## Thermal Stability

**INFLUENCES OF THERMAL STABILITY ON TURBULENT BOUNDARY LAYERS**

OWEN WILLIAMS

Current work being conducted at the Gas Dynamics Lab involves an examination of the turbulence characteristics of thermally stable boundary layers, largely found in the arctic regions. These layers have a buoyant force acting toward the surface over which they flow and have been shown to have significantly reduced heat and momentum fluxes. The objective of this research is to examine the interaction between turbulent coherent structures and internal gravity waves, caused by the buoyancy of the flow. It will then be attempted to relate these interactions to the observed turbulent statistics.

This work is important because melting and freezing rates of arctic ice have been found to be increasingly unpredictable in recent years. As heat transfer rates are significantly affected by the flow of the atmospheric boundary layer over the ice pack, a better understanding of the effects of thermal stability on the turbulence within this layer would be hugely beneficial to a more accurate prediction of the ice melt and an improvement of Global Climate Models (GCM). An additional motivation stems from a need to estimate the dispersion of pollutants at more moderate latitudes where moderately stable nocturnal boundary layers can develop. This can significantly reduce the transport of pollutants away from the source, leading to unsafe air quality.

The extent of thermal stability is usually described by a single similarity parameter called the Richardson number that describes the relative strength of buoyant and inertial forces. A positive Richardson number denotes thermal stability. An inviscid analysis (Miles, 1961) indicates that a critical Richardson number of 0.25 separates two regimes of stability, the weakly stable and strongly stable, which broadly correspond to the two situations laid out above. Weakly stable turbulence is by far the most studied as it is well characterized by another theory called Monin-Obukhov similarity. Strongly stable boundary layers, like those found in the arctic are much more difficult to characterize as this theory breaks down. In addition, the appearance of internal gravity waves and intermittent turbulence has led some to suggest this regime should be broken into further sub-categories (Mahrt, 1998). Atmospheric measurements have been significantly hampered by the complexity and transience of the flow coupled with the significantly reduced heat and momentum fluxes. As a result, characterization of thermally stable boundary layers is currently incomplete.

The current experiment aims to experimentally investigate thermal stability effects in a low Reynolds number boundary layer in order to overcome some of these problems. This experiment is being conducted in a 16 foot long, 4’x2’ cross-section, open-return wind tunnel in which the upper surface is replaced with a half inch aluminum plate covered with strips of heating tape. The plate can be maintained at either an isothermal or constant heat flux condition. The flow is tripped and the tunnel run at a low speed, in order to maintain both a fully turbulent boundary layer and a large Richardson number. A wide range of stabilities are being investigated, with Richardson numbers ranging from 0 to 0.5, covering both the weakly and strongly stable regimes.

Flow characteristics will be measured with a combination of Particle Image Velocimetry (PIV), and a hot-wire anemometer and thermocouple traverse allowing the examination of both turbulence statistics and turbulent coherent structures by analyzing the two-dimensional flow field. The impact of thermal stability on the nature of turbulent coherent structures has not been examined previously and it is hoped that this analysis will help provide more physical insight into the nature of these complex flows.

This research is also being supported by a numerical study of these boundary layers by Prof. Bou-Zeid’s group in civil engineering at Princeton. It is hoped that these Large Eddy Simulations (LES), conducted at a higher Reynolds number, will help us extrapolate the results of these experiments to flows that more closely approximate the atmospheric boundary layer over the arctic ice sheet which has an extremely high Reynolds number.

Mahrt (1998), “Stratified Atmospheric Boundary Layers”, Boundary Layer Meteorology, 90: 375-396

Miles (1961), “On the stability of heterogeneous shear flows”, J . Fluid Mech. 10, 496.