scholarly journals The stability of internal gravity waves in a bounded atmospheric shear layer in the presence of moisture

MAUSAM ◽  
2021 ◽  
Vol 42 (3) ◽  
pp. 249-256
Author(s):  
C.P. JACOVIDES
Keyword(s):  
Gravity Waves ◽  
Equations Of Motion ◽  
Internal Gravity Waves ◽  
Constant Thickness ◽  
Solid Boundary ◽  
Saturated Layer ◽  
Real Atmosphere ◽  
The Stability ◽  
The Waves ◽  
Moist Layer

The stability characteristics of internal gravity waves, generated by an isothermal bounded tangent velocity profile in the presence of a saturated finite layer, are studied. The moist layer with constant thickness the structure of the ness is introduced at different levels in respect to the point of inflection and the variations of moisture content and distance from the origin are examined. The characteristics of the unstable waves are obtained by solving numerically the linearized versions or the full equations of motion, in the inviscid and Boussinesq limit, through the technique of Lalas and Elnaudi (1976).  It is shown that the presence of the moist layer can significantly affect the stability characteristics of the waves. Increases in the moisture and distance of the layer from the Inflection point are found to amplify or decay the wave response, because the saturated layer behaves as a solid boundary to the flow. The presence of such effective layer is shown to stabilize short wavelengths and destabilize. Finally, an application of the model's results to the real atmosphere is discussed.

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.

scholarly journals Internal wave breaking and the fate of planets around solar-type stars

2010 ◽  
Vol 6 (S271) ◽  
pp. 363-364
Author(s):  
Adrian J. Barker ◽  
Gordon I. Ogilvie
Keyword(s):  
Gravity Waves ◽  
Wave Breaking ◽  
Internal Gravity Waves ◽  
Amplitude Dependence ◽  
Tidal Dissipation ◽  
Short Period ◽  
Central Regions ◽  
Solar Type ◽  
The Waves ◽  
Solar Type Star

AbstractInternal gravity waves are excited at the interface of convection and radiation zones of a solar-type star, by the tidal forcing of a short-period planet. The fate of these waves as they approach the centre of the star depends on their amplitude. We discuss the results of numerical simulations of these waves approaching the centre of a star, and the resulting evolution of the spin of the central regions of the star and the orbit of the planet. If the waves break, we find efficient tidal dissipation, which is not present if the waves perfectly reflect from the centre. This highlights an important amplitude dependence of the (stellar) tidal quality factor Q′, which has implications for the survival of planets on short-period orbits around solar-type stars, with radiative cores.

The effect of viscosity and heat conduction on internal gravity waves at a critical level

1967 ◽  
Vol 30 (4) ◽  
pp. 775-783 ◽  
Author(s):  
Philip Hazel
Keyword(s):  
Differential Equation ◽  
Heat Conduction ◽  
Gravity Waves ◽  
Order Differential Equation ◽  
Fluid Velocity ◽  
Attenuation Factor ◽  
Internal Gravity Waves ◽  
Constant Factor ◽  
The Mean ◽  
The Waves

The differential equation for the vertical velocity of a gravity wave in an inviscid shear flow is singular at a level where the mean fluid velocity is equal to the horizontal phase velocity of the waves. It has been shown that a wave travelling through such a layer has its amplitude attenuated by a constant factor dependent on the local Richardson number. In this paper the results obtained by solving numerically the full sixth order differential equation, which is derived by including viscosity and heat conduction in the problem, (and is not singular) are discussed, and the same attenuation factor is found. Some experiments which confirm certain aspects of the theory are described in an appendix.

scholarly journals On the appearance of internal wave attractors due to an initial or parametrically excited disturbance

2013 ◽  
Vol 714 ◽  
pp. 283-311 ◽  
Author(s):  
Janis Bajars ◽  
Jason Frank ◽  
Leo R. M. Maas
Keyword(s):  
Gravity Waves ◽  
Normal Modes ◽  
Internal Gravity Waves ◽  
Harmonic Oscillators ◽  
Two Dimensional ◽  
Boussinesq Model ◽  
Resonant Modes ◽  
The Waves ◽  
Shaped Domain ◽  
Parametric Forcing

