The aim of this contribution is to survey a relatively new form of convection, which is very easy to investigate in the laboratory, plays an important role in the oceans and many chemical engineering situations and is likely to prove essential in the understanding of some areas of stellar convection. Thermosolutal convection (or double-diffusive convection as it is often called) owes its existence to the presence of two components of different molecular diffusivities which contribute in an opposing sense to the locally vertical density gradient.

The possible role that β-decays may play in stellar collapse was first discussed by Gamow and Schoenberg (1940, 1941). The above authors proposed this mechanism a mean of extracting quickly the energy content of the star and transporting it outside. In this way they hypothesized that stellar collapse may proceed.

Convection under the influence of dynamically significant radiation fields occurs routinely in hot stars (Underhill 1949 ab) and probably also in a variety of other objects near the Eddington limit (Joss, Salpeter, and Ostriker 1973). Yet this topic, which is here called photoconvection, has not been actively investigated prior to the present decade. Except for limiting cases, the stability condition does not seem to have been worked out and only some preliminary notions exist about the highly unstable case. This is somewhat surprising since it has long been suspected that some of the vigorous dynamical activity observed in hot stars (Huang and Struve 1960, Reimers 1976) is caused by radiative forces (Underhill 1949 ab). In the hope that this neglect may be compensated for by the application of some of the techniques described at this meeting, I shall sketch some of the main features of this topic.

The evolution of a star through the helium flash depends upon uncertain aspects of convection theory. Observations place some constraints on the theory of convection in stellar cores.

Momentum and energy transport by buoyancy-Coriolis waves is illustrated by means of a simple model example. The need for careful consideration of a complete problem for mean-flow evolution is emphasised, especially when moving media are involved. Then a recent generalisation of the wave-action and pseudomomentum concepts is introduced, and used to exhibit in a very general way the roles of wave dissipation, forcing, or transience in the mean flow problem, for a certain class of ‘nearly-unidirectional’ mean flows. This class includes differentially-rotating stellar interiors, which could well be systematically changed by wave transport of angular momentum. Similar results hold for MHD and self-gravitating fluids. Finally the physical distinction between momentum and pseudomomentum is discussed.

Wave generation processes are classified in (1) strong and (2) weak, and (a) spontaneous and (b) stimulated processes. Then, the case (2b) operating in convective zones is discussed in detail. Both the dynamical and the thermodynamical coupling between pulsation and convection are formulated by use of the diffusion approximation for the turbulent convection. A mixing length variable with time is thereby introduced. The work integral is transformed so that each of its terms can reveal the mechanism responsible for the stellar stability. An important destabilizing mechanism associated with the convective flux is found to exist among other known mechanisms. The mechanical work is shown to be rather important.

Turbulence is usually associated with the idea of chaos, i.e. erratic behaviour of some observable quantity. Let me stress that there are at least two different kinds of chaos.

After the article of Ruelle and Takens, there has been recently much interest in the problem of the “onset of turbulence”. That is, instead of trying to understand the structure of a well established turbulence flow, one studies the way in which a flow “jumps” from a quiet stable laminar state to a turbulent state when its Reynolds (or Rayleigh) number increases.