T - IfB

Example: Lorenz equationIs a simplified system of equations describing the 2-dimensional2flow of fluid of uniform depth in the presence of an imposedtemperature difference taking into account gravity, buoyancy,thermal diffusivity, and kinematic viscosity (friction).σ Prandtl number Rayleigh numberσ = 10 , = 8/3 is varied.Chaos for = 28.'y =σ y - y1 2 1'y = y ρ -y -y2 1 3 2'y = y y - βy3 1 2 3Edward Norton Lorenz(1963)appletC.Sparrow: „The Lorenz Equations: Bifurcations, Chaosand Strange Attractors“ (Springer Verlag, N.Y., 1982)107Example: Lorenz equationChaotic solutions of theLorenz equation exist andare not numerical artefacts(14th math problem of Smale).Warwick Tucker(2002)108