THE EFFECT OF AN EXPLOSION IN A COMPRESSIBLE FLUID UNDER GRAVITY

1961 ◽  
Vol 39 (9) ◽  
pp. 1330-1346 ◽  
Author(s):  
R. A. Ross
Keyword(s):  
Exact Solution ◽  
Viscous Fluid ◽  
Gravity Waves ◽  
Speed Of Sound ◽  
Compressible Fluid ◽  
Asymptotic Methods ◽  
Axially Symmetric ◽  
Linearized Theory ◽  
The Waves ◽  
Special Case

In this paper an investigation is made of the effect of an axially symmetric explosion at any depth in a semi-infinite, compressible, non-viscous fluid, acted upon by gravity. The explosion is represented by a line source of the form δ(x)δ(z – h)δ(t), where h is the depth of the source. An exact solution is given using the linearized theory. This solution is studied in detail by asymptotic methods, for the special case of a surface explosion. It is found that compressibility results in the gravity waves being propagated with a speed less than c, the speed of sound in the fluid. If x is the distance from the explosion and t the time that has elapsed after the explosion, then for [Formula: see text] only "precursor" waves are noticed at the point of observation. For [Formula: see text] large amplitude waves are present, similar to the waves predicted by the incompressible theory.

Contact in a viscous fluid. Part 2. A compressible fluid and an elastic solid

2010 ◽  
Vol 646 ◽  
pp. 339-361 ◽  
Author(s):  
N. J. BALMFORTH ◽  
C. J. CAWTHORN ◽  
R. V. CRASTER
Keyword(s):  
Viscous Fluid ◽  
Half Space ◽  
Compressible Fluid ◽  
Finite Time ◽  
Asymptotic Methods ◽  
Elastic Solid ◽  
Two Dimensional ◽  
Infinite Time ◽  
Elastic Wall ◽  
Final Approach

A lubrication theory is presented for the effect of fluid compressibility and solid elasticity on the descent of a two-dimensional smooth object falling under gravity towards a plane wall through a viscous fluid. The final approach to contact, which takes infinite time in the absence of both effects, is determined by numerical and asymptotic methods. Compressibility can lead to contact in finite time either during inertially generated oscillations or if the viscosity decreases sufficiently quickly with increasing pressure. The approach to contact is invariably slowed by allowing the solids to deform elastically; specific results are presented for an underlying elastic wall modelled as a foundation, half-space, membrane or beam.

scholarly journals Influence of the cloud-level neutral layer on the vertical propagation of topographically generated gravity waves on Venus

2019 ◽  
Vol 71 (1) ◽  
Author(s):  
Takeru Yamada ◽  
Takeshi Imamura ◽  
Tetsuya Fukuhara ◽  
Makoto Taguchi
Keyword(s):  
Layer Thickness ◽  
Gravity Wave ◽  
Local Time ◽  
Gravity Waves ◽  
Analytical Approach ◽  
Wave Activity ◽  
Neutral Layer ◽  
Low Latitudes ◽  
Vertical Propagation ◽  
The Waves

AbstractThe reason for stationary gravity waves at Venus’ cloud top to appear mostly at low latitudes in the afternoon is not understood. Since a neutral layer exists in the lower part of the cloud layer, the waves should be affected by the neutral layer before reaching the cloud top. To what extent gravity waves can propagate vertically through the neutral layer has been unclear. To examine the possibility that the variation of the neutral layer thickness is responsible for the dependence of the gravity wave activity on the latitude and the local time, we investigated the sensitivity of the vertical propagation of gravity waves on the neutral layer thickness using a numerical model. The results showed that stationary gravity waves with zonal wavelengths longer than 1000 km can propagate to the cloud-top level without notable attenuation in the neutral layer with realistic thicknesses of 5–15 km. This suggests that the observed latitudinal and local time variation of the gravity wave activity should be attributed to processes below the cloud. An analytical approach also showed that gravity waves with horizontal wavelengths shorter than tens of kilometers would be strongly attenuated in the neutral layer; such waves should originate in the altitude region above the neutral layer.

scholarly journals On the Bean critical-state model in superconductivity

1996 ◽  
Vol 7 (3) ◽  
pp. 237-247 ◽  
Author(s):  
L. Prigozhin
Keyword(s):  
Variational Inequalities ◽  
Critical State ◽  
Existence And Uniqueness ◽  
Critical State Model ◽  
Type Ii ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Uniqueness Of The Solution ◽  
Type Ii Superconductivity ◽  
Special Case

We consider two-dimensional and axially symmetric critical-state problems in type-II superconductivity, and show that these problems are equivalent to evolutionary quasi-variational inequalities. In a special case, where the inequalities become variational, the existence and uniqueness of the solution are proved.

scholarly journals Observation of mesospheric gravity waves at Comandante Ferraz Antarctica Station (62° S)

2009 ◽  
Vol 27 (6) ◽  
pp. 2593-2598 ◽  
Author(s):  
J. V. Bageston ◽  
C. M. Wrasse ◽  
D. Gobbi ◽  
H. Takahashi ◽  
P. B. Souza
Keyword(s):  
Gravity Waves ◽  
Weather Conditions ◽  
Propagation Direction ◽  
Cyclonic Activity ◽  
Wave Source ◽  
Cold Fronts ◽  
Wave Velocities ◽  
Orographic Forcing ◽  
Sky Imager ◽  
The Waves

Abstract. An airglow all-sky imager was operated at Comandante Ferraz Antarctica Station (62.1° S, 58.4° W), between April and October of 2007. Mesospheric gravity waves were observed using the OH airglow layer during 43 nights with good weather conditions. The waves presented horizontal wavelengths between 10 and 60 km and observed periods mainly distributed between 5 and 20 min. The observed phase speeds range between 5 m/s and 115 m/s; the majority of the wave velocities were between 10 and 60 m/s. The waves showed a preferential propagation direction towards the southwest in winter (May to July), while during spring (August to October) there was an anisotropy with a preferential propagation direction towards the northwest. Unusual mesospheric fronts were also observed. The most probable wave source could be associated to orographic forcing, cold fronts or strong cyclonic activity in the Antarctica Peninsula.

