Constant Flux Layer Research Articles

Boundary-Layer Forcing as a Possible Trigger to a Squall-Line Formation

The study of the life history of the 8 June 1966 squall line by Ogura and Chen (1977) indicates that a well-defined narrow hand of horizontal convergence was present at low levels prior to the appearance of first radar echoes. A two-dimensional model for the dry planetary boundary layer is developed and applied to this case in order to test the hypothesis that the prestorm convergence is produced by boundary-layer processes in association with a strong horizontal temperature gradient. The level 3 turbulence closure approximation by Mellor and Yamada (1974) is incorporated into the model as well as the similarity hypothesis of Businger et al. (1971) for the lowest constant flux layer. The basic driving mechanism is the diurnal variation of the temperature contrast across the observed dry line. Air on the northwest side was warm, while on the southeast side it was cool. The temperature contrast was introduced into the model as a lower boundary condition for the potential temperature. The model is integrated, starting from the early morning conditions through the late afternoon. The results indicate the development of ascending-descending motions as soon as a horizontal temperature gradient is established. In time, the mixed layer also develops and its depth increases. AS expected, it increases faster on the warm side than on the cool side. The intensity of the upward motion increases at a rate larger than that of the downward motion and the center of the ascending motion remains at a certain level (∼800 mb). The center of the downward motion moves up in time. Thus, the upward motion is concentrated in the mixed layer at the location of the sharp gradient in the inversion. The major observed features in the velocity and temperature fields in the prestorm situation are well simulated by the model. Further, the result of a sensitivity test for a different initial wind field indicates that the location and intensity of the. resulting ascending motion is rather sensitive to the initial wind field. It is concluded that, if the synoptic-scale low-level wind blows in the right direction (off shore in sea-breeze terminology), a low-level horizontal temperature gradient of the magnitude observed in the 8 June 1966 squall line case is capable of generating upward motion with sufficient intensity to release the potential instability.

大気境界層中での乱流変動量の鉛直プロフィール

In order to derive simple relations expressing the vertical profiles of turbulence quantities such as the rms values of vertical speed δw and temperature δT, the vertical diffusion coefficient for momentum KM, and the dissipation rate of kinetic energy ε in the planetary boundary layer (PBL), the similarity hypothesis, which was attributed to Monin and Obukhov (1954) and verified in the constant flux layer (CFL), is extended. Unlike the CFL, the horizontally homogeneous PBL is, in general, non-stationary. However, here, approximately stationary conditions are dealt with by taking sampling times for the turbulence quantities which are relatively short when compared with the time change of the conditions. As in the case of the CFL, the fundamental quantities which determine the structure of the PBL are the vertical flux of sensible heat q, and momentum u*, and scale of turbulence l. However, in the PBL, these differ from their CFL behavior q and u* vary with height z, and l is not linearly proportional to z.In the present PBL model, the height variations of q, u*, and l are expressed by suitable empirical relations and the layer thickness is defined by the height at which the extrapolated values of q and u* tend to zero.The vertical profiles of the turbulence quantities in the PBL are derived by replacing q0, u*0, z (suffix o denotes surface value) in the relations for the CFL by q, u* and l.The derived relations are compared with observation and the characteristics of the scale l are considered.

安定接地気層の乱流構造の観測

The turbulent structure under stable conditions in the atmospheric boundary layer (ABL) has been investigated by tower measurements, of the turbulent fluctuations and vertical mean profiles of wind velocity and air temperature. The results are summarized as follows:(1) For the parameter of thickness of the turbulent ABL under stable conditions, the height hq at which turbulent heat flux disappears is a more reasonable choice than the height hθ derived from the potential temperature profile, and hq has linear relation to the Monin-Obukhov stability length.(2) Unlike the constant flux layer near the ground, the absolute values of vertical heat flux (q) and momentum flux (u*) decrease with height in the stable ABL.According to these results, the ABL model proposed by Yokoyama et al. (1977, 1979) is applied to the turbulent ABL under stable conditions. We conclude that the vertical profiles of q and u* are approximated by the power function ζm andζn, respectively (where, ζ=1-z/hq, z: height, hq: thickness of the layer, m _??_3/2, n _??_1/2) and the same relations which described the turbulence quantities, temperature and wind velocity gradients in the constant flux layer are valid for whole stable ABL by replacing surface values of q and u* by their local values.

