[GTP] GTP Seminar May 16

[Silvia Gentile]

CLUSTER OF INTERACTING WAVE TRIADS IN
QG MODEL: QUADRATIC INVARIANTS
Sergey Nazarenko
Mathematics Institute
University of Warwick, UK
Thursday, May 16, 2013
Foothills Laboratory 2, Small Auditorium
Lecture at 10:30 am


We consider clusters of interconnected resonant triads arising from the 
QG model. A cluster consists of N modes forming a total of M connected
triads. We investigate the problem of constructing a linearly independent
set of quadratic constants of motion. We show that this problem is
equivalent to an underlying basic linear problem, consisting of finding the
null space of a rectangular M × N matrix A with entries 1, -1 and 0. In
particular, we prove that the number of independent quadratic invariants 
is equal to J ≡ N – M* ≥ N − M, where M∗ is the number of linearly
independent rows in A. We formulate an algorithm for decomposing large
clusters of complicated topology into smaller ones and show how various
invariants are related to certain parts and linking types of a cluster,
including the basic structures leading to M* < M.



-- 
Silvia Gentile
NCAR IMAGe
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Boulder, CO 80305
303 497 2480
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