Transonic flow past finite wedges

1952 ◽  
Vol 48 (1) ◽  
pp. 178-187 ◽  
Author(s):  
A. G. Mackie ◽  
D. C. Pack
Keyword(s):  
Incompressible Fluid ◽  
Critical Velocity ◽  
Speed Of Sound ◽  
Compressible Fluid ◽  
Transonic Flow ◽  
Ideal Gas ◽  
Hodograph Method ◽  
Subsonic Velocity ◽  
Flow Past ◽  
Axis Of Symmetry

AbstractThe solution for the flow of an incompressible fluid past an infinitely long wedge with a finite sloping edge (a finite wedge) is generalized by the hodograph method. In the flow thus obtained the axis of symmetry and a sloping edge of the wedge are again part of one streamline. It becomes possible to describe the flow of an ideal gas past a finite wedge if the hypothesis is made that the first singularity on this streamline, along the sloping edge, corresponds to the shoulder of the wedge. For a given wedge, with gradually increasing velocity at infinity upstream, the singularity appears at first at subsonic velocity. Beyond a certain critical velocity at infinity the singularity is always associated with the speed of sound. The hypothesis thus implies that put forward by Maccoll(9) and supported by Busemann(l). A qualitative examination shows that the solution reproduces experimentally known features of the flow of compressible fluid past a finite wedge.

scholarly journals COMPARISON OF WAVE ACTIVITY IN THE MESOPAUSE REGION AT MAIMAGA STATION WITH EOS MLS (AURA) TEMPERATURE DATA AND ACTIVITY OF PLANETARY WAVES AT TIKSI STATION

2019 ◽  
pp. 182-189
Author(s):  
В.И. Сивцева ◽  
П.П. Аммосов ◽  
Г.А. Гаврильева ◽  
И.И. Колтовской ◽  
А.М. Аммосова
Keyword(s):  
Gravity Waves ◽  
Internal Gravity Waves ◽  
Temperature Data ◽  
Planetary Waves ◽  
Winter Period ◽  
Temperature Profiles ◽  
Night Temperature ◽  
Mesopause Region ◽  
The Difference ◽  
The Waves

Исследованы данные температуры области мезопаузы, полученные за период 2013-2018 гг. на станции Маймага (63.04N, 129.51E) и за период 2015-2018 гг. на станции Тикси (71.58 N, 128.77 E). В зимний период сезона наблюдений 2014-2015 характеристика активности внутренних гравитационных волн (ВГВ) gwимеет более низкие значения, чем в другие сезоны, а средненочная температура, наоборот, превышает аналогичные значения в другие сезоны. Для сопоставления рассматривались спутниковые данные температурных профилей полученные EOS MLS (Aura). После выделения и вычитания вклада гравитационной составляющей из температурных профилей EOS MLS для области над станцией Маймага заметно отличие в зимней стратопаузе сезона 2014-2015. В этот сезон в зимний период, с учетом вычета вклада флуктуаций температуры обусловленных ВГВ, наблюдается отсутствие резких потеплений в районе стратопаузы в отличие от остальных сезонов. Измерение параметров планетарных волн в течение периода 2015-2018 гг. совместных наблюдений на станциях Маймага и Тикси показали, что фазы наблюдаемых на обеих станциях волн совпадают, а амплитуды на станции Тикси несколько (12 К) превышают амплитуды на станции Маймага. The temperature data of the mesopause region obtained for the period 2013-2018 at the station Maimaga (63.04 N, 129.51 E) and for the period 2015-2018 at the station Tiksi (71.58 N, 128.77 E) was investigated. During the winter period of the 20142015 observation season, the characteristic of the internal gravity waves (IGW) activity sgw has lower values than in other seasons, and the average night temperature of the mesopause region, on the contrary, exceeds corresponding values in other seasons. For comparison, satellite data of temperature profiles obtained by EOS MLS (Aura) are given. After isolating and subtracting the contribution of the gravitaty waves from the EOS MLS temperature profiles for the region above the st. Maimaga, the difference in the winter stratopause of the 2014-2015 season is noticeable. In this season in winter there is a lack of sharp warming in the stratopause region, in contrast to other seasons, taking into account the deduction of the contribution of temperature fluctuations due to IGW. Measurement of the parameters of planetary waves during the period 2015-2018 of joint observations at Maimaga and Tiksi stations showed that the phases of the waves observed at both stations coincide, and the amplitudes at Tiksi station are several (1-2 K) higher than the amplitudes at Maimaga station.

On the asymptotic solution of the Orr–Sommerfeld equation by the method of multiple-scales

1968 ◽  
Vol 34 (1) ◽  
pp. 145-158 ◽  
Author(s):  
K. Kuen Tam
Keyword(s):  
Exact Solution ◽  
Velocity Profile ◽  
Asymptotic Solution ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Order Equation ◽  
Zeroth Order ◽  
Independent Variables ◽  
Sommerfeld Equation ◽  
Special Case

The method of multiple-scales is used to obtain the asymptotic solution of the Orr–Sommerfeld equation. For the special case of a linear velocity profile, the solution so obtained agrees well with an approximation of the exact solution which is known. For the general case, transformations on both the dependent and independent variables are introduced to obtain a zeroth-order equation which differs from the inner equation studied so far. On the ground of the favourable comparison for the special case, the asymptotic solution constructed is expected to be uniformly valid.

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