Convective column above a linear fire in a homogeneous isothermal atmosphere

1977 ◽  
Vol 13 (5) ◽  
pp. 570-579 ◽  
Author(s):  
Yu. A. Gostintsev ◽  
L. A. Sukhanov
Keyword(s):  
Convective Column ◽  
Isothermal Atmosphere

The Determination of Maximum Range for an Unpowered Atmospheric Vehicle

1964 ◽  
Vol 68 (638) ◽  
pp. 111-116 ◽  
Author(s):  
D. J. Bell
Keyword(s):  
Calculus Of Variations ◽  
Lagrange Multipliers ◽  
Digital Computer ◽  
Necessary Conditions ◽  
Lagrange Equations ◽  
Initial Portion ◽  
End Conditions ◽  
Maximum Range ◽  
Isothermal Atmosphere

SummaryThe problem of maximising the range of a given unpowered, air-launched vehicle is formed as one of Mayer type in the calculus of variations. Eulers’ necessary conditions for the existence of an extremal are stated together with the natural end conditions. The problem reduces to finding the incidence programme which will give the greatest range.The vehicle is assumed to be an air-to-ground, winged unpowered vehicle flying in an isothermal atmosphere above a flat earth. It is also assumed to be a point mass acted upon by the forces of lift, drag and weight. The acceleration due to gravity is assumed constant.The fundamental constraints of the problem and the Euler-Lagrange equations are programmed for an automatic digital computer. By considering the Lagrange multipliers involved in the problem a method of search is devised based on finding flight paths with maximum range for specified final velocities. It is shown that this method leads to trajectories which are sufficiently close to the “best” trajectory for most practical purposes.It is concluded that such a method is practical and is particularly useful in obtaining the optimum incidence programme during the initial portion of the flight path.

scholarly journals The nonlinear effects on the characteristics of gravity wave packets: dispersion and polarization relations

2000 ◽  
Vol 18 (10) ◽  
pp. 1316-1324 ◽  
Author(s):  
S.-D. Zhang ◽  
F. Yi ◽  
J.-F. Wang
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
Middle Atmosphere ◽  
Wave Packets ◽  
Nonlinear Effects ◽  
Wave Theory ◽  
Nonlinear Propagation ◽  
Waves And Tides ◽  
Time Variations ◽  
Isothermal Atmosphere

Abstract. By analyzing the results of the numerical simulations of nonlinear propagation of three Gaussian gravity-wave packets in isothermal atmosphere individually, the nonlinear effects on the characteristics of gravity waves are studied quantitatively. The analyses show that during the nonlinear propagation of gravity wave packets the mean flows are accelerated and the vertical wavelengths show clear reduction due to nonlinearity. On the other hand, though nonlinear effects exist, the time variations of the frequencies of gravity wave packets are close to those derived from the dispersion relation and the amplitude and phase relations of wave-associated disturbance components are consistent with the predictions of the polarization relation of gravity waves. This indicates that the dispersion and polarization relations based on the linear gravity wave theory can be applied extensively in the nonlinear region.Key words: Meteorology and atmospheric dynamics (middle atmosphere dynamics; waves and tides)

Internal waves in a viscous atmosphere

1975 ◽  
Vol 72 (4) ◽  
pp. 773-786 ◽  
Author(s):  
W. L. Chang ◽  
T. N. Stevenson
Keyword(s):  
Energy Source ◽  
Incompressible Fluid ◽  
Internal Waves ◽  
Infinite Number ◽  
Similarity Solution ◽  
Small Amplitude ◽  
Horizontal Plane ◽  
Two Dimensional ◽  
The Waves ◽  
Isothermal Atmosphere

The way in which internal waves change in amplitude as they propagate through an incompressible fluid or an isothermal atmosphere is considered. A similarity solution for the small amplitude isolated viscous internal wave which is generated by a localized two-dimensional disturbance or energy source was given by Thomas & Stevenson (1972). It will be shown how summations or superpositions of this solution may be used to examine the behaviour of groups of internal waves. In particular the paper considers the waves produced by an infinite number of sources distributed in a horizontal plane such that they produce a sinusoidal velocity distribution. The results of this analysis lead to a new small perturbation solution of the linearized equations.

scholarly journals Propagation of Rossby waves in stratified shear flows

1989 ◽  
Vol 12 (3) ◽  
pp. 547-557
Author(s):  
Palani G. Kandaswamy ◽  
B. Tamil Selvi ◽  
Lokenath Debnath
Keyword(s):  
Wave Equation ◽  
Relative Frequency ◽  
Shear Flows ◽  
Rossby Waves ◽  
Zonal Flow ◽  
Single Wave ◽  
Beta Plane ◽  
Valve Effect ◽  
The Waves ◽  
Isothermal Atmosphere

