525 research outputs found
Ribbon Turbulence
We investigate the non-linear equilibration of a two-layer quasi-geostrophic
flow in a channel forced by an imposed unstable zonal mean flow, paying
particular attention to the role of bottom friction. In the limit of low bottom
friction, classical theory of geostrophic turbulence predicts an inverse
cascade of kinetic energy in the horizontal with condensation at the domain
scale and barotropization on the vertical. By contrast, in the limit of large
bottom friction, the flow is dominated by ribbons of high kinetic energy in the
upper layer. These ribbons correspond to meandering jets separating regions of
homogenized potential vorticity. We interpret these result by taking advantage
of the peculiar conservation laws satisfied by this system: the dynamics can be
recast in such a way that the imposed mean flow appears as an initial source of
potential vorticity levels in the upper layer. The initial baroclinic
instability leads to a turbulent flow that stirs this potential vorticity field
while conserving the global distribution of potential vorticity levels.
Statistical mechanical theory of the 1-1/2 layer quasi-geostrophic model
predict the formation of two regions of homogenized potential vorticity
separated by a minimal interface. We show that the dynamics of the ribbons
results from a competition between a tendency to reach this equilibrium state,
and baroclinic instability that induces meanders of the interface. These
meanders intermittently break and induce potential vorticity mixing, but the
interface remains sharp throughout the flow evolution. We show that for some
parameter regimes, the ribbons act as a mixing barrier which prevent relaxation
toward equilibrium, favouring the emergence of multiple zonal jets
The effects of Ekman pumping on quasi-geostrophic Rayleigh-Benard convection
Numerical simulations of 3D, rapidly rotating Rayleigh-Benard convection are
performed using an asymptotic quasi-geostrophic model that incorporates the
effects of no-slip boundaries through (i) parameterized Ekman pumping boundary
conditions, and (ii) a thermal wind boundary layer that regularizes the
enhanced thermal fluctuations induced by pumping. The fidelity of the model,
obtained by an asymptotic reduction of the Navier-Stokes equations that
implicitly enforces a pointwise geostrophic balance, is explored for the first
time by comparisons of simulations against the findings of direct numerical
simulations and laboratory experiments. Results from these methods have
established Ekman pumping as the mechanism responsible for significantly
enhancing the vertical heat transport. This asymptotic model demonstrates
excellent agreement over a range of thermal forcing for Pr ~1 when compared
with results from experiments and DNS at maximal values of their attainable
rotation rates, as measured by the Ekman number (E ~ 10^{-7}); good qualitative
agreement is achieved for Pr > 1. Similar to studies with stress-free
boundaries, four spatially distinct flow morphologies exists. Despite the
presence of frictional drag at the upper and/or lower boundaries, a strong
non-local inverse cascade of barotropic (i.e., depth-independent) kinetic
energy persists in the final regime of geostrophic turbulence and is dominant
at large scales. For mixed no-slip/stress-free and no-slip/no-slip boundaries,
Ekman friction is found to attenuate the efficiency of the upscale energy
transport and, unlike the case of stress-free boundaries, rapidly saturates the
barotropic kinetic energy. For no-slip/no-slip boundaries, Ekman friction is
strong enough to prevent the development of a coherent dipole vortex
condensate. Instead vortex pairs are found to be intermittent, varying in both
time and strength.Comment: 20 pages, 10 figure
Deep ocean influence on upper ocean baroclinic instability saturation
In this paper we extend earlier results regarding the effects of the lower
layer of the ocean (below the thermocline) on the baroclinic instability within
the upper layer (above the thermocline). We confront quasigeostrophic
baroclinic instability properties of a 2.5-layer model with those of a 3-layer
model with a very thick deep layer, which has been shown to predict spectral
instability for basic state parameters for which the 2.5-layer model predicts
nonlinear stability. We compute and compare maximum normal-mode perturbation
growth rates, as well as rigorous upper bounds on the nonlinear growth of
perturbations to unstable basic states, paying particular attention to the
region of basic state parameters where the stability properties of the 2.5- and
3-layer model differ substantially. We found that normal-mode perturbation
growth rates in the 3-layer model tend to maximize in this region. We also
found that the size of state space available for eddy-amplitude growth tends to
minimize in this same region. Moreover, we found that for a large spread of
parameter values in this region the latter size reduces to only a small
fraction of the total enstrophy of the system, thereby allowing us to make
assessments of the significance of the instabilities.Comment: To appear \emph{in} O. U. Velasco-Fuentes et al. (eds.),
\textit{Nonlinear Processes in Geophysical Fluid Dynamics}, Kluwer Academi
A simplified model of the Martian atmosphere - Part 1: a diagnostic analysis
In this paper we derive a reduced-order approximation to the vertical and horizontal structure of a simplified model of the baroclinically unstable Martian atmosphere. The original model uses the full hydrostatic primitive equations on a sphere, but has only highly simplified schemes to represent the detailed physics of the Martian atmosphere, e.g. forcing towards a plausible zonal mean temperature state using Newtonian cooling. Three different norms are used to monitor energy conversion processes in the model and are then compared. When four vertical modes (the barotropic and first three baroclinic modes) are retained in the reduced-order approximation, the correlation norm captures approximately 90% of the variance, while the kinetic energy and total energy norms capture approximately 83% and 78% of the kinetic and total energy respectively. We show that the leading order Proper Orthogonal Decomposition (POD) modes represent the dominant travelling waves in the baroclinically-unstable, winter hemisphere. In part 2 of our study we will develop a hierarchy of truncated POD-Galerkin expansions of the model equations using up to four vertical modes
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