Injection of a homogeneous fluid into a linearly stratified and rotating background fluid produced anticyclonic lenses which were studied for up to 600 rotation periods. Velocity measurements showed that the interior core rotates as a solid body with a decreasing, nearly axisymmetric exterior velocity field. Gill's (1981) model predicts well both the velocity and aspect ratio vs. Rossby number of the lenses. Lens decay occurred in two stages: symmetric rapid spin-down, with an associated half-life of ≈ 70 rotation periods followed by asymmetric shedding at a nearly constant core Rossby number, Ro ≈ 0.06.

Experiments on the radial propagation of axisymmetric free-surface solitary waves are reported and compared with theoretical and numerical solutions of the cylinderical Korteweg–de Vries (CKdV) equation. A new experimental technique to obtain a continuous amplitude signature on photographic paper is reported. These measurements show that an isolated disturbance evolves into a slowly varying solitary wave with amplitude decaying as $r^{-\frac{2}{3}}$, where r is the radius measured from the centre of the disturbance. A numerical study of the CKdV equation is made to interpret the transient development of these waves into the nonlinear asymptotic regime. It is further pointed out that the CKdV equation also describes weakly nonlinear axisymmetric internal waves, and a comparison of theory for this case with internal-wave trajectory measurements reported by Maxworthy (1980) exhibit good agreement.

Rigorous bounds are obtained on the mean normal displacement of vorticity or potential vorticity contours from their undisturbed parallel (or concentric) positions for incompressible planar flow, flow on the surface of a sphere, and three-dimensional quasi-geostrophic flow. It is required that the basic flows have monotonic distributions of vorticity, and it is this requirement that turns a particular linear combination of conserved quantities, a combination involving the linear or angular impulse and the areas enclosed by vorticity contours, into a norm when viewed in a certain hybrid Eulerian–Lagrangian set of coordinates. Liapunov stability theorems constraining the growth of finite-amplitude disturbances then follow merely from conservation of this norm. As a corollary, it is proved that arbitrarily steep, one-signed vorticity gradients are stable, including the limiting case of a circular patch of uniform vorticity.

Critical Rayleigh numbers, roll configurations, and growth-rate derivative are calculated at onset of convection for a rigid box with conducting upper and lower plates and insulating sidewalls. When the sidewalls form a square or a near square, the linearized Oberbeck–Boussinesq equations favour crossed rolls, a superposition of three-dimensional rolls in the x- and y-directions, over unidirectional rolls. These crossed rolls preserve the four-fold rotation symmetry about the vertical axis of a square box only when the aspect ratio (ratio of width to depth of the box) demands an even number of rolls in each direction. The analysis explains patterns observed by Stork & Müller.