Characterization of the domain chaos convection state by the largest Lyapunov exponent

Using numerical integrations of the Boussinesq equations in rotating cylindrical domains with realistic boundary conditions, we have computed the value of the largest Lyapunov exponent lambda(1) for a variety of aspect ratios and driving strengths. We study in particular the domain chaos state, which bifurcates supercritically from the conducting fluid state and involves extended propagating fronts as well as point defects. We compare our results with those from Egolf , [Nature 404, 733 (2000)], who suggested that the value of lambda(1) for the spiral defect chaos state of a convecting fluid was determined primarily by bursts of instability arising from short-lived, spatially localized dislocation nucleation events. We also show that the quantity lambda(1) is not intensive for aspect ratios Gamma over the range 20 <Gamma < 40 and that the scaling exponent of lambda(1) near onset is consistent with the value predicted by the amplitude equation formalism.