ACADEMIA Letters
Atlantic Thermohaline Circulation: from Lorenz model of
atmospheric convection toward Ocean Dynamics
Vincenzo de Toma, University of Rome Tor Vergata, Department of Physics, Viale
della Ricerca Scientifca 1, Rome, Italy, 00133
Abstract
In this paper, we study a 2D incompressible fow in the y-z plane in the Oberbeck-Boussinesq
approximation, taken from the problem of atmospheric thermal convection. We add to the sys-
tem an equation for another difusive tracer, i.e. salinity, in order to obtain a simplifed model
which could ideally describe the thermohaline circulation in a square 2D oceanic domain. The
system is rewritten by constructing the vorticity equation, and by means of the introduction
of a stream function, which should represent the overturning of the Atlantic Ocean. The par-
tial diferential equation system is then cast into a system of ordinary diferential equations
passing to the spatial-spectral domain, where the dynamics of the amplitudes for the Fourier
coefcients are investigated and, searching for a nontrivial steady-state solution, a relation
between Fourier wave number and relevant physical parameters of the system are found.
1. Introduction
Among the factors which have a determining role in climate variability, the Atlantic Merid-
ional Overturning Circulation is of undoubted theoretical and practical interest, both for the
lack of knowledge of its driving mechanisms and for the need for a better agreement between
models that try to predict it [4], [5].
Academia Letters, May 2022
Corresponding Author: Vincenzo de Toma, vincenzodetoma.vdt@gmail.com
Citation: de Toma, V. (2022). Atlantic Thermohaline Circulation: from Lorenz model of atmospheric
convection toward Ocean Dynamics. Academia Letters, Article 5339.
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©2022 by the author — Open Access — Distributed under CC BY 4.0