dor_id: 11270

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650.#.4.x: Físico Matemáticas y Ciencias de la Tierra

336.#.#.b: article

336.#.#.3: Artículo de Investigación

336.#.#.a: Artículo

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351.#.#.a: Artículos

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100.1.#.a: Skiba, Yuri N.

524.#.#.a: Skiba, Yuri N. (1993). Dynamics of perturbations of the Rossby-Haurwitz wave and the Verkley modon. Atmósfera; Vol. 6 No. 2, 1993. Recuperado de https://repositorio.unam.mx/contenidos/11270

245.1.0.a: Dynamics of perturbations of the Rossby-Haurwitz wave and the Verkley modon

502.#.#.c: Universidad Nacional Autónoma de México

561.1.#.a: Instituto de Ciencias de la Atmósfera y Cambio Climático, UNAM

264.#.0.c: 1993

264.#.1.c: 2009-10-05

506.1.#.a: La titularidad de los derechos patrimoniales de esta obra pertenece a las instituciones editoras. Su uso se rige por una licencia Creative Commons BY-NC 4.0 Internacional, https://creativecommons.org/licenses/by-nc/4.0/legalcode.es, para un uso diferente consultar al responsable jurídico del repositorio por medio del correo electrónico editora@atmosfera.unam.mx

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001.#.#.#: 022.oai:ojs.pkp.sfu.ca:article/8348

041.#.7.h: eng

520.3.#.a: Stability of the Rossby-Haurwitz wave of subspace H1 Hn and two types of Verkley"s modons is analyzed within the vorticity equation of an ideal incompressible fluid on a rotating sphere. Here Hn is the eigen subspace of the Laplace operator on a sphere corresponding to the eigenvalue n(n + 1). It is shown that arbitrary perturbations of the Rossby-Haurwitz wave can be divided into three invariant sets one of which contains a stable invariant subset Hn. Three invariant sets of small perturbations of the stationary Verkley modon are also found. The- separation of perturbations have been performed with the help of a conservation law for perturbations. Formulas for determining the distance between any two solutions from the whole set of modons and Rossby-Haurwitz waves are derived through the energy and enstrophy of the corresponding perturbation. Necessary and sufficient conditions for the distance between these solutions to be constant are obtained. It is shown that any super-rotation flow on a sphere (belonging to H1) is stable independently of choice of the rotation axis. Liapunov instability of any non-zonal Rossby-Haurwitz wave from H1 Hn where n ≥ 2 as well as of any dipole modon on a sphere is proved. It is shown that the Liapunov instability is caused by the algebraic growth of perturbations due to asynchronous oscillations of waves and has nothing in common with the orbital instability. It is proved that any monopole Verkley (1987) modon, as well as any Legendre polynomial, is linearly Liapunov stable with respect to invariant subsets of perturbations of sufficiently small scale.

773.1.#.t: Atmósfera; Vol. 6 No. 2 (1993)

773.1.#.o: https://www.revistascca.unam.mx/atm/index.php/atm/index

046.#.#.j: 2021-10-20 00:00:00.000000

022.#.#.a: ISSN electrónico: 2395-8812; ISSN impreso: 0187-6236

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handle: 00c726495272d920

harvesting_date: 2023-06-20 16:00:00.0

856.#.0.q: application/pdf

245.1.0.b: Dynamics of perturbations of the Rossby-Haurwitz wave and the Verkley modon

last_modified: 2023-06-20 16:00:00

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Artículo

Dynamics of perturbations of the Rossby-Haurwitz wave and the Verkley modon

Skiba, Yuri N.

Instituto de Ciencias de la Atmósfera y Cambio Climático, UNAM, publicado en Atmósfera, y cosechado de Revistas UNAM

Licencia de uso

Procedencia del contenido

Entidad o dependencia
Instituto de Ciencias de la Atmósfera y Cambio Climático, UNAM
Revista
Repositorio
Contacto
Revistas UNAM. Dirección General de Publicaciones y Fomento Editorial, UNAM en revistas@unam.mx

Cita

Skiba, Yuri N. (1993). Dynamics of perturbations of the Rossby-Haurwitz wave and the Verkley modon. Atmósfera; Vol. 6 No. 2, 1993. Recuperado de https://repositorio.unam.mx/contenidos/11270

Descripción del recurso

Autor(es)
Skiba, Yuri N.
Tipo
Artículo de Investigación
Área del conocimiento
Físico Matemáticas y Ciencias de la Tierra
Título
Dynamics of perturbations of the Rossby-Haurwitz wave and the Verkley modon
Fecha
2009-10-05
Resumen
Stability of the Rossby-Haurwitz wave of subspace H1 Hn and two types of Verkley"s modons is analyzed within the vorticity equation of an ideal incompressible fluid on a rotating sphere. Here Hn is the eigen subspace of the Laplace operator on a sphere corresponding to the eigenvalue n(n + 1). It is shown that arbitrary perturbations of the Rossby-Haurwitz wave can be divided into three invariant sets one of which contains a stable invariant subset Hn. Three invariant sets of small perturbations of the stationary Verkley modon are also found. The- separation of perturbations have been performed with the help of a conservation law for perturbations. Formulas for determining the distance between any two solutions from the whole set of modons and Rossby-Haurwitz waves are derived through the energy and enstrophy of the corresponding perturbation. Necessary and sufficient conditions for the distance between these solutions to be constant are obtained. It is shown that any super-rotation flow on a sphere (belonging to H1) is stable independently of choice of the rotation axis. Liapunov instability of any non-zonal Rossby-Haurwitz wave from H1 Hn where n ≥ 2 as well as of any dipole modon on a sphere is proved. It is shown that the Liapunov instability is caused by the algebraic growth of perturbations due to asynchronous oscillations of waves and has nothing in common with the orbital instability. It is proved that any monopole Verkley (1987) modon, as well as any Legendre polynomial, is linearly Liapunov stable with respect to invariant subsets of perturbations of sufficiently small scale.
Idioma
eng
ISSN
ISSN electrónico: 2395-8812; ISSN impreso: 0187-6236

Enlaces