Hysteresis and metastability in the quenched turbulent dynamics of the complex Ginzburg-Landau equation.
We consider the quenched dynamics of the two-dimensional complex Ginzburg-Landau equation in its turbulent regime. We initialize the system in a frustrated state and observe how frustration affects the evolution towards the turbulent state. This process is performed for parameter values where, for random initial conditions, the system evolves into the turbulent state. We observe that the glassiness of the initial condition can inhibit the occurrence of the absolute instability close to the critical point for that instability in parameter space. Sufficiently far from the critical point, the turbulent state will develop, but only after spending considerable time in a transient metastable state of fixed vortex density. The parameter distance from the critical point is found to scale as an exponential of a power of the lifetime of the metastable state, and with a power exponent depending on the "depth" of the original quench. The limiting regimes of shallow and deep quench are identified by their respective values of the exponent, and the distinct mechanisms leading to the relaxation to turbulence in each case are highlighted.
Kevrekidis
P G
PG
Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Bishop
A R
AR
Rasmussen
K Ø
KØ