The generation of internal waves by vibrating elliptic cylinders. Part 1. Inviscid solution

1997 ◽  
Vol 351 ◽  
pp. 105-118 ◽  
Author(s):  
D. G. HURLEY
Keyword(s):  
Gravity Waves ◽  
Elliptic Cylinder ◽  
Major Axis ◽  
Internal Gravity Waves ◽  
Angular Frequency ◽  
Important Paper ◽  
Fourier Decomposition ◽  
Boussinesq Fluid ◽  
Made In ◽  
Phase Differences

We consider the internal gravity waves that are produced in an inviscid Boussinesq fluid, whose Brunt–Väisälä frequency N is constant, by the small rectilinear vibrations of a horizontal elliptic cylinder whose major axis is inclined at an arbitrary angle to the horizontal. When the angular frequency ω is greater than N, no waves are produced and the governing elliptic equation is solved using conformal transformations. Analytic continuation in ω to values less than N, when waves are produced, is then used to determine the solution. It exhibits the surprising feature that, apart from certain phase differences, the form of the velocity distributions in each of the beams of waves that occur is the same for all values of the thickness ratio of the ellipse, the inclination of its major axis to the horizontal and the plane in which the vibrations are occurring. The Fourier decomposition of the velocity distribution is found and is used in a sequel, Part 2, to investigate the effects of viscous dissipation.In an important paper Makarov et al. (1990) have given an approximate solution for a vibrating circular cylinder in a viscous fluid. We show that the limit of this solution as the viscosity tends to zero is not the exact inviscid solution discussed herein. Further comparison of their work and ours will be made in Part 2.

On resonant over-reflexion of internal gravity waves from a Helmholtz velocity profile

1979 ◽  
Vol 90 (1) ◽  
pp. 161-178 ◽  
Author(s):  
R. H. J. Grimshaw
Keyword(s):  
Velocity Profile ◽  
Gravity Waves ◽  
Second Harmonic ◽  
Phase Speed ◽  
Internal Gravity Waves ◽  
Finite Amplitude ◽  
Weakly Nonlinear ◽  
Velocity Discontinuity ◽  
Interface Displacement ◽  
Boussinesq Fluid

A Helmholtz velocity profile with velocity discontinuity 2U is embedded in an infinite continuously stratified Boussinesq fluid with constant Brunt—Väisälä frequency N. Linear theory shows that this system can support resonant over-reflexion, i.e. the existence of neutral modes consisting of outgoing internal gravity waves, whenever the horizontal wavenumber is less than N/2½U. This paper examines the weakly nonlinear theory of these modes. An equation governing the evolution of the amplitude of the interface displacement is derived. The time scale for this evolution is α−2, where α is a measure of the magnitude of the interface displacement, which is excited by an incident wave of magnitude O(α3). It is shown that the mode which is symmetrical with respect to the interface (and has a horizontal phase speed equal to the mean of the basic velocity discontinuity) remains neutral, with a finite amplitude wave on the interface. However, the other modes, which are not symmetrical with respect to the interface, become unstable owing to the self-interaction of the primary mode with its second harmonic. The interface displacement develops a singularity in a finite time.

scholarly journals On the Application of Fourier Decomposition Parameters

1993 ◽  
Vol 134 ◽  
pp. 157-158
Author(s):  
J. O. Petersen
Keyword(s):  
Fourier Analysis ◽  
Light Curves ◽  
Amplitude Ratios ◽  
Fourier Decomposition ◽  
Practical Applications ◽  
Convincing Argument ◽  
Lee Form ◽  
Modern Form ◽  
Made In ◽  
Phase Differences

The application of Fourier decomposition parameters has revolutionized important areas of investigations of Cepheid type variables since the introduction of Fourier analysis in its modern form by Simon and Lee (1981).In the literature several different representations of the results of Fourier analysis have been utilized. In view of the growing interest for applications of Fourier decomposition it is important to use and publish Fourier data in an optimal way. Most studies until now have used amplitude ratios and phase differences derived from traditional light curves giving the light variation in magnitudes, following the original recipe of Simon and Lee (1981). However, Stellingwerf and Donohoe (1986) advocated the use of phases rather than phase differences. Recently, Buchler et al. (1990) argued that the standard Simon & Lee form contains all relevant physics, and suggested analysis of flux-values rather than of magnitudes, because this removes the distorting effects of constant, false light. Thus there are many choices to be made in practical applications of Fourier analysis, and there is at present no convincing argument for preferring one specific representation.

scholarly journals Synthetic observations of internal gravity waves in the solar atmosphere

2020 ◽  
Vol 633 ◽  
pp. A140
Author(s):  
G. Vigeesh ◽  
M. Roth
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Flux Density ◽  
Solar Atmosphere ◽  
Energy Flux ◽  
Gravity Waves ◽  
Internal Gravity Waves ◽  
Spectral Lines ◽  
Magnetic Flux Density ◽  
Phase Differences

