The geostrophic wind is directed parallel to isobars (lines of constant pressure at a given height).
Despite this, much of the atmosphere outside the tropics is close to geostrophic flow much of the time and it is a valuable first approximation.
Geostrophic flow in air or water is a zero-frequency inertial wave.
As the air accelerated, the deflection would increase until the Coriolis force's strength and direction balanced the pressure gradient force, a state called geostrophic balance.
Geostrophic balance helps to explain why, in the northern hemisphere, low-pressure systems (or cyclones) spin counterclockwise and high-pressure systems (or anticyclones) spin clockwise, and the opposite in the southern hemisphere.
Just as multiple weather balloons that measure pressure as a function of height in the atmosphere are used to map the atmospheric pressure field and infer the geostrophic wind, measurements of density as a function of depth in the ocean are used to infer geostrophic currents.
The effect of friction, between the air and the land, breaks the geostrophic balance.
Friction slows the flow, lessening the effect of the Coriolis force.
The geostrophic wind neglects frictional effects, which is usually a good approximation for the synoptic scale instantaneous flow in the midlatitude mid-troposphere.
[4] Although ageostrophic terms are relatively small, they are essential for the time evolution of the flow and in particular are necessary for the growth and decay of storms.
Quasigeostrophic and semi geostrophic theory are used to model flows in the atmosphere more widely.
Newton's Second Law can be written as follows if only the pressure gradient, gravity, and friction act on an air parcel, where bold symbols are vectors: Here U is the velocity field of the air, Ω is the angular velocity vector of the planet, ρ is the density of the air, P is the air pressure, Fr is the friction, g is the acceleration vector due to gravity and D/Dt is the material derivative.
Neglecting friction and vertical motion, as justified by the Taylor–Proudman theorem, we have: With f = 2Ω sin φ the Coriolis parameter (approximately 10−4 s−1, varying with latitude).
Assuming geostrophic balance, the system is stationary and the first two equations become: By substituting using the third equation above, we have: with z the geopotential height of the constant pressure surface, satisfying Further simplify those formulae above:
Other variants of the equation are possible; for example, the geostrophic wind vector can be expressed in terms of the gradient of the geopotential Φ on a surface of constant pressure: