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- Author or Editor: Pedro L. Silva Dias x
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Abstract
Weakly nonlinear interactions among equatorial waves have been explored in this paper using the adiabatic version of the equatorial β-plane primitive equations in isobaric coordinates. Assuming rigid lid vertical boundary conditions, the conditions imposed at the surface and at the top of the troposphere were expanded in a Taylor series around two isobaric surfaces in an approach similar to that used in the theory of surface–gravity waves in deep water and capillary–gravity waves. By adopting the asymptotic method of multiple time scales, the equatorial Rossby, mixed Rossby–gravity, inertio-gravity, and Kelvin waves, as well as their vertical structures, were obtained as leading-order solutions. These waves were shown to interact resonantly in a triad configuration at the O(ε) approximation. The resonant triads whose wave components satisfy a resonance condition for their vertical structures were found to have the most significant interactions, although this condition is not excluding, unlike the resonant conditions for the zonal wavenumbers and meridional modes. Thus, the analysis has focused on such resonant triads. In general, it was found that for these resonant triads satisfying the resonance condition in the vertical direction, the wave with the highest absolute frequency always acts as an energy source (or sink) for the remaining triad components, as usually occurs in several other physical problems in fluid dynamics. In addition, the zonally symmetric geostrophic modes act as catalyst modes for the energy exchanges between two dispersive waves in a resonant triad. The integration of the reduced asymptotic equations for a single resonant triad shows that, for the initial mode amplitudes characterizing realistic magnitudes of atmospheric flow perturbations, the modes in general exchange energy on low-frequency (intraseasonal and/or even longer) time scales, with the interaction period being dependent upon the initial mode amplitudes. Potential future applications of the present theory to the real atmosphere with the inclusion of diabatic forcing, dissipation, and a more realistic background state are also discussed.
Abstract
Weakly nonlinear interactions among equatorial waves have been explored in this paper using the adiabatic version of the equatorial β-plane primitive equations in isobaric coordinates. Assuming rigid lid vertical boundary conditions, the conditions imposed at the surface and at the top of the troposphere were expanded in a Taylor series around two isobaric surfaces in an approach similar to that used in the theory of surface–gravity waves in deep water and capillary–gravity waves. By adopting the asymptotic method of multiple time scales, the equatorial Rossby, mixed Rossby–gravity, inertio-gravity, and Kelvin waves, as well as their vertical structures, were obtained as leading-order solutions. These waves were shown to interact resonantly in a triad configuration at the O(ε) approximation. The resonant triads whose wave components satisfy a resonance condition for their vertical structures were found to have the most significant interactions, although this condition is not excluding, unlike the resonant conditions for the zonal wavenumbers and meridional modes. Thus, the analysis has focused on such resonant triads. In general, it was found that for these resonant triads satisfying the resonance condition in the vertical direction, the wave with the highest absolute frequency always acts as an energy source (or sink) for the remaining triad components, as usually occurs in several other physical problems in fluid dynamics. In addition, the zonally symmetric geostrophic modes act as catalyst modes for the energy exchanges between two dispersive waves in a resonant triad. The integration of the reduced asymptotic equations for a single resonant triad shows that, for the initial mode amplitudes characterizing realistic magnitudes of atmospheric flow perturbations, the modes in general exchange energy on low-frequency (intraseasonal and/or even longer) time scales, with the interaction period being dependent upon the initial mode amplitudes. Potential future applications of the present theory to the real atmosphere with the inclusion of diabatic forcing, dissipation, and a more realistic background state are also discussed.
Abstract
Past changes of Southern Hemisphere (SH) monsoons are less investigated than their northern counterpart because of relatively scarce paleodata. In addition, projections of SH monsoons are less robust than in the Northern Hemisphere. Here, we use an energetic framework to shed lights on the mechanisms determining SH monsoonal response to external forcing: precession change at the mid-Holocene versus future greenhouse gas increase (RCP8.5). Mechanisms explaining the monsoon response are investigated by decomposing the moisture budget in thermodynamic and dynamic components. SH monsoons weaken and contract in the multimodel mean of midHolocene simulations as a result of decreased net energy input and weakening of the dynamic component. In contrast, SH monsoons strengthen and expand in the RCP8.5 multimodel mean, as a result of increased net energy input and strengthening of the thermodynamic component. However, important regional differences on monsoonal precipitation emerge from the local response of Hadley and Walker circulations. In the midHolocene, the combined effect of Walker–Hadley changes explains the land–ocean precipitation contrast. Conversely, the increased local gross moist stability explains the increased local precipitation and net energy input under circulation weakening in RCP8.5.
Abstract
Past changes of Southern Hemisphere (SH) monsoons are less investigated than their northern counterpart because of relatively scarce paleodata. In addition, projections of SH monsoons are less robust than in the Northern Hemisphere. Here, we use an energetic framework to shed lights on the mechanisms determining SH monsoonal response to external forcing: precession change at the mid-Holocene versus future greenhouse gas increase (RCP8.5). Mechanisms explaining the monsoon response are investigated by decomposing the moisture budget in thermodynamic and dynamic components. SH monsoons weaken and contract in the multimodel mean of midHolocene simulations as a result of decreased net energy input and weakening of the dynamic component. In contrast, SH monsoons strengthen and expand in the RCP8.5 multimodel mean, as a result of increased net energy input and strengthening of the thermodynamic component. However, important regional differences on monsoonal precipitation emerge from the local response of Hadley and Walker circulations. In the midHolocene, the combined effect of Walker–Hadley changes explains the land–ocean precipitation contrast. Conversely, the increased local gross moist stability explains the increased local precipitation and net energy input under circulation weakening in RCP8.5.
