The family of anisotropically scaled equatorial waves

• Published in: Journal of advances in modeling earth systems Vol. 3; no. 4; pp. np - n/a
• Main Authors: Ramírez Gutiérrez, Enver, da Silva Dias, Pedro Leite, Raupp, Carlos, Bonatti, Jose Paulo
• Format: Journal Article
• Language: English
• Published: Washington John Wiley & Sons, Inc 01-04-2011; American Geophysical Union (AGU)
• Subjects: anisotropic scalings; Anisotropy; Approximation; Atmosphere; Equatorial dynamics; Equatorial waves; Gravitational waves; Gravity; Gravity waves; multi-scale non-linear interactions; New family; Ocean dynamics; Shallow water; shallow water model; Tropical climate; Tropical environments; Velocity
• ISSN: 1942-2466; 1942-2466
• DOI: 10.1029/2011MS000078

In the present work we introduce the family of anisotropic equatorial waves. This family corresponds to equatorial waves at intermediate states between the shallow water and the long wave approximation model. The new family is obtained by using anisotropic time/space scalings on the linearized, unforced and inviscid shallow water model. It is shown that the anisotropic equatorial waves tend to the solutions of the long wave model in one extreme and to the shallow water model solutions in the other extreme of the parameter dependency. Thus, the problem associated with the completeness of the long wave model solutions can be asymptotically addressed. The anisotropic dispersion relation is computed and, in addition to the typical dependency on the equivalent depth, meridional quantum number and zonal wavenumber, it also depends on the anisotropy between both zonal to meridional space and velocity scales as well as the fast to slow time scales ratio. For magnitudes of the scales compatible with those of the tropical region, both mixed Rossby‐gravity and inertio‐gravity waves are shifted to a moderately higher frequency and, consequently, not filtered out. This draws attention to the fact that, for completeness of the long wave like solutions, it is necessary to include both the anisotropic mixed Rossby‐gravity and inertio‐gravity waves. Furthermore, the connection of slow and fast manifolds (distinguishing feature of equatorial dynamics) is preserved, though modified for the equatorial anisotropy parameters used δ ∈ 〈 1]. New possibilities of horizontal and vertical scale nonlinear interactions are allowed. Thus, the anisotropic shallow water model is of fundamental importance for understanding multiscale atmosphere and ocean dynamics in the tropics.
Key Points
Family of anisotropically scaled equatorial waves and resonat triad interactions
Multiscale atmosphere and ocean dynamics in the tropics
Intermediate regimes between the shallow water and long wave approximation model