author = "Silva Dias, Pedro L. and Raupp, Carlos F. M. and Ramirez 
                         Gutierrez, Enver Manuel Amador and Raphaldini, Breno",
          affiliation = "{Univesidade de S{\~a}o Paulo (USP)} and {Univesidade de S{\~a}o 
                         Paulo (USP)} and {Instituto Nacional de Pesquisas Espaciais 
                         (INPE)} and {Univesidade de S{\~a}o Paulo (USP)}",
                title = "Connecting tropical diurnal variability to the decadal and longer 
                         time scales through nonlinear resonance",
                 year = "2017",
         organization = "Conference on Atmospheric and Oceanic Fluid Dynamics 19th 
                         Conference on Middle Atmosphere, 21.",
             abstract = "Tropical convection is characterized by strong spectral peaks in 
                         some well defined frequency bands and numerical models do not 
                         always realistically reproduce the observed power. Our goal is to 
                         explore the role of nonlinear resonance as a plausible mechanism 
                         to promote energy transfer from higher frequencies (e.g. the 
                         diurnal scale) to synoptic, intraseasonal, interannual and longer 
                         time scales. The presentation will explore highlights of the 
                         papers published by the authors, discuss some recent advances both 
                         from the point of view of the role of non-hydrostatic processes 
                         and the interaction between the periodic solar forcing and the 
                         resonating triads in the decadal and longer timescales. This work 
                         was initially motivated by the numerical evidence in the late 90s 
                         that models with stronger diurnal variation had a stronger signal 
                         in the intraseasonal band. Non-linear resonance was invoked as a 
                         potential mechanism to explain the connection between the diurnal 
                         and intraseasonal variability in tropical convection. Numerical 
                         integrations of the resonant three-wave problem show that the 
                         energy of the waves in a resonant triad evolves periodically in 
                         time, with the period and amplitude of the energy oscillations 
                         dependent on the magnitude of the initial amplitudes of the waves 
                         and the way in which the initial energy is distributed among the 
                         triad components. The high-frequency modes are found to be 
                         energetically more active than the low-frequency modes. The latter 
                         tend to act as catalytic components in a resonant triad. 
                         Integrations of the problem of two resonant triads coupled by a 
                         single mode point out the importance of gravity waves in the 
                         intertriad energy exchanges, suggesting the significance of these 
                         modes in the redistribution of energy throughout the atmospheric 
                         motion spectrum. The results also show that the inter-triad energy 
                         exchanges provided by the highest frequency mode of two triads 
                         occur in a longer time-scale than the intra-triad interactions. 
                         Therefore, these results also suggest the importance of the 
                         high-frequency modes in the generation of the low-frequency 
                         variability (intraseasonal and even longer term) of the 
                         atmospheric flow. Later, the full primitive equation model was 
                         decomposed in vertical modes and the nonlinear interaction between 
                         internal modes and the external mode were explored. In this case, 
                         it was shown that a Rossby wave associated with the baroclinic 
                         basic state, resonant with the stationary component of the daytime 
                         heat source, and two dispersive modes, given by Mixed 
                         Rossby-gravity wave and a slow barotropic mode (Rossby) may 
                         interact and provoke vacillation in the time scale of many days 
                         (between intraseasonal and interannual time scales). The 
                         importance of the fast modes in the resonant triplets raises the 
                         following question: what is the role of diurnal variation in the 
                         generation of these fast modes? We have also shown, for example, 
                         that a Rossby wave associated with the baroclinic (i.e., 
                         associated with an internal mode) basic state, resonant with the 
                         stationary component of the daytime heat source, and two 
                         dispersive modes, given by Mixed Rossby-gravity wave and a slow 
                         barotropic mode (Rossby) may interact and provoke vacillation in 
                         the time scale of several days (between intraseasonal and 
                         interannual). Another class of resonant modes is identified with 
                         the interaction between two internal modes of gravity generated by 
                         the diurnal forcing with clear manifestation in the intraseasonal 
                         scale. A generalization of the previous results on the role of the 
                         diurnal forcing was also developed in the context of a heat source 
                         parameterized by the simplest form according to the hypothesis 
                         that the heat source intensity is proportional to the low level 
                         moisture convergence. The study was developed in the context of a 
                         two-layer model that allows interaction between the external 
                         (barotropic) mode and the internal (baroclinic) mode. It 
                         introduces a forcing that has meridional dependence and, 
                         therefore, it becomes feasible to explore the non-linear resonance 
                         involving the interaction of only two waves. The reduced dynamics 
                         of the two-layer model shows that a Rossby mode is significantly 
                         modulated in longer time scales when interacting with an internal 
                         gravity mode (interannual to the decadal scale). More recently we 
                         have explored a simplified multi-scale atmosphere-ocean coupled 
                         model for studying the interactions between 
                         synoptic-intraseasonal-interannual scales. Two coupled nonlinear 
                         equatorial beta-plane shallow water equations are considered: one 
                         for the ocean and the other for the atmosphere. The nonlinear 
                         terms are the intrinsic advective nonlinearity and the 
                         atmosphere/ocean coupling. Simplified parameterizations for the 
                         air-sea coupling are developed. To mimic the main differences 
                         between the fast- atmosphere and the slow-ocean, suitable 
                         multi-space and multi-time scaling are applied, yielding a 
                         balanced synoptic/intraseasonal/interannual-El Niņo regime. In 
                         this limit, the synoptic scale is the fastest atmospheric scale, 
                         the intraseasonal is the intermediate air-sea coupling scale and 
                         El Niņo refers to the slowest interannual ocean scale. The model 
                         equations reveal that the slow wave amplitude evolution depends on 
                         both types of nonlinearities. The wind stress parameterization 
                         allows synoptic scale atmospheric waves to force intraseasonal 
                         variability in the ocean. The intraseasonal ocean temperature 
                         anomaly coupled with the atmosphere through evaporation is able to 
                         force higher order atmospheric variability, whereas 
                         wave-convection coupling provides another source for higher order 
                         atmospheric variability. Nonlinear interactions of intraseasonal 
                         ocean perturbations can also force interannual oceanic 
                         variability. Analytical solutions of the reduced model equations 
                         for a discrete resonant triad interacting through the 
                         atmosphere-ocean fluxes illustrate the model potential to connect 
                         synoptic, intraseasonal, interannual and decadal/multi-decadal 
                         time-scales in the coupled system. We have also analyzed the role 
                         of periodic forcing induced by the sun energy output variability 
                         in the decadal and longer timescales. The presence of periodic 
                         forcing leads to larger amplitude effects at the longer 
                         time-scales. In the fast portion of the time scales, we are 
                         exploring possible resonating triads in non-hydrostatic models 
                         with potential applications in the organization of mesoscale 
  conference-location = "Portland, OR",
      conference-year = "26-30 June",
             language = "en",
        urlaccessdate = "23 nov. 2020"