Constant Pressure Surfaces Research Articles

The inclusion of Himalayas in a primitive equation model

A regional primitive equation model has been developed for the Indian region. One of the difficulties in this model is caused by large gradients in mountainous regions. To avoid large truncation errors near the edges of mountains, some models evaluated the pressure gradient force on a constant pressure surface, instead of a sigma surface. More recently, phillips (1974) suggested that truncation errors could be reduced by removing the hydrostatic component of the geopotential field, The resiciual geopotential may then be treated as a dependent variable, which could be integrated with respect to time by the model. To be energetically consistent, a temperature field was similarly defined. This paper discusses the scheme for the Himalayan region. Truncation errors by the present scheme are compared with the earlier method. The conversion from sigma to pressure coordinates was carried out by Lagrangian interpolation. Results are presented with these methods to show the development of circulations in 5 days of model time.

General relativistic magnetofluids

General relativistic hydromagnetic systems are studied in the infinite conductivity limit. It is shown that when the frozen-in magnetic field lies in surfaces of constant pressure, the fluid acceleration and magnetic field are orthogonal. The theorem is proved that a shear-free infinite conductivity magnetofluid is irrotational if and only if the Weyl tensor is pure electric type. A restricted steady state is formulated and discussed, and within that state it is shown that an infinite conductivity magnetofluid cannot be electrically neutral.

Generalized elliptic equilibria in the magnetohydrodynamic approximation

A simple class of static equilibria, in the ideally conducting magnetohydrodynamic approximation, is found to include linear systems having surfaces of constant hydrodynamic pressure with a cylindrical topology and elliptic transverse cross-section functionally dependent on an axial co-ordinate. These suggest a possible mode of behaviour for non-axisymmetric toroidal systems and might themselves be realized experimentally as free boundary configurations of a plasma in an applied quadrupole-like magnetic field.

Toroidal plasma equilibrium with closed magnetic lines of force

The magnetostatic equilibrium is investigated of plasma with a scalar pressure in closed magnetic lines of force. The configuration considered does not reduce to an axisymmetric one, even when the toroidicity of the system tends to zero. An expansion procedure with respect to the ratio of the plasma radius to the period of corrugation of the field is applied. An expression for the constant-pressure surface with an elliptic cross section is obtained.

On the non-linear behaviour of fluid jets

In this paper we consider a one-dimensional theory for the flow of fluid jets, formulated with the help of one-dimensional postulates. The theory is applied to a circular cylindrical jet of incompressible viscous fluid with constant pressure and constant surface tension over its surface. A phase plane analysis is used to obtain some (non-linear) solutions of the governing equations when viscosity is neglected. For steady state problems, including viscosity, earlier work of Matovich and Pearson[2] is obtained as a limiting case of the theory.

Semi -annual oscillation of constant pressure surfaces (1000-100 mb) in the northern hemisphere

Monthly mean values at about 250 stations in the northern hemisphere were analysed for the study of semi-annual pressure oscillation at sea level and at 850, 700, 500, 300, 200 and 1oo mb levels. It is found that at all levels and at all longitudes, the amplitudes are smallest in the equatorial latitudes and largest in sub-tropical or higher latitudes. In the vertical, the amplitudes generally increase upwards upto about 200 mb level. There is a surface of phase reversal or sharp phase shift which slopes equatorwards with increase of height. Below this surface maximum occurs towards the end of April and October, above this surface, the maximum occurs towards the end of January and July. The oscillation is studied in some detail for the Indian region.

Time Spectral Analysis of Mid-Latitude Disturbances

The method of time series analysis is used to study rawinsonde data in middle latitudes. The spectra reveal baroclinically unstable traveling waves with a preferred period of four to five days and a large amount of variance at lower frequencies. The preferred period of the longer-period waves is roughly 30 days, although the character of the disturbances in this range is highly variable. For the waves of periods between three and seven days, phase relations are derived for the northward component of the wind, the temperature, and the height of constant pressure surfaces. The phase relations are characteristic of traveling baroclinic waves and possess reasonable statistical significance. No stable phases were obtained for the eastward component of the wind or for the longer-period oscillations.

Meteorological fields from remote infrared sensing

Modern numerical weather prediction techniques require global observations of the atmospheric state and structure parameters. The current meteorological observing system, which is based on radiosonde balloon observations, has extensive gaps. Remote sensing of the Earth atmosphere emission spectrum from satellites can fill these gaps. The physical basis for extracting information on meteorological fields from such remote observations is explained. The problem reduces to that of solving a linear Fredholm equation of the first kind in the presence of noisy data. There is no unique solution to such a problem. The mathematical techniques-inversion techniques-that are currently used to solve the problem are reviewed. Examples are given of meteorological fields obtained from remote infrared sensing from satellites. Results indicate that meteorological parameters such as temperature and geopotential height of constant pressure surfaces can be measured-in conditions of clear skies-to accuracies approaching that of the radiosonde system. Other meterological variables, e.g., water vapor and ozone, can be determined to a lesser degree of accuracy. Applications of the remotely sensed fields are described. Problem areas and suggested solutions are discussed.

