This study presents analytic solutions that describe the fundamental structure of the Hadley circulation in the tropical atmosphere. Starting from the zonally averaged primitive equations, the weak temperature gradient (WTG) approximation is employed to relate the vertical velocity directly to the prescribed thermal forcing representing large-scale tropical convection. The continuity equation determines the meridional velocity, and the zonal mean momentum equation is solved analytically using the method of characteristics. The resulting zonal mean zonal wind satisfies angular momentum conservation in the upper branch of the circulation, consistent with the classical theory. An arbitrary function introduced in the general solution is constrained by the matching condition between the interior flow and the surface Ekman layer, yielding realistic trade winds near the surface. The analysis reveals that the intensity of the trade winds depends on both surface friction and the strength of tropical convection, demonstrating a direct dynamical link between convective heating and low-level wind structure. The obtained analytic solutions successfully reproduce the essential features of the Hadley circulation, providing a clear physical interpretation of how tropical convection and surface friction jointly determine the tropical Hadley cell's vertical and meridional structures.
We examine the nonlinear interaction of rotating waves of azimuthal wave numbers m1=2 $ m_1=2 $ and m2=1 $ m_2=1 $ (i.e. strong spatial resonance) in an air-filled, differentially heated rotating annulus. Using a weakly nonlinear analysis that combines centre manifold reduction and numerical bifurcation analysis, we determine the dynamics close to a double Hopf bifurcation point where these modes interact. While previous studies have addressed higher-order weak spatial resonances, the strong 2-1 spatial resonance introduces quadratic terms in the reduced equations that can lead to unique dynamics. Our analysis predicts the emergence of stable, phase-locked mixed-mode rotating waves, which is consistent with experimental observations and indicates the distinct dynamics produced by strong spatial resonance.
The transmission of three-dimensional anelastic internal gravity wave packets incident upon a retrograde background jet flow are examined through fully nonlinear numerical simulations. The background winds are chosen to be representative of the eastward and westward flows of the Quasi-Biennial Oscillation (QBO) in the equatorial stratosphere. Transmission, which is quantified by the relative pseudomomentum of waves passing above the jet, is found to be smaller for incident waves with larger initial frequency. Due to anelastic effects, the amplitude of the transmitted wave packets tends to grow exponentially, ultimately inducing a local mean flow that acts to drive the waves to overturn and break turbulently. The results are compared with previous studies that predicted transmission of small amplitude wave packets, and implications are discussed for the influence of wave transmission across the QBO.
We consider the interaction of an anticyclonic vortex (an anticyclone) lying above a basin (a depression in the bathymetry) and an incoming pair of opposite-signed vortices in a two-layer quasi-geostrophic flow. We show that the anticyclone lying above the basin may merge with the anticyclone of the incoming pair. We show that the size of the parameter space where merger occurs is large, indicating that such an interaction may easily occur. This helps explain why such mergers have been observed over oceanic basins such as the Lofoten basin.
Atmospheric gravity waves spontaneously radiated from nearly balanced flows are investigated by the general circulation model of the Venus atmosphere. To resolve small-scale gravity waves, the ultra-high resolution runs with 20- and 0.25-km horizontal and vertical grid intervals are conducted. As the super-rotation evolves over time, gravity waves are spontaneously radiated from thermal tides and baroclinic/barotropic waves in the low-latitudes and the mid- to high-latitudes, respectively. Here, we focus on the generation from baroclinic/barotropic waves by the simulations without diurnal component of the solar heating (c.f. thermal tides are excluded). Then the sensitivities of the static stability are tested. For the cases with larger static stability in the cloud layer, gravity wave radiation is weakened, indicating that the intensity of baroclinic instability is directly related to the amount of spontaneous gravity wave radiation. The small- to medium-scale gravity waves affect the three-dimensional structure of the super-rotation. Especially, we confirmed for the first time that gravity waves can transport zonal momentum vertically to the lower atmosphere (similar to 50-60 km) in mid- to high-latitudes. The momentum transport caused by spontaneous gravity wave radiation should be considered in the Venus atmosphere.