AbstractIn this paper we solve two initial value problems for two-dimensional internal gravity waves. The waves are contained in a uniformly stratified, square-shaped domain whose sidewalls are tilted with respect to the direction of gravity. We consider several disturbances of the initial stream function field and solve both for its free evolution and for its evolution under parametric excitation. We do this by developing a structure-preserving numerical method for internal gravity waves in a two-dimensional stratified fluid domain. We recall the linearized, inviscid Euler–Boussinesq model, identify its Hamiltonian structure, and derive a staggered finite difference scheme that preserves this structure. For the discretized model, the initial condition can be projected onto normal modes whose dynamics is described by independent harmonic oscillators. This fact is used to explain the persistence of various classes of wave attractors in a freely evolving (i.e. unforced) flow. Under parametric forcing, the discrete dynamics can likewise be decoupled into Mathieu equations. The most unstable resonant modes dominate the solution, forming wave attractors.

On the interaction between internal gravity waves and a shear flow

1968 ◽  
Vol 34 (4) ◽  
pp. 711-720 ◽  
Author(s):  
C. J. R. Garrett
Keyword(s):  
Wave Propagation ◽  
Stress Tensor ◽  
Gravity Waves ◽  
Internal Gravity Wave ◽  
Internal Gravity Waves ◽  
Basic Flow ◽  
Radiation Stress ◽  
Interaction Stress ◽  
The Waves ◽  
Uniform Plane

The theory of wave action conservation is summarized, and its interpretation in terms of the working, against the rate of strain of the basic flow, of an interaction stress associated with the waves is discussed. Usually this interaction stress is identical with the radiation stress of a uniform plane wave. The problem of internal gravity wave propagation in an incompressible, stratified Boussinesq liquid is considered in detail for a more general basic flow than has hitherto been treated, and the interaction stress is derived. One component of the interaction stress tensor is only equal to the corresponding component of the radiation stress tensor if we include in the latter, in addition to the Reynolds stress, a term associated with the redistribution of matter, on the average, by the wave. Two other components of the radiation stress tensor are modified in a similar manner, but the corresponding components of the interaction stress tensor are undefined, and so no comparison is possible.

Nonlinear internal gravity waves in a rotating fluid

1975 ◽  
Vol 71 (3) ◽  
pp. 497-512 ◽  
Author(s):  
R. Grimshaw
Keyword(s):  
Gravity Waves ◽  
Wave Structure ◽  
Internal Gravity Waves ◽  
Mean Flow ◽  
Mean Velocity ◽  
Main Effect ◽  
Local Wave ◽  
The Mean ◽  
The Waves ◽  
Circulation Theorem

The interaction between internal gravity waves in a rotating frame and the mean flow is discussed for the case when the properties of the mean flow vary slowly on a scale determined by the local wave structure. The principle of conservation of wave action is established. It is shown that the main effect of the waves on the Lagrangian mean velocity is due to an appropriate ‘radiation stress’ tensor. A circulation theorem and a potential-vorticity equation are derived for the mean velocity.

Internal Gravity Waves in a Continuously Stratified Turbulent Flow Through Porous Media

1984 ◽  
Vol 8 (4) ◽  
pp. 201-207
Author(s):  
N. Rudraiah
Keyword(s):  
Gravity Waves ◽  
Eddy Viscosity ◽  
Internal Gravity Waves ◽  
Flow Through Porous Media ◽  
Amplitude Analysis ◽  
Period Increase ◽  
Gradient Diffusion ◽  
Mixing Coefficients ◽  
Flow Through ◽  
The Waves

