It has been shown that the best explanation for the formation of the tachocline is that of magnetic nature. We present here the first simulations of the solar tachocline, which self-consistently include the meridional circulation. We show that the meridional circulations significantly change the shape and the characteristics of the tachocline. We find that after the inclusion of the meridional ...

We consider the problem of minimizing a separable convex objective function over the linear space given by system Mx = 0 with M a totally unimodular matrix. In particular, this generalizes the usual minimum linear cost circulation and co-circulation problems in a network, and the problems of determining the Euclidean distance from a point to the perfect bipartite matching polytope and the feasi...

In this article, we present a mathematical theory of the Walker circulation of the large-scale atmosphere over the tropics. This study leads to a new metastable state oscillation theory for the El Niño Southern Oscillation (ENSO), a typical inter-annual climate low frequency oscillation. The mathematical analysis is based on 1) the dynamic transition theory, 2) the geometric theory of incompres...

[1] The subtropical terminus of the Hadley circulation is interpreted as the latitude poleward of which vertical wave activity fluxes (meridional eddy entropy fluxes) become sufficiently deep to reach the upper troposphere. This leads to a sign change of the upper-tropospheric divergence of meridional wave activity fluxes (convergence of meridional eddy angular momentum fluxes) and marks the tr...