The Ocean and the Climate System - Ocean in the Earth System - page 70

parameter f , which characterizes the “planetary vorticity” at a given
latitude: f = 2 Ω sin ϕ where Ω is the Earth's angular speed and ϕ the
latitude. This action of planetary rotation is determinant for most
oceanic motions. Let us consider a reference point situated on the
Earth's surface, where the axis O x designates the longitude, O y the
latitude and O z the local vertical. At this point, the planetary vorticity
corresponds to the projection of the Earth's rotation on the local
vertical.

In fact, most of the interior ocean is in a state called “geostrophic
equilibrium”. This equilibrium characterizes a stationary oceanic
circulation, without acceleration or diffusion, where pressure forces
that are exercised within the fluid are in equilibrium with the Coriolis
acceleration:

f k x u h = - 1/ ρ grad p

where k designates the unitary vector of the local vertical, u h is the
vector of horizontal speed in the latitude-longitude plane, with its two
components u zonal speed and v meridional speed,

is the volumic
mass and p the pressure. The equation above translates into the
velocity components by:

ρ

- fv = - 1/ ρ ∂ p / ∂ x

fu = - 1/ ρ ∂ p / ∂ y

Schematically, when a zone of high pressure appears within the
fluid, the water masses will diverge from this zone, and the Coriolis
acceleration will lead them into a rotation to their right, i.e. rotation in
a clockwise direction around this center of high pressure in the
northern hemisphere, and the opposite in the southern hemisphere
(Figure 2.7). This rotation movement around high pressures is called
anticyclonic, whereas that which occurs around low pressures is
cyclonic. Note: the cyclonic-anticyclonic rotation depends on the
hemisphere where it is produced. The fluid motion tends to align itself
with the isobars (the line of equal pressure).