  Turbulent motions due to flux-driven thermal convection is investigated by
numerical simulations and stochastic modelling. Tilting of convection cells
leads to the formation of sheared flows and quasi-periodic relaxation
oscillations for the energy integrals far from the threshold for linear
instability. The probability density function for the temperature and radial
velocity fluctuations in the fluid layer changes from a normal distribution at
the onset of turbulence to a distribution with an exponential tail for large
fluctuation amplitudes for strongly driven systems. The frequency power
spectral density has an exponential shape, which is a signature of
deterministic chaos. By use of a novel deconvolution method, this is shown to
result from the presence of Lorentzian pulses in the underlying time series,
demonstrating that exponential frequency spectra can persist in also in
turbulent flow regimes.
