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1.
Recently Wilson and Flesch (Boundary-Layer Meteorology, 84, 411-426, 1997) suggested that the average increment d z to the orientation = arctan(w/u) of the Lagrangian velocity-fluctuation vector can be used to distinguish the better Lagrangian stochastic models within the well-mixed class. Here it is demonstrated that the specification of d z constitutes neither a sufficient or universally applicable criterion to distinguish the better Lagrangian stochastic models within the well-mixed class. The hypothesis made by Wilson and Flesch that Lagrangian stochastic models with /PE irrotational are zero-spin models, having d z=0, is proven  相似文献   

2.
In the summer of 1988/89 flights were carried out in the Coorong coastal area of South Australia to investigate sea-breeze fronts. The flights yielded data sets of the structure of the fronts in the cross-frontal direction with a spatial resolution of approximately 3 m. The study is focused on the budgets of sensible and latent heat in the vicinity of the front and on frontogenesis/frontolysis processes which are closely related to budget considerations.The frontogenesis relationships and the budgets were established on a 2 km length scale by low-pass filtering of the space series. As the wind components were measured with high accuracy, all processes which determine frontogenesis could be evaluated and are displayed in x,z-cross-sections: these are the confluence, shear and diabatic effects, all of which play a role in q/x-, q/z-, /x- as well as /z-frontogenesis. A detailed analysis is given for two different states of frontal development. The presented results shed much light on the governing physical processes in the frontal region with strong emphasis on the effects of confluence-generated updrafts, on shear instabilities causing bulges and clefts in the frontal surface as well as producing the elevated frontal head, and on processes related to differential heating and moistening.  相似文献   

3.
From measured one-dimensional spectra of velocity and temperature variance, the universal functions of the Monin-Obukhov similarity theory are calculated for the range –2 z/L + 2. The calculations show good agreement with observations with the exception of a range –1 z/L 0 in which the function m , i.e., the nondimensional mean shear, is overestimated. This overestimation is shown to be caused by neglecting the spectral divergence of a vertical transport of turbulent kinetic energy. The integral of the spectral divergence over the entire wave number space is suggested to be negligibly small in comparison with production and dissipation of turbulent kinetic energy.Notation a,b,c contants (see Equations (–4)) - Ci constants i=u, v, w, (see Equation (5) - kme,kmT peak wave numbers of 3-d moel spectra of turbulent kinetic energy and of temperature variance, respectively - kmi peak wave numbers of 1-d spectra of velocity components i=u, v, w and of temperature fluctuations i= - ksb, kc characteristics wave numbers of energy-feeding by mechanical effects being modified by mean buoyancy, and of convective energy feeding, respectively - L Monin-Obukhov length - % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Gabeivayaaraaaaa!3C5B!\[{\rm{\bar T}}\] difference of mean temperature and mean potential temperature - T* Monin-Obukhov temperature scale - velocity of mean flow in positive x-direction - u* friction velocity - u, v, w components of velocity fluctuations - z height above ground - von Kármanán constant - temperature fluctuation - m nondimensional mean shear - H nondimensional mean temperature gradient - nondimensional rate of lolecular dissipation of turbulent kinetic energy - D nondimensional divergence of vertical transports of turbulent linetic energy  相似文献   