Aims. We study the properties of internal gravity waves (IGWs) detected in synthetic observations that are obtained from realistic numerical simulation of the solar atmosphere. Methods. We used four different simulations of the solar magneto-convection performed using the CO5BOLD code. A magnetic-field-free model and three magnetic models were simulated. The latter three models start with an initial vertical, homogeneous field of 10, 50, and 100 G magnetic flux density, representing different regions of the quiet solar surface. We used the NICOLE code to compute synthetic spectral maps from all the simulated models for the two magnetically insensitive neutral iron lines Fe I λλ 5434 Å and 5576 Å. We carried out Fourier analyses of the intensity and Doppler velocities to derive the power, phase, and coherence in the kh − ω diagnostic diagram to study the properties of internal gravity waves. Results. We find the signatures of the internal gravity waves in the synthetic spectra to be consistent with observations of the real Sun. The effect of magnetic field on the wave spectra is not as clearly discernible in synthetic observations as in the case of numerical simulations. The phase differences obtained using the spectral lines are significantly different from the phase differences in the simulation. The phase coherency between two atmospheric layers in the gravity wave regime is height dependent and is seen to decrease with the travel distance between the observed layers. In the studied models, the lower atmosphere shows a phase coherency above the significance level for a height separation of ∼400 km, while in the chromospheric layers it reduces to ∼100–200 km depending on the average magnetic flux density. Conclusion. We conclude that the energy flux of IGWs determined from the phase difference analysis may be overestimated by an order of magnitude. Spectral lines that are weak and less temperature sensitive may be better suited to detecting internal waves and accurately determining their energy flux in the solar atmosphere.

scholarly journals Generation of internal gravity waves by an oscillating horizontal disc

2011 ◽  
Vol 467 (2136) ◽  
pp. 3406-3423 ◽  
Author(s):  
P. A. Martin ◽  
Stefan G. Llewellyn Smith
Keyword(s):  
Frequency Domain ◽  
Gravity Waves ◽  
Time Domain ◽  
Energy Transport ◽  
Radiation Condition ◽  
Internal Gravity Waves ◽  
Forced Oscillations ◽  
Transient Effects ◽  
Fourier Decomposition ◽  
The Time Domain

Internal gravity waves are generated in a stratified fluid by arbitrary forced oscillations of a horizontal disc. The wave fields are calculated in both the time domain and the frequency domain. In the time domain, an initial-value problem is solved using Laplace transforms; causality is imposed. In the frequency domain (time-harmonic oscillations), a radiation condition is imposed: a plane-wave (Fourier) decomposition is used in which waves with outgoing group velocity are selected. It is shown that both approaches lead to the same solution, once transient effects are ignored. Then, a method is given for calculating the far-field, using asymptotic approximations of double integrals. It is shown that the total energy flux is outwards, for arbitrary forcings of the disc. Further investigations of energy transport are made with a view to clarifying the nature of radiation conditions in the frequency domain.

Model of the internal gravity waves excited by lithospheric greenhouse effect gases

2001 ◽  
Vol 7 (2s) ◽  
pp. 26-33 ◽  
Author(s):  
O.E. Gotynyan ◽  
◽  
V.N. Ivchenko ◽  
Yu.G. Rapoport ◽  
◽  
...  
Keyword(s):  
Gravity Waves ◽  
Greenhouse Effect ◽  
Internal Gravity Waves

scholarly journals Shear-induced breaking of internal gravity waves

2021 ◽  
Vol 921 ◽  
Author(s):  
Christopher J. Howland ◽  
John R. Taylor ◽  
C.P. Caulfield
Keyword(s):  
Gravity Waves ◽  
Internal Gravity Waves

Abstract

scholarly journals Rolls of the internal gravity waves in the Earth's atmosphere

2014 ◽  
Vol 32 (2) ◽  
pp. 181-186 ◽  
Author(s):  
O. Onishchenko ◽  
O. Pokhotelov ◽  
W. Horton ◽  
A. Smolyakov ◽  
T. Kaladze ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Gravity Waves ◽  
Closed System ◽  
Wind Shear ◽  
Internal Gravity Waves ◽  
Temperature Gradients ◽  
System Of Equations ◽  
Vertical Temperature ◽  
Earth’S Atmosphere ◽  
Earth's Atmosphere

Abstract. The effect of the wind shear on the roll structures of nonlinear internal gravity waves (IGWs) in the Earth's atmosphere with the finite vertical temperature gradients is investigated. A closed system of equations is derived for the nonlinear dynamics of the IGWs in the presence of temperature gradients and sheared wind. The solution in the form of rolls has been obtained. The new condition for the existence of such structures was found by taking into account the roll spatial scale, the horizontal speed and wind shear parameters. We have shown that the roll structures can exist in a dynamically unstable atmosphere.

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