Scale Analysis for Large-Scale Tropical Atmospheric Dynamics

Abstract

Abstract A systematic scale analysis is performed for large-scale dynamics over the tropics. It is identified that two regimes are competing: 1) a dynamics characterized by balance between the vertical advection term and diabatic heating in the thermodynamic equation, realized at horizontal scales less than L ∼ 103 km given a velocity scale U ∼ 10 m s−1, and 2) a linear equatorial wave dynamics modulated by convective diabatic heating, realized at scales larger than L ∼ 3 × 103 km given U ∼ 3 m s−1. Under the first dynamic regime (balanced), the system may be approximated as nondivergent to leading order in asymptotic expansion, as originally pointed out by Charney. Inherent subtleties of scale analysis at large scales for the tropical atmosphere are emphasized. The subtleties chiefly arise from a strong sensitivity of the nondimensional β parameter to the horizontal scale. This amounts to qualitatively different dynamic regimes for scales differing only by a factor of 3, as summarized above. Because any regime under asymptotic expansion may have a wider applicability than a formal scale analysis would suggest, the question of which one of the two identified regimes dominates can be answered only after extensive modeling and observational studies. Preliminary data analysis suggests that the balanced dynamics, originally proposed by Sobel, Nilsson, and Polvani, is relevant for a wider range than the strict scale analysis suggests. A rather surprising conclusion from the present analysis is a likely persistence of balanced dynamics toward scales as small as the mesoscale L ∼ 102 km. Leading-order nondivergence also becomes more likely the case for the smaller scales because otherwise the required diabatic heating rate becomes excessive compared to observations by increasing inversely proportionally with decreasing horizontal scales.