Geostrophic Drag Coefficient Research Articles

Swinbank on boundary-layer research

In recognition of his pioneer work and notably effective leadership in the experimental investigation of the atmosphere’s surface boundary layer, W. C. ‘Bill’ Swinbank has been called ‘ . . . the arch-apostle of the small, controlled field experiment’ (Priestley, 1974). That this appellation is well deserved is demonstrated by the published record of the research arising from the field programs he conducted in Australia during the 1960’s, under the auspices of the CSIRO Division of Meteorological Physics. Swinbank’s major papers on boundary-layer research were published in the decade before this journal came into existence, although his very last note on the subject (‘The geostrophic drag coefficient’, 1974) did appear in these pages. It therefore seems appropriate that this memorial volume include some more specific reference to his earlier work by quoting selections chosen as much for style as content in order to recall Bill Swinbank td those who knew him, and to introduce him to those who did not. In part because of the work summarized here, we have come to know that, given uniform conditions of weather and terrain, distributions of wind and temperature in the surface boundary layer can be sufficiently steady in the mean to enable micrometeorological measurements approaching laboratory quality to be obtained in the field. Exploiting the fact that such conditions frequently exist over the plains of southeastern Australia, Bill Swinbank organized and led a remarkable series of micrometeorological field expeditions whose measurements set a standard of precision and internal consistency seldom approached during the ensuing decade. His own descriptions of the design, conduct, and analysis of these studies are distributed among a number of papers and reports. Recollected, they provide an account of unique interest to the student of the atmospheric boundary layer. Should some few points made then now seem obvious to the more informed reader (who benefits from more than ten years’ hindsight), one must ask why similarly exacting standards are not universally observed in boundary-layer field work today.

Direct determination of geostrophic drag coefficients at sea

Geostrophic drag coefficients are obtained from direct measurements of the momentum flux and from an objective analysis of the synoptic pressure field by the method of least squares. At a site in the Kiel Bight, a mean geostrophic drag coefficient cg = 0.0223 was obtained with near neutral/ slightly unstable conditions and a surface Rossby Number of 1.2 × 109.

The geostrophic drag coefficient

A power-law formulation for the geostrophic drag coefficient in a neutral atmosphere is presented.

Interaction between the atmospheric and oceanic boundary layers

The two-layer system of an atmosphere over water bodies is reduced to a single-layer problem. Values of the interfacial quantities, such as the friction velocity, the surface velocity, the angles, α and β, between the surface shear stress and the geostrophic wind velocity and the surface wind velocity, respectively, and the surface roughness, all of which depend upon external parameters, such as the geostrophic wind and stratifications, are obtained. The geostrophic drag coefficient Cd, the geostrophic wind coefficient Cf, and the angles α, and β, of the turbulent flow at the sea-air interface are functions of a dimensionless number, mfG/kg, with S1 and S2 as two free stratification parameters. The surface roughness is uniquely determined from the geostrophic wind rather than from the wind profile in the boundary layer.

The Effect of Thermal Stratification and Evaporation on Geostrophic Drag Coefficient in the Atmospheric Boundary Layer

It is shown that the fields of velocity, eddy viscosity, potential temperature, and specific humidity in a planetary boundary layer are decoupled by the introduction of a free parameter, Q, which combines the effects of thermal and humidity stratification. Solutions of the whole system are shown to be obtainable by the method of trial and error on Q. Results show good agreement when both the thermal and humidity stratification are accounted for.

Geostrophic drag coefficients

Data on the relationship of the surface wind to the geostrophic wind at Porton Down, Salisbury Plain, are presented for various stability conditions and analysed in the light of the Rossbynumber similarity theory. For near-neutral conditions, the geostrophic drag coefficients for geostrophic wind speeds 5 to 15 m s-1 are close to those found by other workers but at higher speeds the values are low. Comparisons of geostrophic and radar wind speeds for ⋍900-m height, suggest that undetectably small mean cyclonic curvatures of the trajectories of the air are responsible for this departure.

Computing Evapotranspiration by Geostrophic Drag Concept

A procedure for computing regional evapotranspiration has been derived and tested. The assumptions underlying the model are essentially those used in the one dimensional mass transfer methods, but the shear stress is determined by means of τ o = ρC g ²V go ² in which ρ = the density of the air; C g = the geostrophic drag coefficient as first proposed by Lettau; and V go = the surface geostrophic wind. The main advantage of the method is that all data needed in the computation, i.e., the surface temperature, the pressure of the air, the specific humidity at two levels in the atmospheric boundary layer, and the surface geostrophic wind speed can be obtained from standard meteorological data. Generally, good agreement was obtained between mean monthly evapotranspiration computed for a number of stations and the corresponding evaporation data obtained from Class-A pans.