大気境界層における閉じた乱流モデルに関する覚書

A turbulence closure model for atmospheric boundary layers is examined, under the assumption that the turbulent flow is steady in its ensemble average and the advection and diffusion terms in the turbulent Reynolds stress and heat flux equations are neglected. The constants which are introduced in order to obtain a closure system are determined referring the experimental results obtained in the wind tunnel. The validity of the closure model thus obtained is checked referring the observational results obtained in the constant-flux layer. In order to apply our model to the planetary boundary layer, simple forms for the eddy transport coefficients of momentum and heat are formulated. In this case the parametarization of the scale-length l=l(z) (z: heihgt) which is introduced in estimating the dissipation rate of turbulent kinetic energy with height is discussed in order to satisfy the observational result.

Estimation of momentum and heat fluxes in the constant flux layer from temperature measurements

Global estimates of momentum and heat fluxes are required for the application of any general atmospheric and oceanic circulation model. A new technique for the estimation of these fluxes in a constant flux boundary layer is developed. The new approach is a modification of the dissipation technique but the only required measurements are the mean and fluctuating temperatures at two levels within the constant flux layer. All other flux estimation techniques require measurement of both temperature and velocity. Data are presented to compare flux estimation results with the conventional eddy-correlation technique. Also discussed are the limitations of the procedure and restrictions on its applicability.

Numerical simulation of cold easterly circulations over the Canadian Western Plains using a mesoscale boundary-layer model

Arctic outbreaks over the Canadian Western Plains during the late spring period frequently take the form of a cold east-northeasterly flow over a warmer, sloping surface. A mesoscale numerical model is developed in an attempt to simulate such circulations. Following Lavoie (1972) the atmospheric structure of the cold air mass is represented by three layers: a constant flux layer in contact with the earth's surface, a well-mixed planetary boundary layer capped by an inversion, and a deep stratum of overlying stable air. Averaging the set of governing primitive equations through the depth of the mixed layer yields predictive equations for the horizontal wind components, potential temperature, specific humidity, and the height of the inversion. Time-dependent calculations are limited to this layer by parameterizing the interactions between the mixed layer and both the underlying and overlying layers. Precipitation from limited convective clouds, and latent heat within the layer are included in terms of mesoscale variables.

On the structure of free convection near the surface

The structure of free convection in an atmospheric surface layer is modelled as a field of plumes rising from the ground. The plumes occupy nearly one-half of the total fluid volume and they coalesce slowly as they rise. The model behaviour is consistent with the results obtained commonly by dimensional analysis under the assumption that the friction velocity is an irrelevant parameter in an unstable constant-flux layer.

The Two-Dimensional URBMET Urban Boundary Layer Model

Abstract A two-dimensional, non-steady model of the flow over an infinitely wide, warm, rough city is presented. The model consists of two layers, a lower analytical constant-flux layer, and an upper finite-difference transition layer, in which the vorticity and heat conduction equations are solved. The atmosphere is assumed to be Boussinesq, hydrostatic and slab symmetric, while all motions are assumed to be adiabatic. Finite-difference solutions are obtained over a variable, interlaced grid, with the use of a time-splitting technique, in conjunction with the donor cell method of differencing the advection terms. Simulations were carried out reproducing the daytime flow of a neutral atmosphere over a rough city, and the nighttime flow of stable atmosphere over a rough, warm city. Comparisons are presented to show that the model is capable of reproducing many of the observed characteristics of the urban boundary layer.

A Puff-on-Cell Model for Computing Pollutant Transport and Diffusion

A scheme is developed to minimize the pseudo-diffusion which arises in numerical solutions of finite-difference equations of turbulent diffusion and transport. In the present model, the subgrid scale distribution of the pollutant concentration is parameterized by a Gaussian puff. At each time step the concentration within each grid volume is characterized by a Lagrangian puff. The center of each Lagrangian puff is advected by the mean wind and its boundaries are expanded or contracted by diffusive displacements, computed from the values of concentration, atmospheric turbulent diffusivity, and the gradient of pollutant concentration between the adjacent grid volumes. The standard deviation of the puff is parameterized as a linear combination of the grid length and the diffusive displacement. The constants in the parameterization are determined by calibrating the standard deviation of the puff width predicted by the numerical model against that of an analytical solution. The pollutant is then distributed back to the surrounding Eulerian grid volumes, preserving the first and the second moments of the concentration distribution. The use of the model is illustrated by predicting the vertical concentration distribution of sulfur dioxide and sulfate for a period of 5 days. Furthermore, the requirement for realistic surface-layer parameterization in such numerical models is demonstrated by comparing the results of the constant-flux layer parameterization based upon the modern similarity theory with those of the conventional linear-profile approximation.