The attenuation of internal gravity waves propagating in a weakly stratified turbulent fluid flowing through a coarse porous medium is studied using a gradient-diffusion model. Small amplitude analysis is considered based on the assumption that the action of turbulence is parametrically represented by eddy mixing coefficients. By considering anisotropy of eddy coefficients, it is shown that the damping length and period increase are in general dependent on the porous parameter γ2, the Prandtl number Pr, thickness of the porous layer H, and eddy viscosity parameter Km 1 Subject quantitatively to the choice made for the eddy coefficients, it is shown that the effect of γ2 is to increase the frequency and to decrease the damping length of the waves as a result of energy dissipation due to friction in the bed. The damping is more rapid when H and Km 1 are large. The dependence of the relative damping length on H is in opposite directions for long and short waves. In particular, it is shown that the period increase and relative damping length present a minimum and maximum respectively at the intermediate wave lengths; the positions of these extrema depend on H, Km and Prγ2.

Nonlinear internal gravity waves in a slowly varying medium

1972 ◽  
Vol 54 (2) ◽  
pp. 193-207 ◽  
Author(s):  
R. Grimshaw
Keyword(s):  
Incompressible Fluid ◽  
Gravity Waves ◽  
Time Scale ◽  
Wave Structure ◽  
Internal Gravity Waves ◽  
Transport Equations ◽  
Inviscid Incompressible Fluid ◽  
Local Wave ◽  
The Waves

Nonlinear internal gravity waves in an inviscid incompressible fluid are discussed for the case when the properties of the medium vary slowly on a scale determined by the local wave structure. A two-time-scale technique is used to obtain transport equations which describe the slowly varying modulations of the waves. Various solutions of these transport equations are discussed.

Nonlinear ripples of Kelvin–Helmholtz type which arise from an interfacial mode interaction

1997 ◽  
Vol 341 ◽  
pp. 295-315 ◽  
Author(s):  
M. C. W. JONES
Keyword(s):  
Gravity Waves ◽  
Multiple Scales ◽  
Nonlinear Partial Differential Equations ◽  
Mode Interaction ◽  
Third Order ◽  
Two Fluids ◽  
Power Series Expansions ◽  
The Stability ◽  
Formal Power ◽  
The Waves

An analysis is made of the small-amplitude capillary–gravity waves which occur on the interface of two fluids and which arise out of the interaction between the Mth and Nth harmonics of the fundamental mode. The method employed is that of multiple scales in both space and time and a pair of coupled nonlinear partial differential equations for the slowly varying wave amplitudes is derived. These equations describe, correct up to third order, the progression of a wavetrain and are generalizations of the nonlinear Schrödinger-type equations used by many authors to model wave propagation. The equations are solved and formal power series expansions of the corresponding wave profiles obtained. Many different wave configurations can arise, some symmetric others asymmetric. It is found that an important influence on the type of waves which can occur is whether the ratio of the interacting wave modes is greater or less than two. Finally, an examination of the stability of the waves to plane wave perturbations is carried out.

On internal gravity waves in an accelerating shear flow

1978 ◽  
Vol 88 (4) ◽  
pp. 623-639 ◽  
Author(s):  
S. A. Thorpe
Keyword(s):  
Gravity Waves ◽  
Phase Distribution ◽  
Phase Speed ◽  
Internal Gravity Waves ◽  
Initial Energy ◽  
Constant Density ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean ◽  
The Waves

The investigation of the effects which a changing mean flow has on a uniform train of internal gravity waves (Thorpe 1978a) is continued by considering waves in a uniformly accelerating stratified plane Couette flow with constant density gradient. Experiments reveal a change in the mode structure and phase distribution of the waves, and their eventual breaking near the boundary where the mean flow is greatest, the phase speed of the waves being positive. A linear numerical model is devised which accurately describes the waves up to the onset of their breaking, and this is used to investigate their energetics. The working of the Reynolds stress against the mean velocity gradient results in a very rapid transfer of energy from the waves to the mean flow, so that by the time breaking occurs only a small fraction of their initial energy remains for possible transfer into potential energy of the fluid.The consequences have important applications in oceanography and meteorology, to flow stability and flow generation, and explain some earlier laboratory observations.

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