Stratified Airflow Research Articles

Stratified airflow over one or two hills

Methods for calculating, interpolating and idealising air flow in complex terrain are reviewed. Then the general structure of stratified airflow over a single hill of height H and length L1 is studied in detail and shown to be determined by the upwind velocity profile, the magnitude of a characteristic Froude number and the dimensions of the hill. Let N(L1) be the buoyancy frequency upwind at a height L1, and u* and U0 be the upwind friction and mean velocity respectively; then the flow is effectively neutral if u*/NL1>1. But if u*/NL1>1 and u0/NL1>1, the stratification is weak enough to affect the upwind turbulence and velocity profile but not the dynamics of the flow over the hill. If U0/NL1 1 the buoyancy forces are strong enough to affect the mean flow over the hill but not strong enough to prevent it passing over the top. In this regime the flow is very sensitive to the form of the upwind temperature profile. If U0/NH>1, much of the flow passes round the hill. A similar classification, with different flow patterns, is appropriate for unstably stratified flows. When the wind is weak enough, local slope winds can dominate. Results from the analysis of these different regimes are described and compared with laboratory of field measurements where possible. It is shown how some of these results can be extended to groups of hills.

Numerical studies of stratified air flow over a mountain ridge on the rotating earth

The non-linear equations describing adiabatic, quasi-static flow of stably stratified air over a mountain ridge on the rotating f- plane are integrated numerically in time, using potential temperature as vertical coordinate. The initial state is a horizontal, parallel flow over level ground, and the cosine-shaped, 400 km wide ridge, oriented normal to the initial flow, is allowed to grow to full height in 20 h. The potential vorticity remains constant in each isentropic surface, and this condition is used in the calculations instead of the mass continuity equation. Results of calculations starting with 4 different initial wind profiles are shown. After about 5 model days of integration, the motion within the integration area of length 4 Mm settled down to a nearly steady flow. This flow exhibits a system of gravity-inertia lee waves with dominating wavelengths comparable to the mountain width. The prominent wavelengths seem in all calculations to be limited to waves shorter than the inertia wavelength at the lower boundary (for which the particle frequency equals the Coriolis parameter). The waves are discussed in the light of linear theory and ray tracing. In a case where the initial wind velocity decreases with height, there is a clear tendency towards formation of pure horizontal, undamped inertia waves in the layer of wind shear, with cycloid-shaped horizontal trajectories. Besides the wave pattern, the stationary flow also shows a large-scale turning of the streamlines, to the left on the upstream side and to the right on the lee side, with a distinct anticyclonic bend over the mountain ridge. The formation of this turning is explained as a consequence of the loss of mass through the open boundaries connected with the growth of the mountain; thus the turning depends on the formulation of the inflow and outflow boundary conditions. Unless the large-scale turning is strictly symmetric with respect to the mountain ridge, the flow will possess a component along the ridge, with a corresponding geostrophic pressure gradient which together with the wave drag will contribute to the total horizontal force acting on the mountain. DOI: 10.1111/j.1600-0870.1984.tb00237.x

A model of the feeder–seeder mechanism of orographic rain including stratification and wind‐drift effects

AbstractOrographic enhancement of rain via the ‘feeder‐seeder’ mechanism has been calculated using a stratified airflow model. The effect of wind drift on precipitation has been included. Comparisons have been made using potential flow models both in two and in three dimensions and in the model of M. J. Bader and W. T. Roach.For high windspeeds (≥ 15ms−1), when large enhancements occur, the potential flow treatment is sufficient. Inclusion of stratification does not significantly affect the total washout, although in the case of long hills (half‐length ≥ 10km) the precipitation maximum is moved upwind. For long hills the results are also in close agreement with the model of Bader and Roach. Over shorter hills both wind drift and non‐hydrostatic effects are important. Wind drift decreases both maximum and total enhancements. The Bader and Roach airflow formulation is inaccurate since it overestimates streamline displacements over the hill. Three‐dimensional effects are small except over short steep hills.

Evaporation from a Warm, Wavy Surface: A Laboratory Study

The evaporation rates from small wind-waves by forced convection in a range where the spray of water by strong wind action is not important have been studied in the laboratory. The effects of free stream velocity, wave conditions and temperature differences between air and water (either stable or unstable stratified air flow) on evaporation are investigated. For stably stratified air flow, the evaporation rate correlates well with general dynamical parameters but not for unstably stratified flow. The buoyancy flux near the boundary appears to play an important role in moisture transfer at the air-sea interface. The effect of the buoyancy flux is considered important inside the diffusion sublayer. The thickness of the diffusion sublayer is not only a function of shear velocity and roughness but also a function of buoyancy flux. Based on this, the final form of evaporation rate can be given in a dimensionless form aswhere A is an empirical constant, Sh the Sherwood number, Cf the drag coefficient, B+ the buoyancy flux, and Re the Reynolds number. The above equation applies well to both stable and unstable stratified flow and indicates that the buoyancy flux from the boundary strongly affects the evaporation rate.