4.
A two dimensional model has been set up to investigate the circulation induced by an urban heat island in the absence of synoptic winds. The boundary conditions need to be formulated carefully and due to difficulties arising here, we restrict our attention to cases of initially stable thermal stratification. Heat island circulations are allowed to develop from rest and prior to the appearance of the final symmetric double cell pattern, a transitional multi-cell pattern is observed in some cases. The influence on the steady state circulation of various parameters is studied, among which are eddy transfer coefficients, the heat island intensity, the initial temperature stratification and the heat island size. Some results are presented for a case in which differential surface cooling beneath an initially stable atmosphere produces a circulation and an unstable layer capped by an elevated inversion over the city. It is hoped that this case is vaguely representative of the night-time heat island with no geostrophic wind.Notation cp Specific heat at constant pressure - g Acceleration due to gravity - H Top of integration region - Kz Vertical eddy transfer coefficient - Kx, KxH, Kxm Horizontal eddy transfer coefficients for heat and momentum - l ixing length - p Pressure - p0 Reference surface pressure (1000 mb) - PH (x, t) Pressure at z = H - R Specific gas constant for dry air - t Time - u, w Horizontal and vertical velocities - x, z Horizontal and vertical coordinates - x1, x2 Positions of discontinuities in surface temperature field (see Figure 2) - xa Heat island half-width - xb Boundary of integration region - Parameter in formula for eddy coefficients (variable-K case) = 18.0 - s Intensity of heat island - Potential temperature field - Reference absolute temperature (variable-K case) - r Reference temperature (° C) - s Surface temperature - Q Air density  相似文献   

5.
Horizontal u and vertical w velocity fluctuations have been measured together with temperature fluctuations in the atmospheric surface layer, at a small height above a wheat crop canopy. Marginal probability density functions are presented for both individual fluctuations u, w, and for the instantaneous Reynolds stress uw, and heat fluxes w and u. Probability density functions of the velocity fluctuations deviate less significantly from the Gaussian form than the probability density of temperature. There appears to be closer similarity between statistics of the instantaneous heat fluxes than between the momentum flux and either of the heat fluxes investigated. The mean momentum flux receives equal contributions from the events referred to as ejections and sweeps in laboratory boundary layers. Sweeps provide the largest contribution to the heat fluxes.  相似文献   

6.
The variations of and in the drainage flow in the Brush Creek valley of western Colorado are investigated using data from Doppler acoustic sodars and instrumented towers. The data were obtained on two experimental nights during the 1984 ASCOT field study. There is good agreement between the variations derived from low-level observations of the sodars and those derived from the towers located throughout the valley. The observed hourly average and in the nocturnal drainage flow are about 20 ° to 25 ° and 5 °, respectively; these values are much larger than those generally observed over flat terrain during nighttime stable conditions. After sunrise (about 0600 MST), as the valley warms and the flow direction changes to up-valley, these parameters increase sharply to their peak values at about 0800 MST and then decrease to their normal daytime values after about two hours.In the drainage flow, the hourly average varies inversely with wind speed according to the relation u 0.7ms-1. The vertical standard deviation is much less enhanced by complex terrain than the horizontal standard deviation. The observed values are predicted fairly well by the local similarity theory.Oak Ridge Associated Universities (ORAU) Summer Research Participant at ATDD in 1987 andOak Ridge Associated Universities (ORAU) Summer Research Participant at ATDD in 1987 and  相似文献   

7.
Horizontal diffusion in the surface layer is dependent on the standard deviation of wind direction fluctuations . Diurnal variation of this parameter in complex terrain was studied for the July 1979 Geysers, Cal., experiment using data from a network of 11 short meteorological towers in the 25 km2 Anderson Creek watershed Valley side slopes are roughly 20 ° and maximum terrain difference is about 1 km.Values of for wind directions sampled for one hour at a height of 10 m are about 35 ° during the daytime. They slowly decrease to about 20 ° by 8 to 10 p.m. as stability increases but wind speeds are still relatively high. After 10 p.m. the drainage flow sets in at most stations, with speeds of 1 to 2 m s-1, and average increases to about 30° during the period 11 p.m. to 6 a.m. In general, highest values of at night are associated with lowest values of wind speed and greatest static stability. This enhancement of by the terrain suggests that horizontal diffusion at night always conforms to that expected during nearly neutral stabilities. That is, Pasquill class D diffusion applies to the horizontal component all night in complex terrain.  相似文献   

