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| Titel |
Analytical and numerical investigation of nonlinear internal gravity waves |
| VerfasserIn |
S. P. Kshevetskii |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 8, no. 1/2 ; Nr. 8, no. 1/2, S.37-53 |
| Datensatznummer |
250005287
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| Publikation (Nr.) |
 copernicus.org/npg-8-37-2001.pdf |
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| Zusammenfassung |
| 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. |
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