A three-mode nonlinear slow-fast system with fast forcing is studied here as a model
for filtering turbulent signals from partial observations. The model describes the interaction of two
externally driven fast modes with a slow mode through catalytic nonlinear coupling. The special
structure of the nonlinear interaction allows for the analytical solution for the first and second order
statistics even with fast forcing. These formulas are used for testing the exact Nonlinear Extended
Kalman Filter for the slow-fast system with fast forcing. Various practical questions such as the
influence of the strong fast forcing on the slowly varying wave envelope, the role of observations, the
frequency and variance of observations, and the model error due to linearization are addressed here.
Publié le : 2010-03-15
Classification:
Nonlinear model,
slow-fast system,
extended Kalman filter,
fast forcing,
34A05,
93E11
@article{1266935014,
author = {Gershgorin, Boris and Majda, Andrew},
title = {Filtering a nonlinear slow-fast system with strong fast forcing},
journal = {Commun. Math. Sci.},
volume = {8},
number = {1},
year = {2010},
pages = { 67-92},
language = {en},
url = {http://dml.mathdoc.fr/item/1266935014}
}
Gershgorin, Boris; Majda, Andrew. Filtering a nonlinear slow-fast system with strong fast forcing. Commun. Math. Sci., Tome 8 (2010) no. 1, pp. 67-92. http://gdmltest.u-ga.fr/item/1266935014/