8.
The local similarity theory, presented in the recent papers of Sorbjan (1986a, b), is extended by taking into consideration spectral (u, v, w, ) and cospectral (uw, w, u) densities in the stable-continuous boundary layer. The resulting universal expressions for spectra, cospectra and the reduced frequencies of their peaks are in agreement with empirical data from the Kansas 1968 surface-layer and Minnesota 1973 boundary-layer experiments. In addition, the universal functions for the structure parameters and the dissipation rates are also derived and shown to fit the empirical data well.On leave from Institute of Environmental Engineering, Warsaw Polytechnic University, 00653 Warsaw, Poland.  相似文献   

9.
For an airport site near Visakhapatnam, India, and based on 10 years of data for the months of January, April, August and October, values of are given as a function of wind speed, wind direction and Pasquill diffusion category.  相似文献   

10.
Summary Rainfall in West Africa is examined in relation to monthly mean equivalent potential temperature ( e )at the earth's surface. The study revealed that monthly mean equivalent potential temperature ( e ) and monthly rainfall (R) generally decreased northwards from the equator.A good relationship existed betweenR and e in the northern zone of West Africa (i.e., north of 7.5° N). No definite relationship existed in the southern zone. In the northern zone, the departure of e from its annual mean ( ) first became positive about a month before the onset of the rains. Positive departures from ) generally resulted in more than normal (or average) rainfall in this zone. In general, little or no rainfall occurred in West Africa whenever e was less than 320 K.
Zusammenfassung Der Niederschlag (MonatssummeR) in Westafrika wird in Zusammenhang mit der mittleren monatlichen Äquivalent-temperatur ( e ) an der Erdoberfläche untersucht. Es zeigte sich, daß die Monatswerte beider Elemente im allgemeinen vom Äquator nach Norden abnehmen.ZwischenR und e ergab sich für das nördliche Westafrika (nördlich von 7.5° N) eine gute, für die südliche Zone jedoch keine beweisbare Übereinstimmung. In der nördlichen Zone übertraf e das Jahresmittel erstmals etwa einen Monat vor Beginn der Regenzeit. Positive Abweichungen vom mittleren e hatten immer übernormalen Niederschlag in dieser Zone zur Folge. Dagegen gab es wenig oder keinen Niederschlag in Westafrika, wenn e unter 320 K lag.

With 7 Figures  相似文献   

11.
The turbulent structure of the lake breeze penetration and subsequent development of the thermal internal boundary layer (TIBL) was observed using a kytoon-mounted ultrasonic anemometer-thermometer. The lake breeze penetrated with an upward rolling motion associated with the upward flow near the lake breeze front. After the lake breeze front passed, the behaviors of the velocity and temperature at the top of the lake breeze layer were similar to those found in convective boundary layers (CBL). Comparing gq/*, u /w * and w /w * between the present observation of TIBL development after the passage of the lake breeze front and CBL data from the literature, the /* values showed reasonable agreement; however, u /w * and w /W* had smaller values in the TIBL than in the CBL at higher altitudes. This is due to the differences in the mean velocity profiles. While the CBL has a uniform velocity profile, the TIBL has a peak at lower elevation due to the lake breeze penetration; the velocity then decreases with height.Present address: The Institute of Behavioral Science, 1-35-7 Yoyogi, Tokyo 151, Japan.  相似文献   

12.
Fourth-order mixed moments of velocity and temperature fluctuations, measured within the atmospheric surface layer, are compared with results obtained by assuming the quasi-Gaussian approximation. Standard deviations of the products uw, u and w(u and w are the longitudinal and vertical velocity fluctuations; is the temperature fluctuation) are in good agreement with those obtained using the quasi-Gaussian assumption. Good agreement is also obtained between measured and Gaussian estimates of fourth-order moments including all three fluctuations u, w, Schwarz inequalities, commonly used in the clipping approximation in turbulence modelling, are found to provide bounds for third-order moments of w, that are too conservative. More reasonable, tighter, bounds for these moments are given by inequalities obtained by Lumley.  相似文献   

