Characteristics of intermittent turbulence in the upper stable boundary layer over Greenland

The experiment IGLOS (Investigation of the Greenland Boundary Layer Over Summit) was conducted in June and July 2002 in the central plateau of the Greenland inland ice. The German research aircraft Polar2, equipped with the turbulence measurement system Meteopod, was used to investigate turbulence and radiation flux profiles near research station “Summit Camp”. Aircraft measurements are combined with measurements of radiation fluxes and turbulent quantities made from a 50 m tower at Summit Camp operated by Eidgenössische Technische Hochschule (ETH) Zürich. During all six flight missions, well-developed stable boundary layers were found. Even in high-wind conditions, the surface inversion thickness did not exceed roughly 100 m. The turbulent height of the stable boundary layer (SBL) was found to be much smaller than the surface inversion thickness. Above the surface layer, significant turbulent fluxes occurred only intermittently in intervals on the order of a few kilometres. Turbulent event fraction in the upper SBL shows the same dependence on gradient Richardson number as reported for near-surface measurements. Clear-air longwave radiation divergence was always found to contribute significantly to the SBL heat budget. In low-wind cases, radiative cooling even turned out to be dominant.     

Radiation,evaporation and the maintenance of turbulence under stable conditions in the lower atmosphere

An expression is derived relating the critical flux Richardson number with the critical (gradient) Richardson number. In contrast to an earlier analysis by Townsend (1958), which is restricted to the atmosphere well outside the earth's boundary layer, the present treatment is intended specifically for turbulent flow in the lower atmosphere and it takes account of the effect of evaporation on the stability. The effect of radiation on the rate of destruction of the mean square of the temperature fluctuations is obtained by considering the radiative flux divergence in a stratified atmosphere and by using a simple functional relationship to represent empirical emissivity data.It was found that evaporation and radiation increase the critical Richardson number by a sensible amount depending on the atmospheric conditions, mainly temperature, humidity and the gradients. There is no definite critical Richardson number but rather a range between 0.25, below which turbulence is very likely, and somewhat higher than 0.5, above which turbulence is improbable. The value of the critical Richardson number can be expressed in terms of evaporation, radiation and the ratio ( _w /u _*) which also appears not to have a definite critical value. Evaporation and radiation cause the ratio ( _w /u ^*) to be larger than unity under neutral conditions. These results, based on the assumption of Reynolds' analogy,K ^H =K ^M , are consistent with the available experimental evidence.     

A scaling parameter for turbulence in baroclinic convective boundary layers

The influence of baroclinicity on the structure and levels of turbulence in the convective boundary layer depends on both the magnitude and orientation of geostrophic wind shear and the level of convection. The geostrophic Richardson number, a Richardson number defined in the present work and based on the geostrophic wind shear, is shown to be a single non-dimensional parameter which determines the influence of baroclinicity on convective turbulence structure.     

The dynamic atmospheric structure and the velocity defect profiles in the boundary layer of a neutral atmosphere

The structure of neutral barotropic planetary boundary layers is investigated. The dynamic equations have been numerically solved by an iterative method. Similarity and dissimilarity of the atmospheric boundary layer are explored. The distribution of the velocity defect functions, hypothesized by the similarity theory, is obtained. Comparison between present numerical results, i.e., shear stress, drag coefficient, and cross-isobar angle, and other results and experimental data are made. It appears that the present model is more economical and its results are closer to experimental data than other models. Some properties of the atmospheric structure are inferred directly from the dynamic equations.     

A note on finite-difference schemes for the surface and planetary boundary layers

The solution of the planetary boundary-layer equations by finite-difference methods has recently become very popular. Among recent papers using such methods, several use somewhat arbitrary finite-difference meshes and some do not make use of a constant flux or wall layer near the ground. It is shown that the use of finite differences right down to the ground can be a very inaccurate procedure when used in conjunction with an eddy viscosity or mixing length proportional to (z +z ₀) orz near the ground. Such an approach can lead to results that are highly dependent on the finite-difference scheme used and virtually independent of the roughness length,z ₀. A scheme using an expanding grid, based on the form chosen for mixing length or eddy viscosity, is proposed which gives good results with or without a surface layer in the case of a neutrally stratified atmosphere.     