A study is made of the propagation of Rossby waves in a stably stratified shear flows. The wave equation for the Rossby waves is derived in an isothermal atmosphere on a beta plane in the presence of a latitudinally sheared zonal flow. It is shown that the wave equation is singular at five critical levels, but the wave absorption takes place only at the two levels where the local relative frequency equals in magnitude to the Brunt Vaisala frequency. This analysis also reveals that these two levels exhibit valve effect by allowing the waves to penetrate them from one side only. The absorption coefficient exp(2πμ)is determined at these levels. Both the group velocity approach and single wave treatment are employed for the investigation of the problem.

scholarly journals Nonlinear Atmospheric Adjustment to Momentum Forcing

2008 ◽  
Vol 65 (3) ◽  
pp. 953-969 ◽  
Author(s):  
Adam R. Edson ◽  
Peter R. Bannon
Keyword(s):  
Lamb Wave ◽  
Prediction Models ◽  
Weather Prediction ◽  
Strong Dependence ◽  
Size Characteristic ◽  
Horizontal Momentum ◽  
Compressible Atmosphere ◽  
Isothermal Atmosphere ◽  
Numerical Weather Prediction Models ◽  
Nonlinear Numerical Model

Abstract A nonlinear, numerical model of a dry, compressible atmosphere is used to simulate the hydrostatic and geostrophic adjustment to a localized prescribed injection of momentum applied over 5 min. with a size characteristic of an isolated, deep, cumulus cloud. This theoretical study is relevant to the initialization of updrafts in compressible numerical weather prediction models. The four different forcings studied are vertical, divergent horizontal, and nondivergent horizontal momentum forcings, and a prescribed transverse circulation. These forcings are applied to an isothermal atmosphere, a nonisothermal atmosphere, and an atmosphere with a nonisothermal troposphere capped by an isothermal stratosphere. These scenarios are studied by analyzing the resulting perturbation fields and the energetics of the system. Potential vorticity is used to determine the possibility of steady atmospheric states. The energetics of the system are examined to observe the creation and propagation of atmospheric waves. Both traditional and available energetics are used to determine the presence and strength of these waves. Traditional energetics consist of kinetic, internal, and potential energies while available energetics consist of kinetic, available potential, and available elastic energies. The efficiencies are similar for these different energetics, though they represent different phenomena. The traditional energetics show a strong dependence on the presence of a Lamb wave, whereas in the available energetics the Lamb wave has little or no effect.

scholarly journals Coronal Alfvén speeds in an isothermal atmosphere

2008 ◽  
Vol 491 (1) ◽  
pp. 297-309 ◽  
Author(s):  
S. Régnier ◽  
E. R. Priest ◽  
A. W. Hood
Keyword(s):  
Isothermal Atmosphere

scholarly journals Acoustic-gravity waves in a viscous and thermally conducting isothermal atmosphere

1995 ◽  
Vol 18 (2) ◽  
pp. 371-382 ◽  
Author(s):  
H. Y. Alkahby
Keyword(s):  
Gravity Waves ◽  
Attenuation Factor ◽  
Volume Effect ◽  
Temperature Perturbation ◽  
Oscillatory Process ◽  
Acoustic Gravity Waves ◽  
Perturbation Problem ◽  
The One ◽  
Thermally Conducting ◽  
Isothermal Atmosphere

In this paper we will investigate the effect of Newtonian cooling on the propagation of acoustic-gravity waves in a viscous and thermally conducting isothermal atmosphere for large Prandtl number and for an arbitrary values of Newtonian cooling coefficient. This problem leads to a singular perturbation problem which is solved by matching inner and outer approximations. It is shown that the viscosity creates an absorbing and reflecting layer. Below it the oscillatory process is adiabatic, for small Newtonian cooling coefficient, and above it the solution will decay to constant before it is influenced by the effect of the thermal conductivity. Newtonian cooling is a volume effect and influences mainly the lower adiabatic region, in which it causes attenuation in the amplitude of the wave. Finally it is shown that when Newtonian cooling coefficient goes to infinity it acts directly to eliminate the temperature perturbation associated with the wave and the attenuation factor in the amplitude of the wave. Accordingly the wavelength changes to the one consistent with the Newtonian sound speed. The reflection coefficient and the attenuation factor of the amplitude of the wave are derived for all values of Newtonian cooling coefficient.

scholarly journals Gravity wave generation by large scale bubbles

1988 ◽  
Vol 123 ◽  
pp. 383-386
Author(s):  
Axel Brandenburg
Keyword(s):  
Gravity Wave ◽  
Fourier Transformation ◽  
Large Scale ◽  
Lamb Waves ◽  
Vertical Direction ◽  
Hydrodynamic Equations ◽  
Propagating Waves ◽  
Pressure Scale ◽  
Isothermal Atmosphere ◽  
Small Disturbances

The response of an isothermal atmosphere to small disturbances in entropy is studied taking compressible effects fully into account. The method of Green's functions is applied to solve the linearized hydrodynamic equations by Fourier transformation. A bubble may be created by perturbing the entropy within a finite volume. At first Lamb waves will be then emitted radially and the bubble undergoes a series of Brunt-Väisälä oscillations. We find that horizontally propagating waves are generated only by large bubbles “exceeding a radius of about ten pressure scale heights, whereas smaller bubbles lead to motions propagating principally in the vertical direction.

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