Transonic high-Reynolds-number flows through channels which are so narrow that the classical boundary-layer approach fails locally are considered in the presence of a weak stationary normal shock. As a consequence, the properties of the inviscid core and the viscosity-dominated boundary-layer region can no longer be determined in subsequent steps but have to be calculated simultaneously in a small interaction region. Under the requirement that the core-region flow should be considered to be one-dimensional to the leading order the resulting problem of shock–boundary-layer interaction is formulated by the means of matched asymptotic expansions for laminar flows of dense gases (Bethe–Zel'dovich–Thompson, or BZT, fluids). Such fluids have the distinguishing feature that the fundamental derivative of gas dynamics can become negative or even change sign under the thermodynamic conditions to be considered. The regularizing properties of the mechanism of viscous–inviscid interactions on the different anomalous shock forms possible in the flow of dense gases with mixed nonlinearity, namely rarefaction, sonic, double-sonic and split shocks, will be discussed. To this end we show the consistency of the resulting internal-shock profiles because of strong shock–boundary-layer interaction with a generalized shock admissibility criterion formulated for the case of purely inviscid flows. Representative solutions for the internal-shock structures are presented, and the importance of such flow phenomena in technical applications in the near future are shortly discussed by considering estimates of the actual dimensions of the interaction region for a specific representative situation in which the BZT fluid PP10 (C13F22) has been selected.

The linear stability of the incompressible axisymmetric flow in a buoyant-thermocapillary liquid pool is considered which is heated from above by a heat flux with a parabolic radial profile. Buoyancy forces and radial thermocapillary stresses due to the inhomogeneous surface temperature distribution drive a toroidal vortex. In the absence of buoyancy and for low Prandtl numbers the basic flow becomes unstable typically by a stationary centrifugal instability. At moderate Prandtl numbers the rotational symmetry is broken by hydrothermal waves. In the limit of vanishing Prandtl number two other critical modes are found if the pool is very shallow. One mode is a centrifugally destabilized rotating wave with high azimuthal wavenumber. The other mode is steady and it is driven by the deceleration of the radial inward return flow as it approaches the axis. The deceleration results from an entrainment of fluid into the thin layer of rapid radial outward surface flow. The centrifugal instability of the toroidal vortex flow is assisted by buoyancy in the low-Prandtl-number limit, because the cooling from the sidewall augments the thermocapillary driving. For moderately high Prandtl numbers a stable thermal stratification suppresses the hydrothermal-wave instabilities.

In Rainey (2009) incorrect files for figures 3 and 4 were published. The Publisher apologizes to the author and readers for this error. The correct figures (received 2 September 2009) are shown below.