An improved scheme for time-dependent boundary conditions in atmospheric general circulation models

 Atmospheric general circulation models (AGCMs) are often “coupled” with time varying observations of boundary conditions or some other aspect of the climate system. A typical example is the Atmospheric Model Intercomparison Project (AMIP) experimental protocol, which required the specification of sea surface temperature and sea-ice extent from observed monthly means. AGCMs ordinarily incorporate the prescribed conditions by evaluating an interpolating function at each time step. Typical schemes, such as that used in the second generation GCM (GCM2) of the Canadian Centre for Climate Modelling and Analysis (CCC), do not preserve monthly means and have a smoothing effect on the interpolated time series which tends to reduce the amplitude of annual cycle and interannual variability of sea surface temperature (SST). By solving a large set of linear equations, a simple linear time-interpolation scheme that preserves the observed monthly mean SST and hence its variability can be obtained. The new scheme improves upon that used previously in CCC GCM2 by eliminating the substantial loss of interannual variability (up to 20%) and the small attenuation of the annual cycle (less than 4% on average) incurred with the old scheme. The improved linear interpolation scheme is easily adapted to other quantities. Received: 4 August 1997 / Accepted: 26 November 1997     

Scaling turbulence in the planetary boundary layer

Two different approaches to scaling turbulence in the planetary boundary layer over Lake Ontario are investigated. The height up to the inversion was found to be the appropriate scaling height while u. for near‐neutral and w* for unstable conditions were the appropriate scaling velocities. The results were in general agreement with the numerical models of Deardorff (1972) and Wyngaard, Cote, and Rao (1974).     

A case study of turbulence in the stable nocturnal boundary layer

Velocity and signal intensity data during stable conditions in the nocturnal boundary layer (NBL) were obtained with a minisodar on two consecutive nights with similar mean conditions. There was little turbulence activity during the first night, but during the second night, continuous background Kelvin-Helmholtz waves and instabilities having a 2-min period grew and penetrated above the mean NBL height at approximately 60-min intervals. Enhanced ozone concentrations at the surface occurred during the active periods even though most mean meteorological parameters were unchanged. Vertical profiles of vertical velocity standard deviation, dissipation rate, and temperature variance destruction rate in the NBL were measured and analyzed separately according to levels of turbulence activity. Well-defined differences between inactive and active periods of a factor of two to four were found for each parameter. The temperature structure parameter flux was large and in opposite directions in the upper and lower part of the NBL during active periods of turbulence, but small during other periods.     

Wave-mean flow interactions in the upper atmosphere

The nature of internal gravity waves is described with special emphasis on their ability to transport energy and momentum. The conditions under which these fluxes interact with the mean state of the atmosphere are described and the results are applied to various problems of the upper atmosphere, including the quasi-biennial oscillation, the heat budget of the thermosphere, the general circulation of the mesosphere, turbulence in the mesosphere, and even the 4-day circulation of the Venusian stratosphere.Gravity waves have long been recognized as an important element in the dynamics of the upper atmosphere - largely due to their very large amplitudes in this region. It is the implied purpose of this paper to convey some of the thinking that has gone on about the role of gravity waves in the large-scale circulation of the upper atmosphere. Insofar as gravity waves are now being identified as important entities in the lower atmosphere as well, it is possible that mechanisms identified in the upper atmosphere will prove relevant to the troposphere.Alfred P. Sloan Foundation Fellow. Now at Harvard University.     

A note on the multi-α solutions of the upper bounding problem for thermal convection

The transition to “multi-α” solutions of the upper bounding problem for thermal convection is discussed. For convection in a fluid contained between parallel stress-free perfectly conducting boundaries, the “single-α” solutions of Straus (1973) are used to determine the Rayleigh number R at which the first transition occurs. Two upper bounding problems are treated: one valid for all values of the Prandtl number and one valid only for large Prandtl numbers. A significant difference between the two problems is noted. The former has a transition at R ～ 28200; the latter has no transition within the range of Rayleigh numbers treated here: R ? 2.3 · 10⁵.     

A group-kinetic theory with a closure by memory loss for modeling turbulence in the atmosphere and the oceans

Summary The principle of the group-kinetic method is elucidated. This method of renormalization serves as the basis for analyzing the spectral structure of turbulence. The spectral distributions include the Kolmogoroff lawk ^–5/3 for isotropic turbulence, the power lawk ^–1 for shear turbulence, the spectrum for stratified turbulence not in the power law form, the power lawk ^–3 for two-dimensional geostrophic turbulence, and the power lawsk ^–3,k ^–2 andk ^–5 for two-dimensional Rossby wave turbulence with uniform and differential rotations. We discuss a spectrum-dependent modeling in reference to the problems of the universal functions and parameters in the similarity theories for the atmospheric surface layer and the planetary boundary layer. A renormalization-based modeling of atmospheric turbulence is proposed.     