13.
Plume dispersion in the convective boundary layer (CBL) is investigated experimentally in a laboratory convection tank. The focusis on highly-buoyant plumes that loft near or become trapped in the CBL capping inversion and resistdownward mixing. Such plumes are defined by dimensionless buoyancy fluxes F* 0.1, where F* = Fb/(U w* 2 zi), Fb is the stack buoyancy flux,U is the mean wind speed, w* is the convective velocity scale, and zi is the CBL depth. The aim is to obtain statistically-reliable mean (C) and root-mean-square (rms, c) concentration fields as a function of F* and the dimensionless distance X = w*x/(U zi), where x is the distance downstream of the source.The experiments reveal the following mainresults: (1) For 3 X 4and F* 0.1, the crosswind-integrated concentration (CWIC) fields exhibit distinctly uniform profiles below zi with a CWIC maximum aloft, in contrast to the nonuniform profiles obtained earlier by Willis and Deardorff. (2) The lateral dispersion (y) variation with X is consistent with Taylor's theory for * 0.1 and a buoyancy-enhanced dispersion, y/zi F* 1/3X2/3, forF* = 0.2 and 0.4. (3) The entrapment, the plume fraction above zi, has a mean (E) that follows a systematic variationwith X and F*, and a variability (e/E) that is broad ( 0.3 to 2) near the source but subsides to 0.25 far downstream. (4) Vertical profiles of the concentration fluctuation intensity (c/C) are uniform for z < zi and X > 1.5, but exhibit significant increases: (a) at the surface and close to the source (X 1.5), and(b) in the entrainment zone. (5) The cumulative distribution functions (CDFs) of the scaled concentration fluctuations (c/c) separate into mixed-layer and entrainment-layer CDFs for X 2, with the mixed-layer group collapsing to a single distribution independent of z.These are the first experiments to obtain all components of the lateral and vertical dispersion parameters (rms meander, relative dispersion, total dispersion) for continuous buoyant releases in a convection tank. They also are the first tank experiments to demonstrate agreement with field observations of: (1) the scaled ground-level concentration along the plume centreline, and (2) the dimensionless lateral dispersion _y/z_i of buoyant plumes.  相似文献   

14.
A two-dimensional numerical mesoscale model is used to investigate the internal structure and growth of the stably stratified internal boundary layer (IBL) beneath warm, continental air flowing over a cooler sea. Two situations are studied — steady-state and diurnally varying offshore flow. In the steady-state case, vertical profiles of mean quantities and eddy diffusion coefficients (K) within the IBL show small, but significant, changes with increasing distance from the coast. The top of the IBL is well defined, with large vertical gradients within the layer and a maximum in the coast-normal wind component near the top. Well away from the coast, turbulence, identified by non-zero K, decreases to insignificant levels near the top of the IBL; the IBL itself is characterised by a critical value of the layer-flux Richardson number equal to 0.18. The overall behaviour of the mean profiles is similar to that found in the horizontally homogeneous stable boundary layer over land.A simple physical model is used to relate the depth of the layer h to several relevant physical parameters viz., x, the distance from the coast and U, the large-scale wind (both normal to the coastline) and g/, being the temperature difference between continental mixed-layer air and sea surface, is the mean potential temperature and g is the acceleration due to gravity. Excellent agreement with the numerical results is found, with h = 0.014x 1/2 U (g/)–1/2.In the diurnally varying case, the mean profiles within the IBL show only small differences from the steady-state case, although diurnal variations, particularly in the wind maximum, are evident within a few hundred kilometres of the coast. A mesoscale circulation normal to the coast, and superimposed upon the mean offshore flow, develops seawards of the coastline with maximum vertical velocities about sunset, of depth about 2 km and horizontal scale 500 km. The circulation is related to the advection, and subsequent decay, of daytime convective turbulence over the sea.  相似文献   