Abstract
Here the theory of global nonhydrostatic normal modes has been further developed with the analysis of both linear and weakly nonlinear energetics of inertia–acoustic (IA) and inertia–gravity (IG) modes. These energetics are analyzed in the context of a shallow global nonhydrostatic model governing finite-amplitude perturbations around a resting, hydrostatic, and isothermal background state. For the linear case, the energy as a function of the zonal wavenumber of the IA and IG modes is analyzed, and the nonhydrostatic effect of vertical acceleration on the IG waves is highlighted. For the nonlinear energetics analysis, the reduced equations of a single resonant wave triad interaction are obtained by using a pseudoenergy orthogonality relation. Integration of the triad equations for a resonance involving a short harmonic of an IG wave, a planetary-scale IA mode, and a short IA wave mode shows that an IG mode can allow two IA modes to exchange energy in specific resonant triads. These wave interactions can yield significant modulations in the dynamical fields associated with the physical-space solution with periods varying from a daily time scale to almost a month long.
Abstract
Here the theory of global nonhydrostatic normal modes has been further developed with the analysis of both linear and weakly nonlinear energetics of inertia–acoustic (IA) and inertia–gravity (IG) modes. These energetics are analyzed in the context of a shallow global nonhydrostatic model governing finite-amplitude perturbations around a resting, hydrostatic, and isothermal background state. For the linear case, the energy as a function of the zonal wavenumber of the IA and IG modes is analyzed, and the nonhydrostatic effect of vertical acceleration on the IG waves is highlighted. For the nonlinear energetics analysis, the reduced equations of a single resonant wave triad interaction are obtained by using a pseudoenergy orthogonality relation. Integration of the triad equations for a resonance involving a short harmonic of an IG wave, a planetary-scale IA mode, and a short IA wave mode shows that an IG mode can allow two IA modes to exchange energy in specific resonant triads. These wave interactions can yield significant modulations in the dynamical fields associated with the physical-space solution with periods varying from a daily time scale to almost a month long.
Abstract
Many frost events over southeastern Brazil are accompanied by a large-amplitude upper trough of the middle latitudes that extends well into the Tropics. This paper first illustrates that a mechanism of downstream amplification across the Pacific into South America is generally accompanied in these situations. This is manifested by troughs and ridges that propagate eastward. An analysis of these situations during frost events shows that these features of downstream amplification, illustrated on a Hovmöller (x–t) plot, can be decomposed into a family of synoptic-scale waves that propagate eastward and a family of planetary-scale waves that acquire a quasi-stationary character during the freeze event. It is shown that a global model, at a resolution of 70 km, can be used to predict these features on the decomposition of scales during freeze events. It became apparent from these features that the growth of the long stationary waves during the freeze events may be due to scale interaction among wave components. This paper discusses the nature of these scale interactions, calculated from the energetics in the wavenumber domain, for periods before, during, and after the freeze events. The salient results are that nonlinear barotropic-scale interactions are an important source for the maintenance of the downstream amplification; however, the baroclinic (in scale) contributions dominate through the life cycle of the downstream amplitude where the large-amplitude troughs are indeed accompanied by baroclinic features. Finally, it is shown that a very high resolution regional spectral model can be used to handle the local aspects of the freeze events. This study offers the possibility for designing prediction experiments on the medium-range timescales for the forecast of these frost events.
Abstract
Many frost events over southeastern Brazil are accompanied by a large-amplitude upper trough of the middle latitudes that extends well into the Tropics. This paper first illustrates that a mechanism of downstream amplification across the Pacific into South America is generally accompanied in these situations. This is manifested by troughs and ridges that propagate eastward. An analysis of these situations during frost events shows that these features of downstream amplification, illustrated on a Hovmöller (x–t) plot, can be decomposed into a family of synoptic-scale waves that propagate eastward and a family of planetary-scale waves that acquire a quasi-stationary character during the freeze event. It is shown that a global model, at a resolution of 70 km, can be used to predict these features on the decomposition of scales during freeze events. It became apparent from these features that the growth of the long stationary waves during the freeze events may be due to scale interaction among wave components. This paper discusses the nature of these scale interactions, calculated from the energetics in the wavenumber domain, for periods before, during, and after the freeze events. The salient results are that nonlinear barotropic-scale interactions are an important source for the maintenance of the downstream amplification; however, the baroclinic (in scale) contributions dominate through the life cycle of the downstream amplitude where the large-amplitude troughs are indeed accompanied by baroclinic features. Finally, it is shown that a very high resolution regional spectral model can be used to handle the local aspects of the freeze events. This study offers the possibility for designing prediction experiments on the medium-range timescales for the forecast of these frost events.
