral properties. The influences of scale- separation, as well as the scale selection phenomena first observed by Priyadarshana et al. (\textit{J. Fluid Mech.} \textbf{570}, 2007) are of interest. Scale-separation is quantified using both the difference and ratio of the peak frequencies of the relevant velocity and vorticity components. The scale selection phenomena is clarified by examining the relative behavior of the spectra and associated co-spectra as a function of both $y^+$ and $\delta^+$. Near the wall, scale- separation is due to the rapid spatial confinement of the vortical motions, while the scale selection correlates with the vorticity spectra. Away from the wall, scale-separation is due to the spatial dispersion of the vortical motions, and the scale selection correlates with the velocity spectra.   

On the distribution of the streamwise fluctuation velocity in wall bounded flows

The streamwise velocity fluctuations in wall-bounded flows has recently received renewed interest. Measurements and simulations at low Reynolds numbers ($Re$), as well as high $Re$ wind tunnel studies and data from the atmospheric boundary layer (ABL) are at hand but show sometime conflicting trends with $Re$. However, high $Re$ data often have some uncertainties associated with them, such as poor spatial resolution for laboratory data or other uncertainties associated with ABL experiments. Several models for the wall normal distribution of $u_{rms}$ have recently been proposed, based on various physical ideas together with empirical inputs. Here we propose a new model based on two observations: a) $u_{rms}$ normalized with the local velocity $U$ decreases linearly with respect to $U/U_\infty$ in the outer part of the flow, b) in the inner region $u_{rms}/U$ deviates from the linear trend at a specific value of $U/u_\tau(\approx 17)$, where $u_\tau$ is the friction velocity. Using this information it is possible to formulate a composite description of $u_{rms}$ in the wall normal direction for all Reynolds numbers. This shows two important results, namely the increase in $u_{rms}/u_\tau$ with $Re$ as well as a prediction of a second ``outer'' maximum when $Re$ is high enough, a debated feature that has been observed in ABL experiments as well as in some laboratory experiments at high $Re$.   

The effect of atmospheric stability on the energetic contribution of the large scale structures in turbulent boundary layers

Turbulent boundary layer measurements in wind tunnels and in the near neutral atmospheric surface layer outlined a significant contribution of the large scale motions to turbulent kinetic energy and Reynolds stresses for a wide range of Reynolds number, providing evidence of complex scale interactions across the wall region. In order to understand the effect of the large scales on the near wall turbulence and extend the predictive models of amplitude modulation to more realistic atmospheric conditions, different thermal stability conditions must be explored. In this study, experiments are performed in the atmospheric wind tunnel of the St. Anthony Falls Laboratory independently controlling air flow and floor temperatures. Measurements of fluctuating temperature simultaneously with the streamwise and wall normal velocity components are obtained with an ad hoc calibrated and customized triple-wire sensor. Scaling quantities and the dominant terms in the turbulent kinetic energy and temperature variance budget equations are estimated and discussed. A comparative analysis of the weakly stable, convective and neutral conditions based on the power spectra of the streamwise, wall normal and Reynolds stress contributions is presented. Appreciable differences in the energetic contributions of the large scales were observed.   

Cyclic instabilities, turbulence and heat transfer in rotating channel flow simulations

Fully developed turbulent channel flow subject to spanwise rotation including a passive scalar is studied by direct numerical simulations. The Reynolds number based on the bulk velocity and channel half width is up to 30000 and the rotation rate covers a broad range. At moderate rotation rates the flow partly relaminarizes on the stable side of the channel and in some cases turbulent spots or oblique laminar and turbulent bands can be identified. The turbulent Prandtl number is close to one in non-rotating channel flow, but is it much smaller if the flow is rotating. At high rotation rates and sufficiently high Reynolds numbers cyclic instabilities are observed. The time scale of the instabilities is much longer than any turbulent time scale. Further analysis show that these instabilities are caused by exponentially growing Tollmien-Schlichting (TS) waves which can develop due to the weak turbulence in rapidly rotating channel flow. When the amplitude is large these TS waves become unstable and break down into intense turbulence which decays because of the rotation. After some time the TS waves start growing again when the turbulence is sufficiently weak and the whole process repeats itself. The cyclic instabilities lead to intense bursts of turbulence, strong wall shear stresses and high heat transfer rates.   

The role of stability in modulating the structure and transport efficiency of turbulence in the atmospheric surface layer

A vast body of literature has emerged over the last few decades on the topology, dynamics, and role of coherent structures in turbulent boundary layer flows. The applicability of this knowledge to geophysical flows is problematic due to the often-dominant role of buoyancy. Here we aim to investigate the effect of buoyancy on coherent turbulent structures, with a focus on the ties between these structures and turbulent transport. The results confirm that the topology of the coherent structures is very sensitive to stability. The findings point to a gradual transformation of the structures from hairpin vortices (or horizontal rolls) to thermals, as the upward buoyancy flux increases. More importantly, this change induces a decorrelation of the momentum and scalar fluxes in the surface layer and significant change in the relative efficiencies of momentum and scalar transport. Scalars are transported much more efficiently under unstable conditions. These findings provide a better framework for including the effect of stability in turbulent transport models and open the way for more advanced models based on a better understanding of turbulent scale-interactions under different stabilities.   

Viscous boundary layers in turbulent Rayleigh-B\'{e}nard convection

Thermal convection at high Rayleigh number is a basic and important ingredient for the motion of air or the flow of water in the atmosphere and in the ocean. However, particularly in case of highly turbulent flows the knowledge about the temperature and the velocity field is still limited. Highly resolved 3d-Laser Doppler Velocimetry measurements in a large-scale Rayleigh-B\'{e}nard experiment with air at Rayleigh numbers up to 10$^{10}$ have been carried out and presented by our group on 2010's APS conference. All three velocity components have been measured simultaneously in the vicinity of the cooling plate in the central axis of the cylindrical sample. We found that the profile of the mean wall-normal velocity tends to zero. In the contribution of this year we will enhance the understanding of the heat transport by presenting the fluctuations of the wall-normal velocity component and the temperature. Again, we estimate the profile of the local heat flux from the independently measured velocity and temperature data.   

Reynolds and swirl number effects on turbulent pipe flow in a 90 degree pipe bend

Flows in pipe bends have been studied extensively over the last decades due to their occurrence both in the human respiratory and blood systems as well as in many technical applications. The centrifugal effect of the bend may give rise to Dean vortices and the behaviour of these has been of particular interest. While their motion has nicely been illustrated in laminar flows, the picture of their motion in turbulent flows remains rather blurred. Within the framework of the present work, fully developed turbulent pipe flow from a 100 diameter ($D$) long pipe is fed to a $90^\circ$ bend and the flow field at $0.5D$ downstream the bend has been studied by means of Time-Resolved Stereoscopic Particle Image Velocimetry, covering a Reynolds number range from 7000 to 34000 based on bulk velocity ($U_b$) and $D$. Additionally, a well defined swirl profile could be introduced by rotating the $100 D$ long straight pipe along its axis, yielding a variation in swirl number ($S$), defined as the ratio between the azimuthal velocity of the pipe wall and $U_b$, from 0 (the non-rotating case) to 1.2. The three-dimensional time-averaged and instantaneous flow field illustrating the symmetrical Dean vortices for $S=0$ and the influence by the swirling motion for $S\neq0$, the so-called ``swirl-switching phenomenon,'' as well as the large-scale structures will be presented and discussed.