barotropic

Barotropic describes a property of a fluid in which density is a function of pressure only (ρ = ρ(p)). Equivalently, surfaces of constant density coincide with surfaces of constant pressure, so density gradients are aligned with pressure gradients and there is no baroclinicity. In many practical contexts, especially in incompressible flows, density is treated as constant, which is a special, often-used barotropic case.

In geophysical fluid dynamics, the barotropic assumption simplifies the vertical structure of the flow. In a barotropic atmosphere, there is little or no vertical shear of the horizontal wind because density (and thus temperature) do not vary independently with height to create thermal wind. The flow is effectively depth-averaged, and vertical coupling is reduced. Barotropic models are commonly employed to study large-scale, horizontally varying but vertically uniform dynamics.

In oceanography, a barotropic ocean implies density depends mainly on depth (pressure), leading to flows that are approximately uniform with depth. Such models neglect stable density stratification and internal gravity waves, focusing instead on horizontal, depth-averaged motions.

Distinctions from baroclinic: baroclinicity arises when density depends on both pressure and temperature, causing misalignment between density and pressure gradients. This misalignment generates vertical shear and supports baroclinic instabilities. Real fluids often exhibit both barotropic and baroclinic characteristics across regions and times, so barotropic approximations are used as useful simplifications where appropriate.