Collection Nonlinear and stochastic methods in climate and geophysical fluid dynamics
Organizer(s)
Date(s)
20/04/2024
Unstable periodic orbits in atmospheric models: statistics, linear response, continuation and bifurcations
In this study, we investigate the sensitivity of the local attractor structure of a simple atmospheric model to the changes of system parameters – the strength of the forcing, friction coefficients and height of the orography. Using the continuation method we analyze the impact of the parameter perturbations onto the properties (period and unstable multipliers) of the unstable periodic orbits of the model and detect possible bifurcations in the phase space. We show that the period of the orbits and especially its instability characteristics (number of unstable directions, the value of unstable multipliers) exhibit nonlinear dependence on system parameters, 3% change of the orography and the forcing is sufficient to destroy the majority of the existing UPOs. This nonsmooth behavior of the microscopic structure of the attractor contradicts the observed linearity of the system's macroscopic statistical characteristics with respect to the changes of the system parameters.
