The effect of wall cooling on a compressible turbulent boundary layer

Experimental results are presented for two turbulent boundary-layer experiments conducted at a free-stream Mach number of 4 with wall cooling. The first experiment examines a constant-temperature cold-wall boundary layer subjected to adverse and favourable pressure gradients. It is shown that the boundary-layer data display good agreement with Coles’ general composite boundary-layer profile using Van Driest's transformation. Further, the pressure-gradient parameter β_K found in previous studies to correlate adiabatic high-speed data with low-speed data also correlates the present cooled-wall high-speed data. The second experiment treats the response of a constant-pressure high-speed boundary layer to a near step change in wall temperature. It is found that the growth rate of the thermal boundary layer within the existing turbulent boundary layer varies considerably depending upon the direction of the wall temperature change. For the case of an initially cooled boundary layer flowing onto a wall near the recovery temperature, it is found that δ_T ~ x whereas the case of an adiabatic boundary layer flowing onto a cooled wall gives δ_T ~ x^½. The apparent origin of the thermal boundary layer also changes considerably, which is accounted for by the variation in sublayer thicknesses and growth rates within the sublayer

Turbulent dispersion in cloud-topped boundary layers

Compared to dry boundary layers, dispersion in cloud-topped boundary layers has received less attention. In this LES based numerical study we investigate the dispersion of a passive tracer in the form of Lagrangian particles for four kinds of atmospheric boundary layers: 1) a dry convective boundary layer (for reference), 2) a "smoke" cloud boundary layer in which the turbulence is driven by radiative cooling, 3) a stratocumulus topped boundary layer and 4) a shallow cumulus topped boundary layer. We show that the dispersion characteristics of the smoke cloud boundary layer as well as the stratocumulus situation can be well understood by borrowing concepts from previous studies of dispersion in the dry convective boundary layer. A general result is that the presence of clouds enhances mixing and dispersion ¿ a notion that is not always reflected well in traditional parameterization models, in which clouds usually suppress dispersion by diminishing solar irradiance. The dispersion characteristics of a cumulus cloud layer turn out to be markedly different from the other three cases and the results can not be explained by only considering the well-known top-hat velocity distribution. To understand the surprising characteristics in the shallow cumulus layer, this case has been examined in more detail by 1) determining the velocity distribution conditioned on the distance to the nearest cloud and 2) accounting for the wavelike behaviour associated with the stratified dry environmen

Spectral analysis of boundary layers in Rayleigh-Benard convection

A combined experimental and numerical study of the boundary layer in a 4:1 aspect-ratio Rayleigh-B\'{e}nard cell over a four-decade range of Rayleigh numbers has been undertaken aimed at gaining a better insight into the character of the boundary layers. The experiments involved the simultaneous Laser Doppler Anemometry (LDA) measurements of fluid velocity at two locations, i.e. in the boundary layer and far away from it in the bulk, for Rayleigh numbers varying between $1.6 \times 10^7$ and $2.4 \times 10^9$. In parallel, direct numerical simulations (DNS) have been performed for the same configuration for Rayleigh numbers between $7.0 \times 10^4$ and $7.7 \times 10^7$. The temperature and velocity probability density functions and the power spectra of the horizontal velocity fluctuations measured in the boundary layer and in the bulk flow are found to be practically identical. Except for the smallest Rayleigh numbers, the spectra in the boundary layer and in the bulk central region are continuous and have a wide range of active scales. This indicates that both the bulk and the boundary layers are turbulent in the $\textrm{Ra}$ number range considered. However, molecular effects can still be observed and the boundary layer does not behave like a classical shear-driven turbulent boundary layer.Comment: 10 pages, 6 figures, Accepted for publication in Phys. Rev.

On Reflection of Shock Waves from Boundary Layers

Measurements of the reflection characteristics of shock waves from a flat surface with a laminar and turbulent boundary layer are presented. The investigations were carried out at Mach numbers from about 1.3 to 1.5 and a Reynolds number of 0.9 x 10^4. THe difference in the shock-wave interaction with laminar and turbulent boundary layers, first found in transonic flow is confirmed and ,investigated in detail for supersonic flow. The relative upstream influence of a shock wave impinging on a given boundary layer has been measured for both laminar and turbulent layers. The upstream influence of a shock wave in the laminar layer is found to be of the order of 50 bounday-layer thicknesses as compared with about 5 in the turbulent case. Separation almost always occurs in the laminar boundary layer. The separation is restricted to a region of finite extent upstream of the the shock wave. In the turbulent case no separation was found. A model of the flow near the point of impingement of the shock wave on the boundary layer is given for both cases. The difference between impulse-type and step-type shock waves is discussed and their interactions with the boundary layer are compared. Some general considerations on the experimental production of shock waves from wedges and cones are presented, as well as a discussion of boundary layer in supersonic flow. A few exampies of reflection of shock waves from supersonic shear layers are also presented