Equi-density surfaces in synchronously rotating close binaries built on polytropic model ?=3

A direct numerical method, involving no perturbational procedures, is described and used for the computation of the surfaces of constant potential, pressure and density in synchronously rotating close binaries with both components built on polytropic model ν=3.

Compatibility of Radiosonde and Nimbus 4 SIRS-Derived Data at Stratospheric Constant-Pressure Surfaces

Abstract The usefulness of Nimbus 4 satellite infrared spectrometer (SIRS)-derived temperature and height data for constant-pressure analyses at stratospheric levels is investigated by comparing SIRS data with rawinsonde observations and objective analyses of those data. Results from the various methods of comparison are difficult to interpret since systematic and random errors of observations at stratospheric altitudes do not permit the observed data to be used as an unquestioned standard. In addition, conclusions must be qualified by the fact that the SIRS information derived to date has depended in part on analyses of rawinsonde data. The following conclusions were reached from the various comparison studies: (1) SIRS data are useful for constant-pressure analyses at stratospheric levels, (2) mean differences between analyzed rawinsonde temperatures and SIRS derivations are generally less than 3°C, (3) differences are greater during stratospheric warmings, but SIRS data generally indicate the proper tr...

Fluid flows obtained by geometrical characterizations

A problem in fluid mechanics is considered solved in the usual sense, if we can describe fairly explicitly certain functions such as pressure, density, velocity, etc. over a suitable domain. From such a complete description of a “fluid flow” we can pick out certain purely geometrical attributes such as the family of constant pressure surfaces, or the family of curves determined by the streamlines. In actual fact, of course, we don’t often come up with complete explicit solutions of fluid mechanics problems, and often start our consideration of a problem by focusing our attention on the geometry-for instance, we might begin by assuming the flow is “two dimensional.” Such an assumption is usually motivated by a given physical situation. If we are more concerned with obtaining a general understanding of the nature of solutions in fluid mechanics rather than solving a specific problem, then any one of an endless number of geometrical assumptions might be imposed. Thus we might look for flows whose streamlines form normal congruences of curves, or whose principal normal congruences form normal congruences [I], etc. Rather than pick specific geometrical properties we might ask more general questions of the type “to what extent does the specification of the geometry of a flow determine the flow ?” Or “to what extent do the equations governing the flow restrict the possible shapes of the streamlines, constant pressure surfaces, or other intrinsic geometrical configurations ?” The study of the differential geometry of fluids is old. The spirit is represented (and most results presented) in Refs. [l-9] and references therein. The present contribution is in that spirit. We shall be concerned with steady nondissipative compressible fluid flow

The zonal harmonic standing waves in the southern hemisphere

We have examined the zonal harmonic waves in the southern hemisphere by means of longterm average heights of constant-pressure surfaces from sea level to 100 mb and by daily 500-mb heights, and found that waves 1, 2, and 3 have significant standing components. Wave 1 at extratropical latitudes has one peak in the subpolar regions and another in the subtropics. The ridge of the subpolar region is in the Pacific and the ridge of the subtropical region is in the Atlantic Ocean. The phase changes near 40°S where the amplitude tends toward nought. In summer the wave is biggest near the tropopause but in winter it continues to grow into the stratosphere over the area where the temperature drops poleward. Wave 2 has a large standing component over Antarctica with its ridges over the highest parts of west and east Antarctica. There is a well-defined wave 3 between 25° and 60°S in all months, with ridges near the three lower-latitude continents. In addition the wave has a marked peak in the upper tropical troposphere in summer, which is in phase with that at higher latitudes.

Correlation of fluctuations of ionospheric absorption and atmospheric planetary scale waves

Abstract The values of ƒ- min reported by 12 ionosonde stations between 40° and 60° north geographic latitude, for the 5 hr centered on local noon, during the period 1 November 1964 - 30 April 1965, were subjected to zonal Fourier analysis. The first two zonal harmonics, zonal wave-numbers 1 and 2, were correlated with the corresponding harmonics of the atmospheric pressure fields for the stratosphere. The fluctuations of the f-min harmonic of wave-number 1 are shown to be in phase with approximately simultaneous fluctuations of the same harmonic of the height of the 50 and 10 millibar constant pressure surfaces and the thickness of the 50 - 10 millibar layer. The observed relationship is tentatively explained as due to approximately vertical planetary-scale disturbances of the temperature field which are associated with the fluctuations of the planetary scale waves in the constant pressure surfaces.

