MAL20

Many systems in nature are characterized by the coexistence of different stable states for a given set of environmental parameters and external forcing. Examples for such behavior can be found in different fields of science ranging from mechanical or chemical systems to ecosystem and climate dynamics. As a consequence of the coexistence of a multitude of stable states, the final state of the system depends strongly on the initial condition.  Perturbations, applied to those natural systems can lead to critical transitions from one stable state to another. Such critical transitions are called tipping phenomena in climate science, regime shifts in ecology. They can happen in various ways: (1) due to bifurcations, i.e. changes in the dynamics when external forcing or parameters are varied extremely slow, (2) due to fluctuations which are always inevitable in natural systems, (3) due to rate-induced transitions, i.e. when external forcing changes on characteristic time scales comparable to the intrinsic time scale of the considered dynamical system and (4) due to shocks or extreme events. We discuss these critical transitions and their characteristics and illustrate them with examples from climate science and ecosystem dynamics. Moreover, we discuss the concept of resilience, which has been originally introduced by C.S. Holling in ecology, and formulate it in terms of dynamical systems theory. This formulation offers mathematical and numerical tools to use it as a measure of the persistence of a function of a dynamical system.

How to cite: Feudel, U.: Tipping phenomena and resilience of complex systems: Theory and applications to the earth system, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-10567, https://doi.org/10.5194/egusphere-egu22-10567, 2022.

In 1963 Lorenz discovered what is usually known as “chaos”, that is the sensitive dependence of deterministic chaotic systems upon initial conditions. Since then, this concept has been strictly related to the notion of unpredictability pioneered by Lorenz. However, one of the most interesting and unknown facets of Lorenz ideas is that multiscale fluid flows could spontaneously lose their deterministic nature and become intrinsically random. This effect is radically different from chaos. Turbulent flows are the natural systems when Lorenz ideas can be touched by the hand. They can, indeed, be described via the Navier-Stokes equations, thus conforming to the class of deterministic dissipative systems, as well as, present rich dynamics originating from non-trivial energy fluxes in scale space, non-stationary forcings and geometrical constraints. This complexity appears via non-hyperbolic chaos, randomness, state-dependent persistence and predictability. All these features have prevented a full characterization of the underlying turbulent (stochastic) attractor, which will be the key object to unpin this complexity. 

Here we use a novel formalism to map unstable fixed points to singularities of turbulent flows and to trace the evolution of their structural characteristics when moving from small to large scales and vice versa, providing a full characterization of the attractor. We demonstrate that the properties of the dynamically invariant objects depend on the scale we are focusing on. Our results provide evidence that the large-scale properties of turbulent flows display universal statistical properties that are triggered by, but independent of specific physical properties at small scales. Given the changing nature of such attractors in time, space and scale spaces, we term them chameleon attractors.

How to cite: Alberti, T.: The geometry of scales: chameleon attractors, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-1090, https://doi.org/10.5194/egusphere-egu22-1090, 2022.