15.
The dynamical range of global atmospheric circulations is extended to specialized parameter regions by evaluating the influence of the rotation rate () on axisymmetric, oblique, and diurnally heated moist models. In Part I, we derived the basic range of circulations by altering for moist and dry atmospheres with regular and modified surfaces. Again we find the circulations to be composed of only a few elementary forms. In axisymmetric atmospheres, the circulations consist of a single jet in the rotational midrange (*=1/2–1) and of double jets in the high range (*=2–4), together with one or two pairs of Hadley and Ferrel cells; where (*=/ E ) is the rotation rate normalized by the terrestrial value. These circulations differ from those predicted by firstorder symmetric-Hadley (SH1) theory because the moist inviscid atmosphere allows a greater nonlinearity and prefers a higher-order meridional mode. The axisymmetric circulations do, however, resemble the mean flows of the natural system — but only in low latitudes, where they underlie the quasi-Hadley (QH) element of the MOIST flows. In midlatitudes, the axisymmetric jets are stronger than the natural jets but can be reduced to them by barotropic and baroclinic instablities. Oblique atmospheres with moderate to high tilts ( P =25°–90°) have the equator-straddling Hadley cell and the four basic zonal winds predicted by the geometric theory for the solstitial-symmetric-Hadley (SSH) state: an easterly jet and a westerly tradewind in the summer hemisphere, and a westerly jet and an easterly tradewind in the winter hemisphere. The nonlinear baroclinic instability of the winter westerly produces a Ferrel cell and the same eddy fluxes as the quasi-geostrophic QG element, while the instability of the summer easterly jet produces a QG-Hadley (QGH) element with a unique, vertically bimodal eddy momentum flux. At high P and low *, the oblique atmospheres reach a limiting state having global easterlies, a pole-to-pole Hadley cell, and a warm winter pole. At low tilts P <10°, the oblique circulations have a mix of solstitial and equinoctial features. Diurnal heating variations exert a fundamental influence on the natural-Hadley (NH) circulations of slowly rotating systems, especially in the singular range where the zonal winds approach extinction. The diurnality just modifies the NH element in the upper singular range (1/45*1/16), but completely transforms it into a subsolar-antisolar Halley circulation in the lower singular range (0*<1/45). In the modified NH flows, the diurnality acts through the convection to enhance the generation of the momentum-transferring planetary waves and, thereby, changes the narrow polar jets of the nondiurnal states into broad, super-rotating currents. Circulation theory for these specialized flows remains rudimentary. It does not explain fully how the double jets and the multiple cells arise in the axisymmetric atmospheres, how the QGH element forms in the oblique atmospheres, or how waves propagate in the slowly rotating diurnal atmospheres. But eventually all theories could, in principle, be compared against planetary observation: with Mars testing the QGH elements; Jupiter, the high-range elements; Titan, the equinoctial and solstitital axisymmetric states; and Venus, the diurnally modified NH flows.  相似文献   

16.
A previously published technique for using tethered spherical balloons as anemometers for measuring light low-level winds has been further developed. Earlier data on the relationship between the aerodynamic drag coefficient and the Reynolds number of spherical rubber balloons were combined with a large number of new data and re-analysed; and the errors in the relationship were estimated. The results allowed a more accurate calculation of wind speed from the deflection of a tethered balloon from the vertical. When combined with a new technique for calculating the effects of the tether, this enabled light to moderate low-level winds at fixed heights up to 600 m or more to be measured with simple, cheap, and readily mobile equipment; and a slight modification of the technique allowed measurement of winds in and above fog. Wind speeds measured by the ballon technique showed reasonably good agreement with measurements by an anemometer carried beneath the balloon.Glossary of Symbols a, b, c Coefficients in the relationship between lnC d and lnR - A Quantity under square root in solution for lnV whena0 - C d Wind drag coefficient for balloon - C dc Value ofC d given by calibration curve of Table I - D Dynamic wind pressure force on balloon - F Buoyant free lift of balloon with load - Re Reynold's number of balloon (sphere) - R = Re/105 - r Radius of sphere - T Tension in tether - V Wind speed - 83() =(lnC dc -lnC d ) when 83° , or 0 for other - Error in lnC d - Elevation of tether where attached to balloon - Elevation of balloon from ground tether point - Molecular viscosity of air - Ratio of circumference to diameter of circle - Density of air  相似文献   

