scholarly journals Mixing by Internal Waves

1993 ◽  
Vol 137 ◽  
pp. 281-283
Author(s):  
Josefina Montalbán ◽  
Evry Schatzman
Keyword(s):  
Internal Waves ◽  
Spectral Type ◽  
Rotation Velocity ◽  
Lithium Abundance ◽  
Diffusive Process ◽  
Dissipative Effects ◽  
Non Linear ◽  
Radiative Zone

That mixing take place in the radiative zone of many stars, is an event that cannot be forgotten when we try to explain observational results as the lithium abundance in the atmosphere of different stars, its dependence on spectral type, age or rotation velocity... During the last years many processes have been proposed as being responsible of this mixing: overshooting, turbulence induced by rotational instabilities, internal waves, etc... We will consider, following the results obtained by Press (1981), the role of this last mechanism in the transport of lithium to the burning level, not as generators of turbulence (in Press, 1981, and García-López and Spruit, 1991, it is shown that turbulence induced by internal waves decays very quickly inside the radiative zone), but as generators of a diffusive process due to non linear dissipative effects.

scholarly journals Analytical and numerical investigation of nonlinear internal gravity waves

2001 ◽  
Vol 8 (1/2) ◽  
pp. 37-53 ◽  
Author(s):  
S. P. Kshevetskii
Keyword(s):  
Internal Wave ◽  
Analytical Model ◽  
Internal Waves ◽  
Numerical Models ◽  
Wave Mode ◽  
Vertical Acceleration ◽  
Quasistatic Problem ◽  
Wave Simulation ◽  
Non Linear

Abstract. The propagation of long, weakly nonlinear internal waves in a stratified gas is studied. Hydrodynamic equations for an ideal fluid with the perfect gas law describe the atmospheric gas behaviour. If we neglect the term Ͽ dw/dt (product of the density and vertical acceleration), we come to a so-called quasistatic model, while we name the full hydro-dynamic model as a nonquasistatic one. Both quasistatic and nonquasistatic models are used for wave simulation and the models are compared among themselves. It is shown that a smooth classical solution of a nonlinear quasistatic problem does not exist for all t because a gradient catastrophe of non-linear internal waves occurs. To overcome this difficulty, we search for the solution of the quasistatic problem in terms of a generalised function theory as a limit of special regularised equations containing some additional dissipation term when the dissipation factor vanishes. It is shown that such solutions of the quasistatic problem qualitatively differ from solutions of a nonquasistatic nature. It is explained by the fact that in a nonquasistatic model the vertical acceleration term plays the role of a regularizator with respect to a quasistatic model, while the solution qualitatively depends on the regularizator used. The numerical models are compared with some analytical results. Within the framework of the analytical model, any internal wave is described as a system of wave modes; each wave mode interacts with others due to equation non-linearity. In the principal order of a perturbation theory, each wave mode is described by some equation of a KdV type. The analytical model reveals that, in a nonquasistatic model, an internal wave should disintegrate into solitons. The time of wave disintegration into solitons, the scales and amount of solitons generated are important characteristics of the non-linear process; they are found with the help of analytical and numerical investigations. Satisfactory coincidence of simulation outcomes with analytical ones is revealed and some examples of numerical simulations illustrating wave disintegration into solitons are given. The phenomenon of internal wave mixing is considered and is explained from the point of view of the results obtained. The numerical methods for internal wave simulation are examined. In particular, the influence of difference interval finiteness on a numerical solution is investigated. It is revealed that a numerical viscosity and numerical dispersion can play the role of regularizators to a nonlinear quasistatic problem. To avoid this effect, the grid steps should be taken less than some threshold values found theoretically.

scholarly journals Sensitivity of wavepackets in jets to non-linear effects: the role of the critical layer

2015 ◽  
Author(s):  
Gilles Tissot ◽  
Mengqi Zhang ◽  
Francisco C. Lajús ◽  
André V. Cavalieri ◽  
Peter Jordan ◽  
...  
Keyword(s):  
Critical Layer ◽  
Non Linear ◽  
Linear Effects

scholarly journals A Unified Mathematical Formalism for First to Third Order Dielectric Response of Matter: Application to Surface-Specific Two-Colour Vibrational Optical Spectroscopy

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 153 ◽  
Author(s):  
Christophe Humbert ◽  
Thomas Noblet
Keyword(s):  
Dielectric Response ◽  
Structure And Properties ◽  
Linear Optics ◽  
Third Order ◽  
Mathematical Functions ◽  
Sum Frequency ◽  
Non Linear Optics ◽  
Non Linear ◽  
Light Excitation

To take advantage of the singular properties of matter, as well as to characterize it, we need to interact with it. The role of optical spectroscopies is to enable us to demonstrate the existence of physical objects by observing their response to light excitation. The ability of spectroscopy to reveal the structure and properties of matter then relies on mathematical functions called optical (or dielectric) response functions. Technically, these are tensor Green’s functions, and not scalar functions. The complexity of this tensor formalism sometimes leads to confusion within some articles and books. Here, we do clarify this formalism by introducing the physical foundations of linear and non-linear spectroscopies as simple and rigorous as possible. We dwell on both the mathematical and experimental aspects, examining extinction, infrared, Raman and sum-frequency generation spectroscopies. In this review, we thus give a personal presentation with the aim of offering the reader a coherent vision of linear and non-linear optics, and to remove the ambiguities that we have encountered in reference books and articles.

In search of lost space: The process of space planning through remembering and history

Organization ◽  
2015 ◽  
Vol 23 (1) ◽  
pp. 71-89 ◽  
Author(s):  
Fabio James Petani ◽  
Jeanne Mengis
Keyword(s):  
Production Of Space ◽  
Space Planning ◽  
The Past ◽  
Time Space ◽  
Non Linear ◽  
Over Time ◽  
Contested Narratives

This article explores the role of remembering and history in the process of planning new spaces. We trace how the organizational remembering of past spaces enters the conception (i.e. planning) of a large culture center. By drawing on Henri Lefebvre’s reflections on history, time and memory, we analyze the processual interconnections of his spatial triad, namely between the planned, practiced, and lived moments of the production of space. We find that over time space planning involves recurrent, changing, and contested narratives on ‘lost spaces’, remembering happy spaces of the past that articulate a desire to regain them. The notion of lost space adds to our understanding of how space planning involves, through organizational remembering, a sociomaterial and spatiotemporal work of relating together different spaces and times in non-linear narratives of repetition.

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