Resonant Wave Interactions in the Presence of a Diurnally Varying Heat Source

Abstract

Resonant interactions among equatorial waves in the presence of a diurnally varying heat source are studied in the context of the diabatic version of the equatorial b-plane primitive equations for a motionless, hydrostatic, horizontally homogeneous and stably stratified background atmosphere. The heat source is assumed to be periodic in time and of small amplitude [i.e., O(«)] and is prescribed to roughly represent the typical heating associated with deep convection in the tropical atmosphere. In this context, using the asymptotic method of multiple time scales, the free linear Rossby, Kelvin, mixed Rossby-gravity, and inertiogravity waves, as well as their vertical structures, are obtained as leading-order solutions. These waves are shown to interact resonantly in a triad configuration at the O(«) approximation, and the dynamics of these interactions have been studied in the presence of the forcing.It is shown that for the planetary-scale wave resonant triads composed of two first baroclinic equatorially trapped waves and one barotropic Rossby mode, the spectrum of the thermal forcing is such that only one of the triad components is resonant with the heat source. As a result, to illustrate the role of the diurnal forcing in these interactions in a simplified fashion, two kinds of triads have been analyzed. The first one refers to triads composed of a k 5 0 first baroclinic geostrophic mode, which is resonant with the stationary component of the diurnal heat source, and two dispersive modes, namely, a mixed Rossby-gravity wave and a barotropic Rossby mode. The other class corresponds to triads composed of two first baroclinic inertio-gravity waves in which the highest-frequency wave resonates with a transient harmonic of the forcing. The integration of the asymptotic reduced equations for these selected resonant triads shows that the stationary component of the diurnal heat source acts as an ''accelerator'' for the energy exchanges between the two dispersive waves through the excitation of the catalyst geostrophic mode. On the other hand, since in the second class of triads the mode that resonates with the forcing is the most energetically active member because of the energy constraints imposed by the triad dynamics, the results show that the convective forcing in this case is responsible for a longer time scale modulation in the resonant interactions, generating a period doubling in the energy exchanges. The results suggest that the diurnal variation of tropical convection might play an important role in generating lowfrequency fluctuations in the atmospheric circulation through resonant nonlinear interactions.

Climate science in the tropics: waves, vortices and PDEs

“…An interesting way of looking at the problem is by considering resonant triad interactions involving barotropic Rossby waves and equatorially trapped waves. See for example the work of Reznik and Zeitlin [114,115], Raupp and Silva Dias [116,117], and Raupp, Tabak, and Milewski [118]. Here we discuss in detail the results of Raupp and Silva Dias in [117] where they considered the case when the resonant triads interact with the diurnal cycle of convection.…”

“…To ease the transition to the original paper for the interested reader, we keep here the exact same notion as in [117] where u, v, ω are the zonal, meridional, and pressure-vertical velocity (ω = Dp/Dt), φ is the geopotential and Q is the diabatic (convective) heating. Here is the equatorial Rossby number which is considered to be a small parameter and is used for asymptotic expansion.…”

Intraseasonal Variability of the Diurnal Cycle of Precipitation in the Philippines

“…Inclusion of the diurnal cycle dramatically improves the representation of the MJO in a general circulation model (Slingo et al 2003, Bernie et al 2008, indicating that understanding this interaction could be important for an understanding of the MJO. There is also evidence that the diurnal cycle can precondition the atmosphere for MJO propagation, and modulate it through diurnally generated gravity waves (Raupp andSilva Dias 2009, Majda andQ. Yang 2016).…”

Trends and variability in extremes of precipitation in Curitiba – Southern Brazil

“…SAM, SACZ and LISAM are included until 1990 (Figure 15(d)), 2000 (Figure 15(e)) and 2010 (Figure 15(f)). For longer data series (1 Ext, SOI, AMO and PDO), the COI includes The analysis of the oscillations can be made for several cycles and indices, remembering that there are delays between different cycles and possible non-linear interactions (Raupp and Silva Dias, 2009). Furthermore, for 1Ext and for all indices, we examined there are natural factors causing the pattern of stable peaks and moving peaks as far as accumulating energy is concerned.…”