17.
This is one of a series of papers on the Askervein Hill Project. It presents results on the variations in mean wind speed at fixed heights (z) above the ground from linear arrays of anemometer posts and towers. Most of the data are for z = 10 m but some are for z = 3 m. Selected and directionally grouped data from the 55 Mean Flow runs are presented together with mean flow data from Askervein '83 Turbulence runs. Comparisons are made between the data and guideline estimates of fractional speed-up ratio at hilltop locations and between the data and MS3DJH/3 model predictions along the tower lines. There is good agreement in most cases.  相似文献   

18.
Measurements in the atmospheric surface layer of sixth-order velocity structure functions and of sixth-order mixed velocity-temperature structure functions support values of and previously obtained in the laboratory at moderate turbulence Reynolds numbers.  相似文献   

19.
Stability Effects on Heat and Moisture Fluxes at Sea   总被引：1，自引：0，他引：1  
During the 1996 ASGAMAGE experiment we measured windspeed, air temperature Ta, watertemperature Ts, humidity and the momentum,heat and moisture fluxes at a research platform offthe Dutch coast. For each quantity we used several(sets of) instruments simultaneously. This allowed usto make an extensive assessment of the quality of themeasurements and to find optimal values for thevarious quantities for each run. From these values wecalculated CH and CE, theStanton and Dalton numbers, and reduced them to 10-mheight and neutral conditions. For this reductionwe made a separate analysis for the effect ofinclusion or non-inclusion of the assumption that theroughness length for heat or moisture is the same forthe neutral and non-neutral cases. Differences inthe reduced data due to this assumption turned out tobe well within the measurement error.For CH we distinguished three separategroups of data: stable (A), unstable witha s (B) and unstablewith thetas;a > s (C), with indicating the potential temperature.The stable data separate into two groups, depending onwater temperature and/or the wave field. The data ofgroup B showed a relation with wave age. The data ofgroup C consistently gave negative values forCH, a result that might indicate conversion oflatent heat into sensible heat through condensation ofwater vapour just above the water surface. An attemptto re-analyse the data in terms of density fluxes,combining the effects of heat and moisture, still gavenegative transfer coefficients for group C.For the moisture flux we found the more conventionalresult of a separation in stable and unstable values;these categories showed a clear difference, but notrends with, for example, wind speed.We conclude that standard Monin-Obukhov similaritytheory cannot explain our data.  相似文献   

