Does geostrophic wind cross isobars into lows?

Not in this ideal balance. With friction and ageostrophic acceleration, real near-surface winds can cross isobars; this page isolates the frictionless along-isobar component.

Why does a temperature gradient create vertical shear?

Horizontal temperature gradients imply changing thickness between pressure surfaces. That makes the horizontal pressure gradient vary with height, so the geostrophic wind at 300 hPa differs from the wind near 1000 hPa.

Geostrophic Balance & Thermal Wind

Geostrophic balance is the leading-order synoptic-scale balance between the horizontal pressure-gradient force and the Coriolis force. This page draws a schematic pressure field with isobars and geostrophic wind arrows using u_g = −(1/ρf)∂p/∂y and v_g = (1/ρf)∂p/∂x. The lower panel adds the thermal-wind relation in pressure coordinates: a north-south temperature gradient changes the geostrophic wind with height, here approximated as Δu_g ≈ −(R/f)(∂T/∂y)ln(p_s/p_top) between 1000 and 300 hPa. The model is deliberately diagnostic rather than predictive: no ageostrophic acceleration, friction, curvature, fronts, or hydrostatic thickness integration are solved.

Who it's for: Synoptic meteorology, physical oceanography, or geophysical fluid dynamics introductions.

Key terms

Geostrophic balance
Thermal wind
Coriolis force
Isobars
Vertical wind shear

This is the synoptic-scale limit: away from friction and sharp curvature, winds follow isobars; temperature contrasts tilt pressure surfaces so the geostrophic wind changes with height.

Live graphs

How it works

A beta-plane-style classroom sketch of geostrophic balance and the thermal wind relation: isobars set near-surface geostrophic flow, while a meridional temperature gradient creates vertical shear.

Key equations

f k × u_g = −(1/ρ)∇p; u_g = −(1/ρf) ∂p/∂y, v_g = (1/ρf) ∂p/∂x

Δu_g ≈ −(R/f)(∂T/∂y) ln(p_s/p_top) between 1000 and 300 hPa

Frequently asked questions

Does geostrophic wind cross isobars into lows?: Not in this ideal balance. With friction and ageostrophic acceleration, real near-surface winds can cross isobars; this page isolates the frictionless along-isobar component.
Why does a temperature gradient create vertical shear?: Horizontal temperature gradients imply changing thickness between pressure surfaces. That makes the horizontal pressure gradient vary with height, so the geostrophic wind at 300 hPa differs from the wind near 1000 hPa.

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Frequently asked questions

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