This thesis is concerned with numerical and analytical modellig of over sloping terrain, also called katabatic winds. These winds are induced when a stably stratified atmospheric boundary layer is cooled from below. A horizontal potential temperature difference is produced between an air parcel close to the slope and one further away but at the same height, providing the near-surface air parcel with a negative buoyancy force with respect to its environment, which will make the air descend down the slope. Katabatic winds are characterized by persisting wind profiles exhibiting a wind maximum of the order of several metres per second. The wind maximum is normally located close to the surface. Consequently, the wind profiles have large vertical gradients, and the associated wind shear is a key factor in the production of turbulence. Turbulence is an important feature of katabatic winds; it is responsible for the vertical mixing of momentum and heat in the lowest part of the boundary layer. The mixing effectively transports heat from the boundary layer to the ground, thus acting to heat the surface. The numerical technique called large-eddy simulation (LES) is used to study katabatic winds. First, numerical results are validated by comparison with observations. Numerical results of first order moments agree rather well with the observations. Less satisfactory results for the comparison of observed higher-order moments with the numerical results are a result of low-quality observations and idealized setting in the simulations. Katabatic winds are moderated by several factors such the surface forcing (e.g. buoyancy flux), stratification of the ambient atmosphere, and the slope angle. The effect of one single factor is virtually impossible to determine from in-situ measurements. LES is therefore employed to study the effects of the three aforementioned variables on katabatic winds. The results show that the height and magnitude of the katabatic wind maximum increase with increasing surface buoyancy flux, but decrease with larger slope angle and ambient stratification. The negative buoyancy in the katabatic layer increases for larger surface buoyancy fluxes and smaller slope angles, whereas it is only slightly affected by a change in the stratification of the ambient atmosphere. The LES results of the turbulence kinetic energy (TKE) budget show in the bulk of the boundary layer an approximate balance between shear production and turbulent dissipation of TKE. Near the wind maximum height, the balance is between the (positive) turbulent transport of TKE and turbulent dissipation. A newly developed analytical model of katabatic flows induced by an infinitely long cold strip with limited width is also discussed. Due to the inhomogeneous surface forcing in the cross-slope direction, the buoyancy and downslope velocity fields have maximum values at the centre of the strip, which spread outward in the cross-slope direction. The cross-slope variation in the surface buoyancy produces cross-slope and slope-normal velocities. These two velocity fields combined show the present of two vortices near each strip edge
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