Evolution of Jupiter-style critical latitudes: Initial laboratory
altimetry results
Abstract
This is a laboratory zonal-jet study using a rotating water tank. The
bottom topography has a tent-shaped radial cross section designed to
generate two critical latitudes, i.e. two positions where βe, the radial
gradient of the potential vorticity (PV), changes sign. This
configuration is motivated by observations indicating Jupiter and Saturn
have not only multiple zonal jets, but multiple stable critical
latitudes. It is known that “supersonic” critical latitudes (with
respect to Rossby waves) are stable, whereas “subsonic” critical
latitudes are posited to be unstable. Because Rossby waves are
uni-directional, “supersonic” critical latitudes come in two
varieties: Rossby Mach number MR > 1
and MR < 0, where the latter holds when
the waves are directed downstream. Experiments focus on: i) how do zonal
jets emerge from localized forcing in a system with alternating PV
gradients? and ii) what differences are there between the evolution of
various types of critical latitudes? The water is forced by mass
injection along one radius. Laboratory altimetry provides accurate,
unobtrusive records of the circulations that reveal the emergence of
counter-propagating β-plumes (Rossby-wave envelopes), which expand into
tank-encircling zonal jets. The tank’s negative βe annulus is
characterized by MR ~ 1, which is
the condition surmised for Jupiter and Saturn. The weaker critical
latitude (in terms of jumps in the PV-gradient) adjusts its position by
~4% of the tank radius and maintains
MR ~ 1. In contrast, the stronger
one vacillates while maintaining
|MR| << 1,
and may be relevant to steep oceanic seamounts.