A review of flux-profile relationships

Flux-profile relationships in the constant flux layer are reviewed. The preferred relationships are found to be those of Dyer and Hicks (1970), namely, φ H =φ W =(1−16(z/L))−1/2, φ M =(1−16(z/L))−1/4 for the unstable region, and φ H =φ W =φ M = 1+5(z/L) for the stable region. The carefully determined results of Businger et al. (1971) remain a difficulty which calls for considerable clarification.

A Theoretical Study of the Sea and Land Breezes of Circular Islands

Abstract The axisymmetric sea and land breezes of circular islands are studied. First we show, from the equation of turbulent energy, that the marked horizontal convergence of the sea breeze intensifies the turbulence in the flow and that this conclusion affects the equations that model the turbulence. Next, the equations of motion are integrated numerically for two circular islands: a “large” island of radius 51.25 km and a “small” island of radius 26.25 km. The horizontal grid is 2.5 km and the vertical 100 m beginning from the top of a postulated constant-flux layer 25 m thick. Large island. The sea-breeze front (SBF) is much better developed than in the case of a straight coast. In the first hours of the afternoon the low-level winds ahead of the front are nearly opposite in direction to those of the sea breeze behind the front. There is a strong horizontal convergence in advance of, and divergence behind, the front up to an altitude of 400–500 m; the reverse distribution is the case aloft, where the ...

Analytic Prediction of the Properties of Stratified Planetary Surface Layers

Abstract By considering the complex of one-point, turbulent moment equations for velocity, pressure and temperature, it appears possible to predict some properties of diabatic, density-stratified planetary layers using empirical information obtained from laboratory turbulence data in the absence of density stratification. In this paper attention is focused on the near-surface, constant-flux layer. The results, like the empirical input, are simple and, hopefully, will be instructive and useful in the formulation of improved and possibly more complicated models in the future.

An observational study of the vertical profile of the high frequency fluctuations of the wind in the atmospheric boundary layer

This paper summarizes some measurements of high-frequency turbulence made at Cardington during the years 1968, 1969 and 1970 at heights up to 900 m. It discusses the statistical distribution of the data which appears to be closely log-normal. Also it is shown how the mean profiles of the derived dissipation of turbulent kinetic energy (ɛ) can be rationalized to some extent in terms of atmospheric stability and low-level wind speed. A close correlation betweenɛ and the mean wind and temperature profiles up to 900 m is illustrated and some discussion of the turbulent energy budget throughout the boundary layer is presented. The use and limitations of the constant flux layer relations in calculatingz 0 andL from the estimates ofɛ, at the lower heights, is brought out.

A Mesoseale Numerical Model of Lake-Fffect Storms

The atmospheric structure upwind of the Great takes during arctic air outbreaks is represented by three layers: a lower constant flux layer in contact with the ground, a well-mixed planetary boundary layer surmounted by an inversion, and a deep stratum of overlying stable air. The set of primitive equations is averaged through the depth of the mixed layer to yield predictive equations for the horizontal components of velocity, potential temperature and specific humidity in the layer, and the height of the inversion. Interactions between the well-mixed convective layer and both the underlying and overlying layers are parameterized so that time-dependent calculations can be limited to a single layer. Precipitation from cumulus clouds within the layer is represented in terms of the mesoscale variables and latent heat is included. The equation set has been solved numerically for a 2000-point grid mesh centered on Lake Erie. Grid separation was 6 km in the cross-lake direction and 12 km along the lake axis. Initial conditions were specified to be balanced and everywhere uniform. Terrain influences, surface roughness and temperature variations, and moisture fluxes were then allowed to perturb the mixed layer until the resulting mesoscale disturbance approached a steady state. Experiments revealed that each of the surface forcing factors contributed significantly and tended to complement each other in shaping the lake-effect storm. Alterations in prevailing flow produced realistic changes in storm morphology. Patterns of disturbance in the height of the inversion appear to be well correlated with observed radar and snowfall patterns. A case study of the 1–2 December 1966 storm demonstrated quite good simulators of precipitation patterns and amounts but data are insufficient to test many other aspects of the model results. It is concluded that a single layer can be used to represent many of the significant aspects of lake-effect storms and that the mesoseale disturbance provides effective control over the location and intensity of convective activity.

