Substructure layers and modes in the stratified boundary layer

Geophysical flows include small-scale substructures that support shear instabilities where the smoothed mean profiles indicate only stability. The substructures must draw their energy from the mean flow, probably through wave interactions, and it is shown that the substructures themselves give rise to a type of mode that is well suited for nonlinear interactions with the flow in and around them. The study indicates that substructures and their associated modes form a dynamically interacting system that may contribute to the chaotic nature of a stably stratified region.     

Field observations of stratified atmospheric flow above an obstacle

In a study using the plume from the Four Corners power plant, near Farmington, N.M., lee waves were observed during times when the plume flowed across the Hogback. Wavelengths were typically about 1.2 km; wave amplitudes were more variable, ranging from 20 to 100 m. The observed amplitudes imply an obstacle that is broader and shallower than is actually the case. This is in agreement with laboratory studies that show the existence of regions of complex flow both upstream and downstream from an obstacle, which have the effect of broadening the region over which laminar flow occurs. Visual observation, measurement of the plume cross-sectional area both upstream and downstream from the Hogback, and measurement of plume aerosol concentrations show that turbulent and eddy flow over and downwind from the Hogback increase the rate of mixing of the plume with the surrounding atmosphere. This in turn increases the rate at which plume components come into contact with the ground.     

Stably stratified flow in a marine atmospheric surface layer

Data from the marine atmospheric surface layer have been analysed. The data set consists of about two weeks with tower measurements up to 31 m of mean profiles of wind, temperature, and humidity, together with 20 Hz turbulence data. Mean wind, temperature, and humidity profiles up to 2000 m are also available from pibal trackings and radio soundings. Wave height was measured at 2 Hz, using an inverted echo-sounder.It was found from pibal wind profiles that low level jets were present during 2/3 of the measurements, having their maxima in the height interval 40 to 300 m. Here only data from the remaining 1/3 of the measurements, without low level jets, have been analysed.Non-dimensional wind and temperature gradients agree with results over homogeneous land surfaces as regards stability dependence during stable conditions that prevailed during this experiment. Linear regression gave _m = 1 + 6.8z/L and _m = 1 + 8.3z/L. No significant sea wave influence was found. The same was vrue for me dimensionless standard deviations of the three wind components, except for the vertical component. The expected wind speed dependence was found for the neutral drag coefficient, givingC _dN = 0.109U + 0.33 at 10 m, and a dependence on the wave parameter,C/u _*, was confirmed. Note, however, that the data set was restricted to low and moderate wind speeds and that stratification was mainly stable.Power spectra, non-dimensionalized according to suface-layer theories, do not follow the expected stability dependence. It was shown that this may be a consequence of the presence of gravity waves in the stable marine boundary layer. Indicators of gravity waves were found in most runs. The TKE budget agrees with findings over homogeneous land areas. The pressure transport term was found to be a source of energy also for near neutral conditions.     

Internal gravity waves in a stably stratified boundary layer

Often, a combination of waves and turbulence is present in the stably stratified atmospheric boundary layer. The presence of waves manifest itself in the vertical profiles of variances of fluctuations and in low-frequency contributions to the power spectra. In this paper we study internal waves by means of a linear stability analysis of the mean profiles in a stably stratified boundary layer and compare the results with observed vertical variance profiles of fluctuating wind and temperature along a 200 m mast. The linear stability analysis shows that the observed mean flow is unstable for disturbances in a certain frequency and wavenumber domain. These disturbances are expected to the detectable in the measurements. It is shown that indeed the calculated unstable frequencies are present in the observed spectra. Furthermore, the shape of the measured vertical variance profiles, which increase with height, is explained well by the calculated vertical structure of the amplitude of unstable Kelvin-Helmholtz waves, confirming the contribution of waves to the variances. Because turbulence and waves have quite distinct transport properties, estimates of diffusion from measurements of variances would strongly overestimate this diffusion. Therefore it is important to distinguish between them.     

Temperature above the surface layer

Three published data sets of upper-air global temperatures, two from radiosondes and one from satellites, are examined and compared for the lower stratosphere and troposphere.The global lower stratosphere exhibits a downward trend for the past 16+ years of -0.53 °C (-0.33 °C per decade). Since the 1960's (using radiosondes before 1979 which are subject to known and unknown inhomogeneities) it is likely that there has been a downward trend of about the same magnitude. Significant issues of the stratospheric radiosonde data are: (1) that the long-term time series is biased toward spurious cooling; and (2) the earliest years of Angell display unrealistic variability. Inhomogeneities in satellite data due to orbit drifting and instrument calibration are examined.The tropospheric temperature has shown a downward trend of -0.11 °C since 1979 (-0.07 °C per decade). Beginning in earlier years, (relying only on radiosonde data before 1979) the estimated warming trend since the late 1950's is +0.07 to +0.11 °C per decade.Tropospheric and surface temperature anomalies are compared. There is concern that the disproportionate representation of extratropical continents, with their high temperature variance, may bias any long term global surface trend toward a maximum-possible value than would be calculated had all regions (including those with much lower responsiveness) been monitored.     

