60 research outputs found
Rapidly rotating plane layer convection with zonal flow
The onset of convection in a rapidly rotating layer in which a thermal wind
is present is studied. Diffusive effects are included. The main motivation is
from convection in planetary interiors, where thermal winds are expected due to
temperature variations on the core-mantle boundary. The system admits both
convective instability and baroclinic instability. We find a smooth transition
between the two types of modes, and investigate where the transition region
between the two types of instability occurs in parameter space. The thermal
wind helps to destabilise the convective modes. Baroclinic instability can
occur when the applied vertical temperature gradient is stable, and the
critical Rayleigh number is then negative. Long wavelength modes are the first
to become unstable. Asymptotic analysis is possible for the transition region
and also for long wavelength instabilities, and the results agree well with our
numerical solutions. We also investigate how the instabilities in this system
relate to the classical baroclinic instability in the Eady problem. We conclude
by noting that baroclinic instabilities in the Earth's core arising from
heterogeneity in the lower mantle could possibly drive a dynamo even if the
Earth's core were stably stratified and so not convecting.Comment: 20 pages, 7 figure
A two-fluid single-column model of the dry, shear-free, convective boundary layer
This is the final version. Available on open access from Wiley via the DOI in this record.A single-column model of the dry, shear-free, convective boundary layer is presented
in which nonlocal transports by coherent structures such as thermals are represented
by the partitioning of the fluid into two components, updraft and environment, each
with a full set of prognostic dynamical equations. Local eddy diffusive transport and
entrainment and detrainment are represented by parameterizations similar to those
used in Eddy Diffusivity Mass Flux schemes. The inclusion of vertical diffusion of the
vertical velocity is shown to be important for suppressing an instability inherent in the
governing equations. A semi-implicit semi-Lagrangian numerical solution method is
presented and shown to be stable for large acoustic and diffusive Courant numbers,
though it becomes unstable for large advective Courant numbers. The solutions are
able to capture key physical features of the dry convective boundary layer. Some of the
numerical challenges posed by sharp features in the solution are discussed, and areas
where the model could be improved are highlighted.Natural Environment Research Council (NERC
Large time behavior and asymptotic stability of the two-dimensional Euler and linearized Euler equations
We study the asymptotic behavior and the asymptotic stability of the
two-dimensional Euler equations and of the two-dimensional linearized Euler
equations close to parallel flows. We focus on spectrally stable jet profiles
with stationary streamlines such that , a case that
has not been studied previously. We describe a new dynamical phenomenon: the
depletion of the vorticity at the stationary streamlines. An unexpected
consequence, is that the velocity decays for large times with power laws,
similarly to what happens in the case of the Orr mechanism for base flows
without stationary streamlines. The asymptotic behaviors of velocity and the
asymptotic profiles of vorticity are theoretically predicted and compared with
direct numerical simulations. We argue on the asymptotic stability of these
flow velocities even in the absence of any dissipative mechanisms.Comment: To be published in Physica D, nonlinear phenomena (accepted January
2010
Asymptotic stability of solitary waves
We show that the family of solitary waves (1-solitons) of the Korteweg-de Vries equation is asymptotically stable. Our methods also apply for the solitary waves of a class of generalized Korteweg-de Vries equations, In particular, we study the case where f(u)=u p+1 / (p+1) , p =1, 2, 3 (and 30, with f ∈ C 4 ). The same asymptotic stability result for KdV is also proved for the case p =2 (the modified Korteweg-de Vries equation). We also prove asymptotic stability for the family of solitary waves for all but a finite number of values of p between 3 and 4. (The solitary waves are known to undergo a transition from stability to instability as the parameter p increases beyond the critical value p =4.) The solution is decomposed into a modulating solitary wave, with time-varying speed c(t) and phase γ( t ) ( bound state part ), and an infinite dimensional perturbation ( radiating part ). The perturbation is shown to decay exponentially in time, in a local sense relative to a frame moving with the solitary wave. As p →4 − , the local decay or radiation rate decreases due to the presence of a resonance pole associated with the linearized evolution equation for solitary wave perturbations.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46489/1/220_2005_Article_BF02101705.pd
Organizing to support internal diversification
http://deepblue.lib.umich.edu/bitstream/2027.42/35563/2/b140717x.0001.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/35563/1/b140717x.0001.001.tx
Minimally Invasive Spinal Surgery with Intraoperative Image-Guided Navigation
We present our perioperative minimally invasive spine surgery technique using intraoperative computed tomography image-guided navigation for the treatment of various lumbar spine pathologies. We present an illustrative case of a patient undergoing minimally invasive percutaneous posterior spinal fusion assisted by the O-arm system with navigation. We discuss the literature and the advantages of the technique over fluoroscopic imaging methods: lower occupational radiation exposure for operative room personnel, reduced need for postoperative imaging, and decreased revision rates. Most importantly, we demonstrate that use of intraoperative cone beam CT image-guided navigation has been reported to increase accuracy
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