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Starting from the classical Saltzman 2D convection equations, we derive via asevere spectral truncation a minimal 10 ODE system which includes the thermaleffect of viscous dissipation. Neglecting this process leads to a dynamicalsystem which includes a decoupled (generalized) Lorenz system. Theconsideration of this process breaks an important symmetry, couples thedynamics of fast and slow variables, ensuing modifications of the structuralproperties of the attractor and of the spectral features. When the relevantnondimensional number (Eckert number Ec) is different from zero, the system isergodic and hyperbolic, the slow variables feature long term memory with 1/f3/2 power spectra, and the fast variables feature amplitude modulation on timescale of 1/Ec. Increasing the strength of the thermal-viscous feedback has astabilizing effect, as both the metric entropy and the Kaplan-Yorke attractordimension decrease monotonically with Ec. The analyzed system features veryrich dynamics: it overcomes some of the limitations of the Lorenz system andmight have prototypical value in relevant processes in complex systemsdynamics, such as the interaction between slow and fast variables. the presenceof long term memory and the associated extreme value statistics. Analysis showshow, neglecting the coupling of slow and fast variables only on the basis ofscale analysis can be catastrophic. In fact, this leads to spurious invariancesthat affect essential dynamical properties (ergodicity, hyperbolicity) and thatcause the model losing ability in describing intrinsically multiscaleprocesses.

Symmetry-break, mixing, instability, and low frequency variability in a minimal Lorenz-like system