Plumes in rotating convection. Part 1. Ensemble statistics and dynamical
balances
Authors: JULIEN KEITH , LEGG SONYA , McWILLIAMS JAMES , WERNE JOSEPH 
Published: July 2002

Atmospheric and oceanic convection often occurs over areas occupied by many
localized circulation elements known as plumes. The convective transports therefore
may depend not only on the individual elements, but also on the interactions between
plumes and the turbulent environment created by other plumes. However, many
attempts to understand these plumes focus on individual isolated elements, and
the behaviour of an ensemble is not understood. Geophysical convection may be
influenced by rotation when the transit time of a convecting element is long compared
to an inertial period (for example in deep oceanic convection). Much recent attention
has been given to the effect of rotation on individual plumes, but the role of rotation
in modifying the behaviour of an ensemble is not fully understood. Here we examine
the behaviour of plumes within an ensemble, both with and without rotation, to
identify the influence of rotation on ensemble plume dynamics.

We identify the coherent structures (plumes) present in numerical solutions of
turbulent Rayleigh–Bénard convection, a canonical example of a turbulent plume
ensemble. We use a conditional sampling compositing technique to extract the typical
structure in both non-rotating and rotating solutions. The dynamical balances of
these composite plumes are evaluated and compared with entraining plume models.
We find many differences between non-rotating and rotating plumes in their transports
of mass, buoyancy and momentum. As shown in previous studies, the expansion
of the turbulent plume by entrainment of exterior fluid is suppressed by strong rotation.
Our most significant new result is quantification of the continuous mixing
between the plume and ambient fluid which occurs at high rotation without any
net changes in plume volume. This mixing is generated by the plume–plume interactions
and acts to reduce the buoyancy anomaly of the plume. By contrast, in the
non-rotating case, no such loss of buoyancy by mixing occurs. As a result, the total
buoyancy transport by upwardly moving plumes diminishes across the layer in the
rotating case, while remaining approximately constant in the non-rotating case. At
high values of rotation, the net vertical acceleration is considerably reduced compared
to the non-rotating case due to loss of momentum through entrainment and mixing
and a decelerating pressure gradient which partially balances the buoyancy-driven
acceleration of plumes. As a result of the dilution of buoyancy, the pressure-gradient
deceleration and the loss of momentum due to mixing with the environment in the
rotating solutions, the conversion of potential energy to kinetic energy is significantly
less than that of non-rotating plumes.

The combination of efficient lateral mixing and slow vertical movement by the
plumes accounts for the unstable mean temperature gradient that occurs in rotating
Rayleigh–Bénard convection, while the less penetrative convection found at low
Rossby number is a consequence of the reduced kinetic energy transport. Within the
ensemble of plumes identified by the conditional sampling algorithm, distributions
of vertical velocity, buoyancy and vorticity mimic those of the volume as a whole.
Plumes cover a small fraction of the total area, yet account for most of the vertical
heat flux.