We validate a new law for the aspect ratio
of vortices in a rotating, stratified flow, where
and
are the vertical half-height and horizontal length scale of the vortices. The aspect ratio depends not only on the Coriolis parameter
and buoyancy (or Brunt–Väisälä) frequency
of the background flow, but also on the buoyancy frequency
within the vortex and on the Rossby number
of the vortex, such that
. This law for
is obeyed precisely by the exact equilibrium solution of the inviscid Boussinesq equations that we show to be a useful model of our laboratory vortices. The law is valid for both cyclones and anticyclones. Our anticyclones are generated by injecting fluid into a rotating tank filled with linearly stratified salt water. In one set of experiments, the vortices viscously decay while obeying our law for
, which decreases over time. In a second set of experiments, the vortices are sustained by a slow continuous injection. They evolve more slowly and have larger
while still obeying our law for
. The law for
is not only validated by our experiments, but is also shown to be consistent with observations of the aspect ratios of Atlantic meddies and Jupiter’s Great Red Spot and Oval BA. The relationship for
is derived and examined numerically in a companion paper by Hassanzadeh, Marcus & Le Gal (J. Fluid Mech., vol. 706, 2012, pp. 46–57).