三维层结流中地形上空湍流边界层结构特征研究

利用中尺度数值模式ARPS,在理想条件下研究了旋转、地表摩擦的共同作用下,均匀来流条件下,三维层结大气中地形上空及其边界层结构特征.重点讨论了不同的山地流动Fr数、不同上游来流方向情况下,山地流动及其边界层的特征.在大气稳定层结条件下,山地流动具有上游阻挡、下游急流加速以及重力波破碎等流动特征,这些山地流动特征在柯氏力的影响下,均表现出了南北非对称性.当山地流动的Fr数增加(增加地形高度)时,山地流动的南北急流增强,由于柯氏力的影响,南侧急流的增幅更为显著,流动的南北非对称性增强.在干过程山地流动中,由急流所导致的强烈的垂直风切变,是湍流边界层产生和发展的直接决定因素.     

Numerical studies of neutrally stratified planetary boundary-layer flow above gentle topography

A numerical model of planetary boundary-layer flow above two-dimensional gentle topography is developed as an extension of the surface-layer model described by Taylor (1977). Comparisons are made with surface-layer predictions for flow over Gaussian hills; and the flow at various angles above hills, valleys and escarpments is modelled. Some simple case studies of the influence of gentle two-dimensional topography on pollutant dispersion are made which indicate relatively minor effects on surface pollutant concentrations in comparison with results for dispersion above a plane surface.     

Numerical simulation of the boundary layer above waves

A new approach to investigations of the structure of the boundary layer above waves is discussed. The approach is based on direct numerical simulation of wave motions in the boundary layer produced by a moving curved surface. Model equations are derived, which are the Reynolds equations in a curvilinear nonstationary system of co-ordinates, evolution equations for turbulent kinetic energy, and Kolmogorov's approximate similarity formulae relating the coefficient of turbulent viscosity to the dissipation of turbulent energy; the length scale is assumed to grow linearly with increasing distance from the surface. Principles of constructing the model numerical scheme are described. Results are given of modelling the structure of the boundary layer above a nonsteady surface, which, in a general case, is a superposition of progressive waves with assigned dispersion relations and amplitudes. Mechanisms of energy and momentum transfer to the surface, effects of density stratification and energy structure in the boundary layer are studied. Merits and demerits of the approach are discussed.     

Local isotropy and anisotropy in the sheared and heated atmospheric surface layer

Longitudinal velocity and temperature measurements above a uniform dry lakebed were used to investigate sources of eddy-motion anisotropy within the inertial subrange. Rather than simply test the adequacy of locally isotropic relations, we investigated directly the sources of anisotropy. These sources, in a daytime desert-like climate, include: (1) direct interaction between the large-scale and small-scale eddy motion, and (2) thermal effects on the small-scale eddy motion. In order to explore these two anisotropy sources, we developed statistical measures that are sensitive to such interactions. It was found that the large-scale/small-scale interaction was significant in the inertial subrange up to 3 decades below the production scale, thus reducing the validity of the local isotropy assumption. The anisotropy generated by thermal effects was also significant and comparable in magnitude to the former anisotropy source. However, this thermal anisotropy was opposite in sign and tended to counteract the anisotropy generated by the large-scale/smallscale interaction. The thermal anisotropy was attributed to organized ramp-like patterns in the temperature measurements. The impact of this anisotropy cancellation on the dynamics of inertial subrange eddy motion was also considered. For that purpose, the Kolmogorov-Obukhov structure function equation, as derived from the Navier-Stokes equations for locally isotropic turbulence, was employed. The Kolmogorov-Obukhov structure function equation in conjunction with Obukhov's constant skewness closure hypothesis reproduced the measured second- and third-order structure functions. Obukhov's constant skewness closure scheme, which is also based on the local isotropy assumption, was verified and was found to be in good agreement with the measurements. The accepted 0.4 constant skewness value derived from grid turbulence experiments overestimated our measurements. A suggested 0.26 constant skewness value, which we derived from Kolmogorov's constant, was found to be adequate.     

