Geostrophie

Geostrophie, or geostrophic balance, is the approximate equilibrium between the Coriolis force due to Earth’s rotation and the horizontal pressure gradient force that governs large-scale flows in the atmosphere and oceans. In conditions where accelerations and friction are small, fluid motion tends to run along lines of constant geopotential height, i.e., parallel to isobars or isohypses. The Coriolis parameter f = 2Ω sin φ (with φ the latitude) couples with the horizontal momentum to yield the geostrophic relation: f v = -(1/ρ) ∂p/∂x and -f u = -(1/ρ) ∂p/∂y, or in vector form f k × v = -(1/ρ) ∇p.

Geostrophic wind components are u_g = -(1/ρ f) ∂p/∂y and v_g = (1/ρ f) ∂p/∂x. Using geopotential height Z, these can be written as u_g = -(g/f) ∂Z/∂y and v_g = (g/f) ∂Z/∂x. Practically, the geostrophic flow tends to run parallel to height contours, and, in the Northern Hemisphere, circulates around high and low pressure in a characteristic manner: upper-level winds blow along the contours of constant geopotential height.

The geostrophic balance is applicable to large-scale, quasi-steady flows on synoptic to planetary scales, away from the equator where f is small. It is a foundational concept in weather forecasting, oceanography, and climate modeling, used to infer wind and current directions from pressure or height fields. The theory neglects ageostrophic terms such as friction, acceleration, and diabatic heating; near the equator or in boundary layers, these effects become significant and the geostrophic approximation breaks down.