Comments on “Geostrophic Drag, Heat and Mass Transfer Coefficients for the Diabetic Ekman Layer”

Comments on “Geostrophic Drag, Heat and Mass Transfer Coefficients for the Diabetic Ekman Layer”

Geostrophic Drag, Heat and Mass Transfer Coefficients for the Diabatic Ekman Layer

The “asymptotic matching” principle has been applied to the equilibrium Ekman layer with vertical but flux. This principle requires that the properties of the “surface” or “inner” layer overlap asymptotically (at large z) with those of the “outer” layer, or rather, with the asymptotic behavior of the latter as z→0. In this manner, it is possible to derive relationships for the geostrophic drag, heat transfer, and mass transfer coefficients (i.e., relate surface fluxes to large-scale properties of the motion) without considering the detailed dynamics of the outer Ekman layer, by relying on the fairly accurately known surface, layer distributions of nondimensional velocity, temperature and humidity gradients. Such bulk transfer coefficients are presented as functions of nondimensional parameters involving large-scale measures of the flow only. Extrapolation of the calculated drag coefficients to strong stability suggests that the shear stress vanishes when the negative buoyant acceleration due to air-ground temperature difference becomes large enough compared to surface pressure gradient. For strong instability the transfer coefficients become independent of the Coriolis force.

The geostrophic drag coefficient and the ‘effective’ roughness length

AbstractAn ‘effective’ roughness length is defined for use over heterogeneous terrain as the roughness length which homogeneous terrain would have to give the correct surface stress over a given area. A method is suggested to compute geostrophic drag coefficient, wind‐contour angle and surface heat flux, given this roughness length, latitude, geostrophic wind speed and insolation or ground‐air temperature differences.

NUMERICAL STUDIES OF EFFECTS OF SURFACE FRICTION ON LARGE-SCALE ATMOSPHERIC MOTIONS1

Abstract A simple relationship is obtained between pressure changes associated with friction and the geostrophic drag coefficient. From this, the imbalance between frictionally induced mass inflow and outflow is shown to be one or two orders of magnitude smaller than either the inflow or outflow. Numerical integrations using the primitive equations are performed for an axially symmetric autobarotropic low-pressure system. The velocity components and pressure tendencies are found to depend critically on the drag coefficient. Two actual synoptic cases are studied using a quasi-geostrophic numerical model incorporating release of latent heat. Computations are performed with and without surface friction. When friction is excluded, the 1000-mb Highs and Lows are more intense. Two methods of computing the surface stress are compared. One is based on variations in terrain height and the other on the nature of the vegetation. Differences are large, especially over the western part of North America.

THERMALLY AND FRICTIONALLY PRODUCED WIND SHEAR IN THE PLANETARY BOUNDARY LAYER AT LITTLE AMERICA, ANTARCTICA

Abstract Pilot balloon wind profiles obtained by the first and second Byrd Antarctic Expeditions are analyzed to show that the mean observed wind shear between the surface and 1,000 m. can be resolved into a frictional component which produces a normal boundary layer wind spiral, and a thermal component resulting from the temperature gradient at the ice edge, which deforms the normal wind spiral. Values of surface stress, surface Rossby number, geostrophic drag coefficient, energy dissipation, and roughness length derived from the wind profiles are collectively sufficiently different from values obtained over land or water surfaces, to suggest that the ice surface produces its own characteristic wind distribution.

On the “Resistance Law” of a Turbulent Ekman Layer

Abstract The turbulent Ekman layer differs from the two-dimensional turbulent boundary layer in that it may exist with its thickness remaining constant in the direction of the flow. Dimensional arguments show that the layer equilibrium thickness and the magnitude and the direction of the shear stress at the boundary surface are functions of the surface Rossby number U/Fz0. In analogy with two dimensional turbulent boundary layers, similar “wall layer” velocity profiles near the boundary and a “velocity defect law” in the outer region of the Ekman layer may be postulated. The overlapping of the two laws produces a logarithmic velocity profile and yields a resistance law for an Ekman layer, for both the magnitude and the direction of the shear stress, connecting these to the surface Rossby number. What experimental evidence there is on the geostrophic drag coefficient appears to agree with the resistance law so derived.

A meteorological study of Dry-fallout of radioactive debris

A general expression is derived for the intensity of dryfallout based on time variations of beta-activity in surface air, due to worldwide tropospheric distribution of debris from nuclear testings. Model assumptions are outlined for the consideration of large-scale effects of horizontal divergence of air flow, and small-scale effects of eddy diffusion. The parameterization is based on the concept of geostrophic drag coefficients and atmospheric boundary layer theory. The model is completed by a two-parameter representation of tropospheric profiles of beta activity. Case studies of dry-fallout in 1962 and 1963 at three stations of the United States Public Health Service (USPHS) network are discussed. Dry-fallout rates per day are found to be approximately 10% of average wet-fallout rates of the same period. The average residence time of debris in the troposphere is estimated to be about 65 days if dry-fallout would be the only cleansing process.