The inviscid compressible instability of columnar-vortex flows to three-dimensional perturbations with large wavenumbers is considered. The sufficient conditions for instability obtained are compared with recently published results for incompressible fluids.

A grid-generated, nearly isotropic turbulent flow was subjected to a spectrally local disturbance whose scale was close to but larger than the Kolmogorov scale. A nearly sinusoidal ripple in the velocity was introduced by placing a low-solidity screen of very fine wires (called a ‘zither’ by Kellogg & Corrsin 1980) downstream of a classical biplane grid. Measurements of the fluctuating velocity components normal to the screen wires show strong spatial oscillations of the second-order moments. Close to the screen the flow is quite inhomogeneous and anisotropic, but relaxes toward isotropy. After a short period of initial growth, the longitudinal one-dimensional spectrum E11(k1) exhibits an unusual decay behaviour, especially after the Reynolds stress created by the mean shear of the boundary layers and ‘laminar’ wakes of the screen wires has vanished. Bispectra and one-dimensional transfer terms do not show evidence of any preferred interaction between longitudinal wavenumbers, but an increased energy transfer to large wavenumbers is observed at small x1/d. The resulting increase of energy in the high-wavenumber end of the spectra is consistent with results of Townsend (1951). An energy budget downstream of the zither shows that the pressure–velocity correlations are important in the nonlinear interactions.

A nonlinear analysis of Bénard–Marangoni convection in a horizontal fluid layer of infinite extent is proposed. The nonlinear equations describing the fields of temperature and velocity are solved by using the Gorkov–Malkus–Veronis technique, which consists of developing the steady solution in terms of a small parameter measuring the deviation from the marginal state. This work generalizes an earlier paper by Schlüter, Lortz & Busse wherein only buoyancy-driven instabilities were handled. In the present work both buoyancy and temperature-dependent surface-tension effects are considered. The band of allowed steady states of convection near the onset of convection is determined as a function of the Marangoni number and the wavenumber. The influence of various dimensionless quantities like Rayleigh, Prandtl and Biot numbers is examined. Supercritical as well as subcritical zones of instability are displayed. It is found that hexagons are allowable flow patterns.