Tokamak Equilibrium

Axisymmetric hydromagnetic equilibria are obtained from an ideal fluid model by means of an asymptotic expansion in the inverse aspect ratio. The calculation is carried sufficiently far so that the equilibrium condition J×B = ≇p is satisfied to second order. This provides expressions for the eccentricity of the constant pressure surfaces as well as for their displacements, and for both the magnitude and the curvature of the external field that must be provided to support the equilibrium. Scaling considerations are invoked to show how the external field must be altered to compress the plasma to a smaller major radius and thus obtain additional heating. Elementary hydromagnetic considerations indicate that the configuration may be stable with respect to modes which have the symmetry of the equilibrium. Application is made to a specific compression heating experiment.

Motions in planetary atmospheres and the interpretation of radio occultation data

Atmospheric motions can produce variations in the height of constant pressure surfaces which must be taken into account in any comparison of occultation data from different points on the same planet.

VERTICAL MOTION FIELD IN THE MIDDLE THERMOSPHERE FROM SATELLITE DRAG DENSITIES

The vertical motion field in the thermosphere is calculated from the continuity equation. This calculation is based on a field of horizontal winds and an intermediate model of the thermospheric temperature field consistent with the density structure inferred from satellite drag data. The vertical motion consists of a component due to rise and fall of constant pressure surfaces and a component due to horizontal maas divergences, both components being of the order of 1 m. sec.−1 Only the latter component is of importance for thermodynamic considerations. The adiabatic warming associated with the diurnally variable part of the vertical motion due to mass divergence gives a second heat source which is of magnitude comparable to the heating by solar radiation. The time-averaged meridional circulation also implies large adiabatic warming and cooling. This computed mean meridional circulation cannot be reconciled with the heat balance of the thermosphere. The thermospheric temperature field at low levels in high latitudes can be changed so as to reverse the direction of the mean meridional pressure gradient and thus to give a mean meridional circulation consistent with heat balance considerations. Existing global thermospheric models could be improved by adjustment of the temperature field at low levels in such a way that vertical motions computed from horizontal winds give a plausible adiabatic heating field.

Experiments in Objective Frontal Contour Analysis

Abstract Following the methods of Clarke and Renard, experiments were made in the objective analysis of upper level fronts, using wet-bulb potential temperature, layer thickness and geostrophic horizontal wind shear as parameters. The objective fronts show significant differences from classical models which assume an identity between fronts and quasi-substantial air-mass boundaries. Frequency distributions in constant pressure surfaces suggest that the wet-bulb potential temperature is not entirely satisfactory as a frontal tracer.

On the flux of heat through laminar wavy liquid layers

Dynamically passive transfer of heat across a layer of liquid supporting a progressive, periodic surface wave is approached from a Lagrangian viewpoint. The model layer considered is the region between two constant pressure surfaces of a Gerstner wave and the thermal boundary conditions are that the average temperature of any surface particle remains constant and that there is horizontal homogeneity of the average temperature field.It is shown that fluctuations in the temperature of any particle are negligibly small for ordinary liquids and a uniformly valid approximation to the average temperature of each particle is presented.The extent to which the flux of heat through the layer is augmented is computed for typical cases and it is shown to be at most doubled. Indication is given of extensions of the method to other kinds of progressive waves and to situations in which the boundary conditions are unsteady and spatially inhomogeneous.

SYNOPTIC ANALYSES OF THE 5-, 2-, AND 0.4-MILLIBAR SURFACES FOR THE IQSY PERIOD

Rocket data from the Meteorological Rocket Network and other sources, in addition to high-level rawinsonde observations, are being employed to analyze a series of 5-, 2-, and 0.4-mb. charts. The broadscale analyses are being constructed for each week of the International Years of the Quiet Sun period, and primarily cover the North American and adjacent ocean areas. Methods employed for processing the various types of data as well as the analysis procedure are described. Analyses completed thus far confirm the existence of large-scale systems, such as the wintertime polar cyclone, and the Aleutian anticyclone, to at least the level of the stratopause. In addition there is evidence of large-scale periodic oscillations in the heights of upper-stratospheric constant-pressure surfaces during autumn and early winter. Furthermore, a significant tidal component is apparent in summertime rocketsonde winds, for which adjustment must be made in order to obtain consistent quasi-synoptic patterns.

Analytic Approximations of Boundary-Layer Problems

The investigation of the approximate solution of boundary-layer problems by variational techniques is extended beyond earlier work based on a single-parameter collocation approach. A multiparameter treatment is considered and shown to result in a much improved approximation. More powerful minimization conditions for the single-parameter case are also studied. Finally, an approximate solution to a flow problem concerning the development of a boundary layer on a constant pressure surface after having traversed an upstream pressure gradient is presented and discussed.