The analysis of the instabilities of convection rolls in a fluid layer heated from below with no-slip boundaries exhibits a close competition between various oscillatory modes in the range 2 [lsim ] P [lsim ] 12 of the Prandtl number P. In addition to the even-oscillatory instability known from earlier work two new instabilities have been found, each of which is responsible for a small section of the stability boundary of steady rolls. The most interesting property of the new instabilities is their close relationship to the hot-blob oscillations known from experimental studies of convection. In the lower half of the Prandtl-number range considered the B02-mode dominates, which is characterized by two blobs each of slightly hotter and colder fluid circulating around in the convection roll in a spatially and time-periodic fashion. At higher Prandtl numbers the BE 1-mode dominates, which possesses one hot blob (and one cold blob) circulating with the convection velocity. Just outside the stability boundary there exist other growing modes exhibiting three or four blobs which may be observable in experiments.

Surface skewness is a statistical measure of the vertical asymmetry of the air-sea interface – exemplified by the sharp crests and rounded troughs of surface gravity waves. Some authors have proposed a constant ratio between surface skewness and the ‘significant slope’ of the waves. Here it is shown theoretically that no such simple relation is to be expected.

Wave records are of at least two different types; Eulerian (as made with a fixed probe) or Lagrangian (as with a free-floating buoy). The corresponding statistical properties are examined. At first sight it might appear that the degree of skewness in corresponding records would be different. However it is shown that to lowest order the skewness is invariant; only the apparent mean level is different, at second order.