Turbulence – a resolved problem? 17 November 2010

This was the third of the ‘classic papers’ meetings and was introduced by Malcolm Walker who gave a brief talk on the early career of G. I. Taylor, in particular his time as meteorologist on the ice-patrol vessel Scotia during a cruise to study icebergs and meteorology off Newfoundland after the sinking of the Titanic. During this time Taylor used kites to make measurements of winds, temperature and humidity above the surface, subsequently using the observations to investigate the transfers of heat and momentum by turbulence in the lower atmosphere. The use of poison gases in World War I meant that understanding dispersion of gases in the atmosphere became a problem of national importance. Dave Thomson (Met Office) reviewed Diffusion by continuous movement (Taylor, 1920) and Atmospheric diffusion shown on a distance-neighbour graph (Richardson, 1926), which laid the foundations for our understanding of dispersion in the atmosphere. Taylor considered how a plume emitted from a point source would grow. The paper used a Lagrangian description of dispersion, following fluid particles assuming that the correlation between the velocity of a fluid particle at two different times decreased over a finite timescale, tL. For times much greater than tL the width of the plume grows diffusively. For times less than tL the growth is proportional to time. The Lagrangian approach to diffusion described by Taylor is used in dispersion models intended for practical applications, as illustrated by the Met Office Numerical Atmospheric-dispersion Modelling Environment (NAME) model. Richardson was struck by the large increase in diffusivity that occurred with increasing scale. He was also exercised by the question of whether the wind possesses a velocity. Taylor assumed it did, but Richardson considered that it was worth constructing a theory of dispersion without this assumption, so he investigated how the separation of pairs of particles increased with time in a turbulent flow. Turbulent eddies with scales much larger than the separation of the pair will move the particles together but eddies with scales comparable to or smaller than the separation of the pairs will pull them further apart. As the larger eddies are more energetic the diffusivity increases with the separation of the particles. Richardson's work on particle pairs has important applications in modelling fluctuations in concentration. Andy Brown (Met Office) reviewed Numerical investigation of neutral and unstable planetary boundary layers by Deardorff (1972). Turbulent motions in the atmospheric boundary layer range in scale from approximately 1000m down to approximately 1cm. Even with today's computers it is not possible to model the full range of scales. However, most of the energy in the turbulence is contained in the large scales, while dissipation of turbulent kinetic energy occurs at the smallest scales. Deardorff's model solved the equations of motion explicitly for the large eddies, while the effects of the smaller, unresolved, scales on the large eddies were parametrized. Near boundaries, such as the surface or inversions, the scale of the turbulent eddies decreases and the numerical resolution becomes insufficient for them to be resolved. Despite these problems large-eddy simulation is used extensively to study boundary layer turbulence. The parametrization of entrainment in a stratocumulus-capped boundary layer was given as an example of the application of large-eddy simulation. Gabriel Rooney (Met Office) reviewed Turbulent gravitational convection from maintained and instantaneous sources by Morton, Taylor and Turner (MTT, 1956). This paper developed a model of a turbulent plume, driven by a buoyancy flux, rising into a stratified fluid (an example might be smoke rising from a chimney into the nocturnal boundary layer). Entrainment of ambient fluid into the plume at some height due to turbulence was assumed to be proportional to the characteristic plume velocity at that height. From this, similarity solutions could be derived and the height to which the plume would rise obtained. Since its publication the MTT model has been extended to jets (plumes with initial momentum), wakes and thermals. Simple plume models remain of considerable interest because they can be used in practical dispersion models. It was shown how large-eddy simulation could be used to suggest modifications to the parametrization of entrainment in these models. The last two speakers described some current work in atmospheric and oceanic boundary layer turbulence. Bert Holtslag (Wageningen University) considered the stable boundary layer and its representation in climate and numerical weather prediction (NWP) models. Some of the largest errors in near-surface temperatures in climate models occur in regions of stable stratification (e.g. over Siberia during the winter). GABLS (GEWEX (Global Energy and Water Cycle Experiment), Atmospheric Boundary Layer Study) brings together people using large-eddy simulation and parametrization scientists with the aim of improving the representation of the stable boundary layer in large scale numerical models. The strategy is based on devising case studies with increasing realism which can be simulated using large-eddy simulation and single-column models based on the parametrization schemes in climate and NWP models. Stephen Belcher (University of Reading) described the use of large-eddy simulation to study mixing in the ocean surface boundary layer. While it might seem that the oceanic boundary layer is broadly an upside-down version of the atmospheric boundary layer, in reality this is not the case. The wind action on the sea surface generates surface waves; these can affect turbulent mixing through breaking and, more subtly, through the generation of Langmuir circulations, which are responsible for foam streaks and lines of floating material that can be seen on the surface of the sea when it is windy. These lines mark convergence zones between horizontal vortices in the upper part of the ocean that are aligned in the direction of the wind. It is now known that these circulations arise from an interaction between the propagating surface waves and vorticity in the ocean. This talk showed how large-eddy simulation can be used to study the effect of these circulations on turbulent mixing, with the aim of developing improved parametrizations. This interesting meeting showed how the subject of turbulence has developed. Is it a resolved problem? Computationally, the answer is strictly no but techniques such as large-eddy simulation are leading to a better understanding of it in the atmospheric and oceanic boundary layer.

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