A multi-limit formulation for the equilibrium depth of a stably stratified boundary layer

Currently no expression for the equilibrium depth of the turbulent stably-stratified boundary layer is available that accounts for the combined effects of rotation, surface buoyancy flux and static stability in the free flow. Various expressions proposed to date are reviewed in the light of what is meant by the stable boundary layer. Two major definitions are thoroughly discussed. The first emphasises turbulence and specifies the boundary layer as a continuously and vigorously turbulent layer adjacent to the surface. The second specifies the boundary layer in terms of the mean velocity profile, e.g. by the proximity of the actual velocity to the geostrophic velocity. It is shown that the expressions based on the second definition are relevant to the Ekman layer and portray the depth of the turbulence in the intermediate regimes, when the effects of static stability and rotation essentially interfere. Limiting asymptotic regimes dominated by either stratification or rotation are examined using the energy considerations. As a result, a simple equation for the depth of the equilibrium stable boundary layer is developed. It is valid throughout the range of stability conditions and remains in force in the limits of a perfectly neutral layer subjected to rotation and a rotation-free boundary layer dominated by surface buoyancy flux or stable density stratification at its outer edge. Dimensionless coefficients are estimated using data from observations and large-eddy simulations. Well-known and widely used formulae proposed earlier by Zilitinkevich and by Pollard, Rhines and Thompson are shown to be characteristic of the above interference regimes, when the effects of rotation and static stability (due to either surface buoyancy flux, or stratification at the outer edge of the boundary layer) are roughly equally important.     

The temperature structure in a stably stratified internal boundary layer over a cold sea

Data from the Öresund experiment are used to investigate the structure of the stably stratified internal boundary layer (SIBL) which develops when warm air is advected from a heated land surface over a cooler sea. The present study is based on a theory developed by Stull (1983a, b, c). He proposed that the turbulence and the mean structure of the nocturnal boundary layer is controlled by the time-integrated value of surface heat flux and that the instantaneous heat flux is of less importance.Dimensional arguments are used to define simple, physically consistent, temperature, velocity and length scales. The dimensionless surface heat flux has a high value immediately downwind of the shoreline and it decreases rapidly in magnitude with increasing distance from the coast. Farther away, it is essentially constant. The dimensionless potential temperature change exhibits an exponential profile. It is estimated that turbulence accounts for 71% of boundary-layer cooling while clear-air radiational cooling is responsible for the remaining 29%.Finally it is found that theoretical predictions for the height of the SIBL are in a good agreement with observations.     

On an instability mechanism in a stably stratified atmospheric layer over a moistened surface

In air stratified by a specific humidity gradient, the vertical motions result in variations in specific humidity (mixing ratio) near the underlying surface. This, in turn, causes a variation of evaporation from the surface, resulting in horizontal thermal inhomogeneities on the surface, which under certain conditions can strengthen the initial vertical motions. The linear problem of the stability of the system under consideration is solved in this paper, boundaries of the unstable region are defined, and specific values of growth rates of disturbances are investigated. The estimates show that even in a density-stratified atmospheric layer over a moist surface, rapid development of disturbances with horizontal scales of several hundred metres is possible. The horizontal sizes of the most rapidly growing modes, as a rule, are an order of magnitude larger than the vertical sizes. The possibility of observing this instability under natural conditions is discussed.     

Study of near-surface models for large-eddy simulations of a neutrally stratified atmospheric boundary layer

In large-eddy simulations (LES) of the atmospheric boundary layer (ABL), near-surface models are often used to supplement subgrid-scale (SGS) turbulent stresses when a major fraction of the energetic scales within the surface layer cannot be resolved with the temporal and spatial resolution at hand. In this study, we investigate the performance of both dynamic and non-dynamic eddy viscosity models coupled with near-surface models in simulations of a neutrally stratified ABL. Two near-surface models that are commonly used in LES of the atmospheric boundary layer are considered. Additionally, a hybrid Reynolds- averaged/LES eddy viscosity model is presented, which uses Prandtl’s mixing length model in the vicinity of the surface, and blends in with the dynamic Smagorinsky model away from the surface. Present simulations show that significant portions of the modelled turbulent stresses are generated by the near-surface models, and they play a dominant role in capturing the expected logarithmic wind profile. Visualizations of the instantaneous vorticity field reveal that flow structures in the vicinity of the surface depend on the choice of the near-surface model. Among the three near-surface models studied, the hybrid eddy viscosity model gives the closest agreement with the logarithmic wind profile in the surface layer. It is also observed that high levels of resolved turbulence stresses can be maintained with the so-called canopy stress model while producing good agreement with the logarithmic wind profile.     

