Planetary or Rossby waves are the predominant way in which the ocean adjusts on long (year to decade) timescales. The motion of long planetary waves is westward, at speeds Ն1 cm s Ϫ1. Until recently, very few experimental investigations of such waves were possible because of scarce data. The advent of satellite altimetry has changed the situation considerably. Curiously, the speeds of planetary waves observed by TOPEX/Poseidon are mainly faster than those given by standard linear theory. This paper examines why this should be. It is argued that the major changes to the unperturbed wave speed will be caused by the presence of baroclinic eastwest mean flows, which modify the potential vorticity gradient. Long linear perturbations to such flow satisfy a simple eigenvalue problem (related directly to standard quasigeostrophic theory). Solutions are mostly real, though a few are complex. In simple situations approximate solutions can be obtained analytically. Using archive data, the global problem is treated. Phase speeds similar to those observed are found in most areas, although in the Southern Hemisphere an underestimate of speed by the theory remains. Thus, the presence of baroclinic mean flow is sufficient to account for the majority of the observed speeds. It is shown that phase speed changes are produced mainly by (vertical) mode-2 east-west velocities, with mode-1 having little or no effect. Inclusion of the mean barotropic flow from a global eddy-admitting model makes only a small modification to the fit with observations; whether the fit is improved is equivocal.

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A brief discussion of, and a little speculation about, the relevance of the polar regions on climate is given. The main body of the paper gives a survey of the known deep convection areas of the world ocean. There are two distinct types of convection. The first is the classic sinking occurring on continental shelf slope systems, as typified by various locations around the Antarctic coast. The freezing of sea ice, and resulting brine ejection, creates dense salty water on the shelf which descends the slope under a balance of Coriolis, gravity, and frictional forces, entraining the surrounding warm deep water as it goes. The second process is the more recently observed open‐ocean convection, occurring in locations such as the Mediterranean, the Labrador Sea, and two locations in the Weddell gyre, and is hypothesized to occur in the Greenland Sea. Open‐ocean convection has many overall similarities in all these areas: it occurs in narrow (20–50 km) areas; it forms about 10 m³ s−l of deep water; it occurs only in regions of cyclonic mean circulation; more than one water mass in the mean circulation is involved; a preconditioning seems to be required; some surface forcing (cooling or sea ice formation) is necessary; a violent breakup of the water mass frequently occurs on time scales of 2 weeks.

A systematic intercomparison of three realistic eddy-permitting models of the North Atlantic circulation has been performed. The models use different concepts for the discretization of the vertical coordinate, namely geopotential levels, isopycnal layers, terrain-following (sigma) coordinates, respectively. Although these models were integrated under nearly identical conditions, the resulting large-scale model circulations show substantial differences. The results demonstrate that the large-scale thermohaline circulation is very sensitive to the model representation of certain localised processes, in particular to the amount and water mass properties of the overflow across the Greenland-Scotland region, to the amount of mixing within a few hundred kilometers south of the sills, and to several other processes at small or sub-grid scales. The different behaviour of the three models can to a large extent be explained as a consequence of the different model representation of these processes. 

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The Stewartson–Warn–Warn (SWW) solution for the time evolution of an inviscid, nonlinear Rossby-wave critical layer, which predicts that the critical layer will alternate between absorbing and over-reflecting states as time goes on, is shown to be hydrodynamically unstable. The instability is a two-dimensional shear instability, owing its existence to a local reversal of the cross-stream absolute vorticity gradient within the long, thin Kelvin cat's eyes of the SWW streamline pattern. The unstable condition first develops while the critical layer is still an absorber, well before the first over-reflecting stage is reached. The exponentially growing modes have a two-scale cross-stream structure like that of the basic SWW solution. They are found analytically using the method of matched asymptotic expansions, enabling the problem to be reduced to a transcendental equation for the complex eigenvalue. Growth rates are of the order of the inner vorticity scale δq, i.e. the initial absolute vorticity gradient dq0/dy times the critical-layer width scale. This is much faster than the time evolution of the SWW solution itself, albeit much slower than the shear rate du0/dy of the basic flow. Nonlinear saturation of the growing instability is expected to take place in a central region of width comparable to the width of the SWW cat's-eye pattern, probably leading to chaotic motion there, with very large ‘eddy-viscosity’ values. Those values correspond to critical-layer Reynolds numbers δ−1 [Lt ] 1, suggesting that for most initial conditions the time evolution of the critical layer will depart drastically from that predicted by the SWW solution. A companion paper (Haynes 1985) establishes that the instability can, indeed, grow to large enough amplitudes for this to happen.The simplest way in which the instability could affect the time evolution of the critical layer would be to prevent or reduce the oscillations between over-reflecting and absorbing states which, according to the SWW solution, follow the first onset of perfect reflection. The possibility that absorption (or over-reflection) might be prolonged indefinitely is ruled out, in many cases of interest (even if the ‘eddy viscosity’ is large), by the existence of a rigorous, general upper bound on the magnitude of the time-integrated absorptivity α(t). The bound is uniformly valid for all time t. The absorptivity α(t) is defined as the integral over all past t of the jump in the wave-induced Reynolds stress across the critical layer. In typical cases the bound implies that, no matter how large t may become, |α(t)| cannot greatly exceed the rate of absorption predicted by linear theory multiplied by the timescale on which linear theory breaks down, say the time for the cat's-eye flow to twist up the absolute vorticity contours by about half a turn. An alternative statement is that |α(t)| cannot greatly exceed the initial absolute vorticity gradient dq0/dy times the cube of the widthscale of the critical layer. In typical cases, therefore, a brief answer to the qu...

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