20.
Summary The standard equations for the theory of atmospheric tides are solved here by an integral representation on the continuous spectrum of free oscillations. The model profile of back-ground temperature is that of the U.S. Standard Atmosphere in the lower and middle atmosphere, and in the lower thermosphere, above which an isothermal top extends to arbitrarily great heights. The top is warm enough to bring both the Lamb and the Pekeris modes into the continuous spectrum.Computations are made for semidiurnal lunar tidal pressure at sea level at the equator, and the contributions are partitioned according to vertical as well as horizontal structure. Almost all the response is taken up by the Lamb and Pekeris modes of the slowest westward-propagating gravity wave. At sea level, the Lamb-mode response is direct and is relatively insensitive to details of the temperature profile. The Pekeris mode at sea level has an indirect response-in competition with the Lamb mode-and, as has been known since the time of its discovery, it is quite sensitive to the temperature profile, in particular to stratopause temperature. In the standard atmosphere the Lamb mode contributes about +0.078 mb to tidal surface pressure at the equator and the Pekeris mode about –0.048 mb.The aim of this investigation is to illustrate some consequences of representing the tide in terms of the structures of free oscillations. To simplify that task as much as possible, all modifying influences were omitted, such as background wind and ocean or earth tide. Perhaps the main defect of this paper's implementation of the free-oscillation spectrum is that, in contrast to the conventional expansion in the structures of forced oscillations, it does not include dissipation, either implicity or explicity, and thus does not satisfy causality. Dissipation could be added implicity by means of an impedance condition, for example, which would cause up-going energy flux to exceed downgoing flux at the base of the isothermal top layer. To achieve complete causality, however, the dissipation must be modeled explicity. Nevertheless, since the Lamb and Pekeris modes are strongly trapped in the lower and middle atmosphere, where dissipation is rather weak (except possibly in the surface boundary layer), more realistic modeling is not likely to change the broad features of the present results.Symbols a earth's mean radius; expansion coefficient in (5.3) - b recursion variable in (7.4); proximity to resonance in (9.2) - c sound speed in (2.2); specific heatc p in (2.2) - f Coriolis parameter 2sin in (2.2) - g standard surface gravity - h equivalent depth - i ; discretization index in (7.3) - j index for horizontal structure - k index for horizontal structure; upward unit vectork in (2.2) - m wave number in longitude - n spherical-harmonic degree; number of grid layers in a model layer - p tidal pressure perturbation; background pressurep 0 - q heating function (energy per mass per time) - r tidal state vector in (2.1) - s tidal entropy perturbation; background entropys 0 - t time - u tidal horizontal velocityu - w tidal vertical component of velocity - x excitation vector defined in (2.3); vertical coordinate lnp */p 0 [except in (3.8), where it is lnp /p 0] - y vertical-structure function in (7.1) - z geopotential height - A constant defined in (6.2) - C spherical-harmonic expansion coefficient in (3.6) - D vertical cross section defined in (5.6) and (5.9) - E eigenstate vector - F vertical-structure function for eigenstate pressure in (3.2) [re-defined with WKB scaling in (7.2)] - G vertical-structure function for eigenstate vertical velocity in (3.2) [re-defined with WKB scaling in (7.2)] - H pressure-scale height - I mode intensity defined in (8.1) - K quadratic form defined in (4.4) - L quadratic form defined in (4.4); horizontal-structure magnification factor defined in (5.11) - M vertical-structure magnification factor defined in (4.6) - P eigenstate pressure in (3.2); tidal pressure in (6.2) - R tidal state vector in (5.1) - S eigenstate entropy in (3.2); spherical surface area, in differential dS - T background molecular-scale (NOAA, 1976) absolute temperatureT 0 - U eigenstate horizontal velocityU in (3.2); coefficient in (7.3) - V horizontal-structure functionV for eigenstate horizontal velocity in (3.2); recursion variable in (7.3) - W eigenstate vertical velocity in (3.2) - X excitation vector in (5.1) - Y surface spherical harmonic in (3.7) - Z Hough function defined in (3.6) - +dH/dz - (1––)/2 - Kronecker delta; Dirac delta; correction operator in (7.6) - equilibrium tide elevation - (square-root of Hough-function eigenvalue) - ratio of specific gas constant to specific heat for air=2/7 - longitude - - - background density 0 - eigenstate frequency in (3.1) - proxy for heating functionq =c P/t - latitude - tide frequency - operator for the limitz - horizontal-structure function for eigenstate pressure in (3.2) - Hough function defined in (6.2) - earth's rotation speed - horizontal gradient operator - ()0 background variable - ()* surface value of background variable - () value at base of isothermal top layer - Õ state vector with zerow-component - , energy product defined in (2.4) - | | energy norm - ()* complex conjugate With 10 Figures  相似文献   

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