Extension of a fluctuating plume model of tracer dispersion to a sheared boundary layer and to a large array of obstacles

Fluctuating plume models provide a useful conceptual paradigm in the understanding of plume dispersion in a turbulent flow. In particular, these models have enabled analytical predictions of higher-order concentration moments, and the form of the one-point concentration probability density function (PDF). In this paper, we extend the traditional formalism of these models, grounded in the theory of homogeneous and isotropic turbulent flow, to two cases: namely, a simple sheared boundary layer and a large array of regular obstacles. Some very high-resolution measurements of plume dispersion in a water channel, obtained using laser-induced fluorescence (LIF) line-scan techniques are utilised. These data enable us to extract time series of plume centroid position (plume meander) and dispersion in the relative frame of reference in unprecedented detail. Consequently, experimentally extracted PDFs are able to be directly compared with various theoretical forms proposed in the literature. This includes the PDF of plume centroid motion, the PDF of concentration in the relative frame, and a variety of concentration moments in the absolute and relative frames of reference. The analysis confirms the accuracy of some previously proposed functional forms of model components used in fluctuating plume models, as well as suggesting some new forms necessary to deal with the complex boundary conditions in the spatial domain.     

The stably stratified boundary layer over the great plains

Airplane measurements of the stably stratified boundary layer obtained during the Severe Environmental Storms and Mesoscale Experiment (SESAME) over rolling terrain in south-central Oklahoma indicate that considerable horizontal variability exists in the flow on scales of several kilometers. Much of this wave-like structure appears to be tied to the terrain. The criteria for existence of stationary gravity waves indicate that these waves can exist under the observed conditions. The spectrum of terrain variations also supports the existence of these waves. Observed spectra of the vertical velocity have two peaks: one at wavelengths of several kilometers, which is due to waves and the other at wavelengths of about 100 m, which is due to turbulence. The variance at several kilometers wavelength increases somewhat with height at least up to about 800 m, but the variance contributed by turbulence decreases rapidly with height.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The growth of the mixed layer in a stratified fluid due to penetrative convection

This paper describes a theoretical and experimental study of penetrative convection within an initially thermally stably stratified fluid heated from below. Emphasis is placed on the experimental investigation of the growth of the mixed layer and the entrainment at its boundary. Both processes play an important role in density-induced geophysical phenomena such as the lifting of an inversion layer during the morning and the deepening of a thermocline in a lake during the fall.Many laboratory experiments with water as the experimental fluid were performed, in which the convection process was generated and visualised. The height of the mixed layer, heat transfer across the bottom interface and temperature profiles were measured as functions of time.Theoretically-based analytical equations are given, which predict the thickness and temperature of the mixed layer. The equations involve one empirical factor characterising the entrainment rate at the interface between the mixed and the upper stable layer.The experimental results confirm the theoretical equations and show that the empirical factor is a constant. From this, an entrainment rate is calculated which agrees well with values presented in the meteorological literature.Work performed at Sonderforschungsbereich 80, University of Karlsruhe.     

Similarity of structure-function parameters in the stably stratified boundary layer

The structure-function parametersC _T ² andC _v ² of temperature and velocity, respectively, from the 1973 Minnesota experiments and from large-eddy and direct numerical simulations show a smooth transition from M–O similarity to the local scaling hypothesized by Nieuwstadt for the outer regions of the stable boundary layer. Under that hypothesis, turbulence statistics aloft depend on the local vertical fluxes of momentum and temperature, so these results suggest that remote-sensing measurements ofC _T ² andC _v ² could be used to infer vertical profiles of those fluxes. We argue that the sensitivity of the fluxes to unsteadiness, baroclinity, terrain slope, and breaking gravity waves precludes the universality of the vertical profiles of structure-function parameters in the stable PBL. We find that theC _T ² profile is particularly sensitive to these effects, which is consistent with observations that it varies considerably from case to case.     

Unstable interannual oscillation modes in a linearized coupled ocean-atmosphere model and their associations with ENSO

Summary By using a coupled ocean-atmosphere model with an oceanic surface boundary layer, including linear atmospheric and oceanic dynamics and linearized SST prognostic equation with respect to spatially varying climatological background states, we have investigated the eigenvalue problem of the linearized coupled system in the tropical Pacific, including the characteristic periods, horizontal structures, temporal-spatial evolution and instability of the unstable interannual oscillation characteristic modes and their associations with ENSO. The main results show that the quasi-biennial (QB) oscillation was found to act as the most unstable mode in the tropical Pacific coupled air-sea system. Only the most unstable QB mode displays the ENSO-like structure and temporalspatial evolution, and its existence seems likely to have no essential dependence on the climatological annual cycle (AC). Unfortunately, from the linearized coupled system we have not derived a most unstable mode relevant to the observed principle mode with the preferred 3–4 year lower-frequency (LF) oscillation period in the real world ENSO variability. Therefore, we infer that the LF mode would likely result from certain nonlinear interaction, in which the QB mode that acts as the shortest ENSO cycle could be fundamentally important. Also, we believe that the results in present work could be helpful to fully understand the multiple time scales and the associated mechanism responsible for the real world ENSO variability.With 7 Figures