A simple climatological model of the dynamics and energetics of the nocturnal circulation at Lake Victoria

AbstractThe local atmospheric night‐time circulation at Lake Victoria (East Africa) is simulated by a simple model which is cylindrically symmetric. It consists of an upper layer (linearized, steady state, hydrostatic, incompressible, saturated over the lake) above a surface boundary layer (constant flux layer, log + lin profile). Analytical solutions are derived for the dynamical, energetical, and hydrological parameters. They mainly depend on the surface temperature difference between land and lake, which is the driving mechanism of the motion, and the choice of representative mesoscale transport coefficients Km, Kh. The results are compared with the climatological features of the nocturnal circulation.

Comparison of sensible and latent heat fluxes computed from measurements by ship and spar buoy in the tropical Atlantic ocean

Computations of sensible and latent heat fluxes from measurements taken aboard a ship and from a spar buoy east of Barbados in July and August, 1968 are reported. A detailed comparison of the diurnal variation of the fluxes shows that the ship creates an island of turbulence quite different from open sea conditions. Measurements from the buoy, which are believed to be more typical of open ocean conditions indicate that the constant flux layer may be less than 6 m thick.

The spatial variability of eddy fluxes in the constant flux layer

AbstractAt the 1970 International Comparison of Turbulence Instruments held at Tsimlyansk, U.S.S.R., a large number of momentum and heat flux measurements were obtained simultaneously with two Fluxatrons. The data are analysed from the point of view of spatial variation of eddy fluxes, bearing in mind the limitations of the sensors, the variability of the eddy fluxes themselves, and the possibility of errors due to tilt. It is concluded that, at the Tsimlyansk site, the variation of heat and momentum fluxes both in the vertical (4 – 14 m) and the horizontal (1 – 150 m) is of the order 10 per cent or less. This result is in accord with traditional opinion, and provides a satisfactory experimental basis for the concept of a ‘constant flux layer’.

The spatial variability of eddy fluxes in the constant flux layer

The spatial variability of eddy fluxes in the constant flux layer

A note on the log‐linear velocity profile in stable conditions

AbstractIf we consider a stably stratified (H<0) constant flux layer, 0 <z <zr, within which we know the heat flux, Hi, and have measured only the mean velocity Ur at one height zr we may wish to determine the friction velocity, u*, by assuming a log‐linear velocity profile with a fixed value for the Monin‐Obukhov parameter, a. This approach leads to a cubic equation for u* which may have either two or no real positive roots. A condition for the existence of positive roots is derived and it is conjectured that the larger of the two roots is the one required. This condition leads to an upper bound, In \documentclass{article}\pagestyle{empty}\begin{document}$ \left({\frac{{z_r + z_o}}{{z_o}}} \right) $\end{document} / (2α) on z/L for the applicability of a ‘log‐ linear’ velocity profile.

A note on the log-linear velocity profile in stable conditions

If we consider a stably stratified (H<0) constant flux layer, 0 <z <zr, within which we know the heat flux, Hi, and have measured only the mean velocity Ur at one height zr we may wish to determine the friction velocity, u*, by assuming a log-linear velocity profile with a fixed value for the Monin-Obukhov parameter, a. This approach leads to a cubic equation for u* which may have either two or no real positive roots. A condition for the existence of positive roots is derived and it is conjectured that the larger of the two roots is the one required. This condition leads to an upper bound, In \documentclass{article}\pagestyle{empty}\begin{document}$ \left({\frac{{z_r + z_o}}{{z_o}}} \right) $\end{document} / (2α) on z/L for the applicability of a ‘log- linear’ velocity profile.