  Three-dimensional (3D) hydrodynamic simulations of shell oxygen burning
(Meakin and Arnett, 2007b) exhibit bursty, recurrent fluctuations in turbulent
kinetic energy. These are shown to be due to a general instability of the
convective cell, requiring only a localized source of heating or cooling. Such
fluctuations are shown to be suppressed in simulations of stellar evolution
which use mixing-length theory (MLT).
  Quantitatively similar behavior occurs in the model of a convective roll
(cell) of Lorenz (1963), which is known to have a strange attractor that gives
rise to chaotic fluctuations in time of velocity and, as we show, luminosity.
Study of simulations suggests that the behavior of a Lorenz convective roll may
resemble that of a cell in convective flow. We examine some implications of
this simplest approximation, and suggest paths for improvement.
  Using the Lorenz model as representative of a convective cell, a
multiple-cell model of a convective layer gives total luminosity fluctuations
which are suggestive of irregular variables (red giants and supergiants
(Schwarzschild 1975)), and of the long secondary period feature in semi-regular
AGB variables (Stothers 2010, Wood, Olivier and Kawaler 2004). This
"tau-mechanism" is a new source for stellar variability, which is inherently
non-linear (unseen in linear stability analysis), and one closely related to
intermittency in turbulence. It was already implicit in the 3D global
simulations of Woodward, Porter and Jacobs (2003). This fluctuating behavior is
seen in extended 2D simulations of CNeOSi burning shells (Arnett and Meakin
2011b), and may cause instability which leads to eruptions in progenitors of
core collapse supernovae PRIOR to collapse.
