The Non-traditional Coriolis force drives Westward tilts in Multiscale
Theories and Laboratory Experiments of Tropical Dynamics.
Abstract
Twenty years ago, Andy Majda and Rupert Klein developed a multiscale
asymptotic theory of tropical dynamics which they named IPESD. IPESD is
a linear, forced, dynamical theory on the tropical synoptic scales
coupled to a linear, slower, weak temperature gradient theory on the
tropical planetary scales. The two scales interact with one another
through upscale fluxes of momentum and temperature (the Reynolds
stresses) and downscale advection from the planetary scale (developed by
B. and Majda as the IMMD theory in 2010). Majda and myself used these
theories in the following years to develop a multiscale kinematic model
of the Madden Julian oscillation. Criticisms of this theory have missed
the essential fact that the mathematics of the asymptotic analysis are
inexorable, and verified by observation - the forcing is stronger on
small scales and weaker on large scales; that’s all that is really
needed to derive IMMD. In our MJO models, we showed that, in order to
capture the westerly wind burst structure of the MJO, it was sufficient
to force the planetary scales with momentum fluxes (Reynolds stresses)
from westward tilted convective structures on the synoptic scales. Left
unanswered was the cause of the westward tilted convection, though
westward tilts had been observed repeatedly in MJO observing campaigns.
The non-traditional terms in the Coriolis force (NCT) seem to provide an
excellent candidate for westward tilts, but it is well known that these
terms are too weak on scales greater than the mesoscale to affect the
dynamics. However, the multiscale theories provide a distinct route for
the NCT to affect the planetary scales - through upscale fluxes of
momentum. We will show analytically that the net-NCT affects tropical
convection by generating zero force in the vertical direction, a
westward velocity field in regions of upward flow, and a recirculation
in regions of downward flow, around a convective structure. The upscale
fluxes from these circulations drive the vertical/westward tilt that was
necessary to generate the westerly wind burst in the Majda/Biello models
of the MJO. We will also show how these results, westward tilt and the
westerly wind burst, can be created in simple laboratory experiments. We
sincerely hope that Andy would have been gratified by these results, and
excited by our experiment.