|
||
|
|
Research Interests
I'm currently
devoted to the following research efforts:
Lagrangian
ocean and atmosphere dynamics. The focus of this effort is applications of
nonintegrable Hamiltonian systems to problems in geophysical fluid dynamics.
The principal mathematical tools applied in this effort are results relating to
Kolmogorov-Arnold-Moser theory (which addresses the stability of Hamiltonian
systems under perturbation) and results relating to the structure of stable and
unstable manifolds of hyperbolic trajectories in unsteady flows. These
manifolds are often referred to as Lagrangian coherent structures, or LCSs, in
fluid dynamical applications. Specific applications which are being considered
include: (a) biological applications of oceanic LCSs including problems
involving harmful algal blooms, plankton patchiness, and understanding observed
biogeographical boundaries; (b) the connection between LCSs and the predominant
Eulerian features of the general ocean circulation; (c) the connections between
jets, transport barriers and potential vorticity barriers in the ocean and
stratosphere; and (d) assessing the
impact of high-resolution wide-swath altimetry on the determination of the
surface ocean Lagrangian circulation. Collaborators in this effort are: F. Beron-Vera and M.
Brown (RSMAS/AMP); H. Koçak (Computer Science); L. Brand (RSMAS/MBF); and G.
Goni (NOAA/AOML).
|
|
Strong
KAM Stability in Planetary Atmospheres |
Observed vs simulated 2004 HAB on theWest Florida Shelf Figure adapted from Hu et al. (2005)
and Olascoaga et al. (2008). |
Jupiter’s
weather layer (Cassini data) |
MERHAB 2009 Monitoring harmful algal Blooms on the
West Florida Shelf using Lagrangian coherent structures
We propose to thoroughly test a
methodology that takes into account often overlooked e_ects of Lagrangian ocean
circulation to help improving the detection, tracking, and forecasting of
harmful algal blooms (HABs) on the West Florida (WFS), where the largest and
most frequent HABs caused by the toxic dinoagellate Karenia brevis tend to
occur. The West Coast Governor's Agreement on Ocean Health and the Gulf of Mexico
Alliance has identified HABs in the Gulf of Mexico as a priority issue; the proposed
effort responds to this concern. The basis for the proposed methodology are
ideas borrowed from the field of dynamical systems. More specifically, ideas
that relate to the theory of Lagrangian coherent structures (or LCSs). Roughly
speaking, LCSs are distinguished material fluid curves (i.e., curves composed
always of the same elementary uid elements or particles) which completely
determine the fate of passively advected tracers. The proposers have recently
demonstrated that LCSs can: (i) unveil low mixing regions where HAB development
is favored; and (ii) delineate potential pathways for HAB evolution. The
proposed activity consists in systematically exploiting these two fundamentally
important properties of LCSs, concurrently with population dynamics simulations,
to track the evolution of HABs detected using satellite imagery and in-situ
measurements. During the planned testing activity the proposed tool will be
distributed as a beta product by the NOAA CoastWatch Project to complement
currently distributed products by this program. Satellite imagery for the
planned testing activity will be available through the RSMAS Remote Sensing
Group. In-situ K. brevis sampling will be available as the result of _ve
oceanographic cruises to the WFS, which are funded by the RSMAS Ocean and Human
Health Center through an NSF grant and will be carried out during 2010-2011.
Additional in-situ K. brevis observations are planned to be obtained using a
45-ft boat. The K. brevis survey using the 45-ft boat will be carried out as
frequently as possible each time bloom activity is detected in satellite imagery
for ground-trusting.
Baroclinic
instability saturation. This effort centers on the application of results
relating to the stability of generalized Hamiltonian systems to the problem of baroclinic
instability in the ocean. Such results allow to set a priori bounds on the
amplitude of baroclinic instability waves, which play a critical role in
providing controls for mixed-layer restratification and deep-ocean convection.
By means of low order and fully nonlinear numerical simulations, I'm currently
investigating the accuracy of the aforementioned bounds and their utility in
constructing eddy closures. This effort is being carried out in collaboration
with F. Beron-Vera (RSMAS/AMP).
If you
are interested in pursuing graduate studies at RSMAS in any of these areas
there are opportunities within the group.
Teaching
RSM
671: Lagrangian Fluid
Dynamics and Predictability
Personal



Last update: 21 October 2009.