Wind and pressure oscillations in the upper atmosphere

Summary Observations of the diurnal (S ₁) and semidiurnal (S ₂) wind oscillations between 80 and 100 km show that their amplitudes are of the same magnitude as the mean winds. Both periods show pronounced seasonal changes in the same sense as, but much larger than would be expected from surface data forS ₂, and in agreement with the idea of a thermal cause forS ₁. From the observed wind oscillations the pressure oscillations can be computed. The pressure amplitudes are about 5 percent or, especially forS ₂, more of the mean pressure, indicating a fifty to hundred-fold increase compared to the low atmosphere, as suggested by theory. But the phase ofS ₂ does not show the expected reversal relative to the ground.S ₁ seems to be much more regular than at the earth's suface where it is greatly disturbed by local influences. The few data on the lunar semidiurnal (L ₂) oscillation show also the increse of the amplitudes with height.

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Zusammenfassung Bestimmungen der ganztägigen (S ₁) und halbtägigen (S ₂) Windperioden in 80 bis 100 km Höhe ergeben Amplituden von derselben Größenordnung wie die mittleren Winde. Beide Perioden zeigen starke jahreszeitliche Schwankungen. FürS ₂ wird das Maximum wie an der Erdoberfläche im Winter, das Minimum im Sommer erreicht; aber die jahreszeitliche Änderung ist in der Höhe viel größer. FürS ₁ fällt das Maximum in den Sommer, wie man im Falle einer durch Erwärmung erzeugten Oszillation erwarten würde. Aus den beobachteten Windschwankungen können die entsprechenden Luftdruckschwankungen berechnet werden. Diese betragen 5 Prozent des mittleren Luftdruckes in diesen Höhen, oder besonders fürS ₂ auch mehr, d. h. sie sind 50 bis 100 mal größer als am Erdboden. Eine derartige Zunahme mit der Höhe ist nach der Theorie zu erwarten. Die Phase vonS ₂ zeigt jedoch nicht die erwartete Umkehr im Vergleich zu der Welle am Boden.S ₁ scheint viel regelmäßiger zu sein als am Erdboden, wo es durch lokale Einflüsse sehr gestört ist. Die wenigen Daten für die halbtägige Mondgezeit (L ₂) zeigen ebenfalls eine starke Zunahme mit der Höhe, die Phase ist aber ähnlich wie am Erdboden.

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Résumé Les observations des oscillations diurnes (S ₁) et semi-diurnes (S ₂) du vent entre les niveaux de 80 km et 100 km au-dessus du sol indiquent que leurs amplitudes sont du même ordre de grandeur que leurs valuers moyennes. Ces deux périodes sont caractérisées par des changements saisonniers prononcés. PourS ₂ ces changements bien que dans la même direction sont beaucoup plus considérables que ce que les données de surface nous porteratient à croire. PourS ₁ ces changements sont en bon accord avec l'idée d'une cause thermique. Les oscillations de pression peuvent être obtenues à partir des oscillations observées du vent. Les amplitudes d'oscillation de la pression sont de l'ordre de 5 pour cent ou, spécialement dans le cas deS ₂, plus encore des valuers moyennes de la pression. Ceci indique une augmentation de cinquante à cent fois par rapport à la basse atmosphère, fait d'ailleurs suggéré par la théorie. Toutefois la phase deS ₂ ne présente pas d'inversion par rapport au sol.S ₁ paraît beaucoup plus régulier qu'au sol où la situation sest fortement affectée par les influences locales. Les quelques données concernant les oscillations semi-diurnes (L ₂) causées par la lune indiquent une augmentation des amplitudes avec l'altitude.

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With 4 Figures

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Dedicated to Dr.W. Mörikofer on the occasion of his 70 th birthday.     

激光波段大气湍流模型初探

将射频波段大气湍流模型的精细结构模式转换到激光波段,计算结果表明：湍流常数的量级和高度变化趋势与我们对已有的了解是一致的,但是它随气象条件的变化很大,其起伏可以达到数个量级。