In Cartesian coordinates
the gradient Richardson number
is the ratio between the square of the buoyancy frequency
N and the square of the vertical shear
S,
, where
and
, with
ρ potential density,
the horizontal velocity components and
g gravity acceleration. In isopycnic coordinates
,
is expressed as the ratio between
and the squared diapycnal shear
,
. This could suggest that a decrease (increase) in stratification brings a decrease (increase) in dynamic stability in Cartesian coordinates, but a stability increase (decrease) in isopycnic coordinates. The apparently different role of stratification arises because
S and
are related through the stratification itself,
. In terms of characteristic times, this is equivalent to
, which is interpreted as a critical dynamic time
that equals the buoyancy period
normalized by the ratio
, where
is the deformation time. Here we follow simple arguments and use field data from three different regions (island shelf break, Gulf Stream and Mediterranean outflow) to endorse the usefulness of the isopycnal approach. In particular, we define the reduced squared diapycnal shear
and compare it with the reduced squared vertical
, both being positive (negative) for unstable (stable) conditions. While both
Ri and
remain highly variable for all stratification conditions, the mean
values approach
with increasing stratification. Further, the field data follow the relation
, with a subcritical
for both the island shelf break and the Mediterranean outflow. We propose
and
to be good indexes for the occurrence of effective mixing under highly stratified conditions.
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