The oceans are looked on as a heat engine, and the points are made, firstly, that the effect operating this engine is modest, and, secondly, that the engine efficiency is extremely small. It is argued that a parameter, called the "thermal stiffness", generally increases when certain phenomena: new instabilities, turbulence, noise, etc., appear in thermodynamically forced systems. For the ocean system, this indicates that the temperature rise associated with the greenhouse effect may be overestimated in numerical ocean models which do not include, or do not properly resolve, such phenomena.

A new type of double-diffusive instability of the oscillatory type is predicted for a statically stable fluid layer with two components which have practically the same diffusivity (for example, two suitable types of salts in a molecular case, heat and salt in a case where mixing is due to small-scale turbulence). It is necessary that one component has the concentration value and the other the flux value fixed at the boundaries. A simple example is worked out in detail. The phenomenon should appear in a properly arranged laboratory experiment, and possibly in the oceans, when warmer, saltier water underlies a surface layer of colder, fresher water, and sufficient vertical turbulent mixing is present.

Limnology and OceanographyVolume 33, Issue 3 p. 488-488 Book ReviewFree Access Stommel, H. 1987. A view of the sea. Princeton University Press, Princeton, New Jersey. 165 p. $ 19.95. Pierre Welander, Pierre Welander School of Oceanography, WB-10 University of Washington SeattleSearch for more papers by this author Pierre Welander, Pierre Welander School of Oceanography, WB-10 University of Washington SeattleSearch for more papers by this author First published: May 1988 https://doi.org/10.4319/lo.1988.33.3.0488AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume33, Issue3May 1988Pages 488-488 RelatedInformation

A special three-dimensional solution of similarity type is given for a meridionally closed ocean with dynamic according to Stommel's classical transport model, and with the density determined by three-dimensional advection and vertical diffusion. The boundary current exhibits a rapidly varying scale depth; this depth becomes zero at a critical latitude where the current must separate. The solution requires an upwelling everywhere, to be balanced by abyssal sources of water and a deep circulation, as described by Stommel and Arons. It is proposed that a more general similarity form may be useful in future analytical as well as numerical studies of the ocean circulation.

Vagn Walfrid Ekman’s classical paper on the “spiral” (Ekman, 1905) is well known to the oceanographers, but his other contributions to the theory of the general oceanic circulation, several of which were written in German and Swedish, have escaped notice even of some experts in this field. The paper “Über Horizontalzirkulation bei windezeugten Meeresströmungen” (Ekman, 1923) gives, for the first time, a complete formulation of the problem of the steady wind-driven circulation in a homogeneous sea, when variable topography, bottom friction, and the βeffect are included. The final equation, when written in terms of a transport stream function, takes essentially the same form as the model equations of the oceanic circulation given later by Stommel1 (1948), which lead to the explanation of the westward intensification of ocean currents. Stommel, H. 1948. The westward intensification of wind driven ocean currents. Trans. Amer. Geophys. Un., 29, no. 2

Elementary Current, and defines the transport when the stratification is included (identical with the modern “mass transport”). He proceeds to consider the effects of precipitation and evaporation, and estimates the magnitude of the currents which these can provide, which he correctly finds to be negligibly small. In Section IV, he gives the complete set of field equations for the problem, in a form analogous to the ones found in his 1923 paper, but now with stratification included. Firstly, he deals with the problem in an ∫-plane, but later the β-effect is introduced. One can track down expressions that essentially reproduce the Sverdrup relation (see, for example, the formula just before eq. (33) in the following translation) for a case with no net divergence, stating that the meridional transport is proportional to curl T.

Rossby's (1936) wake stream theory of the Gulf Stream is revived and generalized. Including the β-effect, the volume transport of the Stream should increase faster than predicted by the Tollmien-Rossby formula, in agreement with observations. The idea that the Gulf Stream is forced by the pressure head in the Florida Straits, with the wind-stress curl at the higher latitude playing a secondary role, finds some support from observations.

A continuously stratified inertial boundary current in a β-plane possesses a similarity solution for the pressure of the formwhere A0(y), k0(y), z0(y) are arbitrary functions, n is an arbitrary constant. It can satisfy the condition u = 0 at x = 0, and be matched to a known interior solution (the thermocline solution of the power law type) but does not generally satisfy the condition w = 0 at z = 0.

The pressure along a closed hydrographic section can be correctly calculated from density data, in the ideal case of perfectly steady, geostrophic, density-conserving flow; and from dense, error-free data, excluding certain degenerate cues. A corresponding practical method, aimed at an estimate of the pressure from real hydrographic data, has been designed. The calculation is made by a minimization of the volume enclosed by the surface B = F(ro,P) in the P-ro-B space, where ro is the density. P = froz the potential vorticity, and B = B* + p0 the Bernoulli function, split in a known baroclinic part B* and an unknown pressure p0, defined at a chosen depth z0. The minimization is made under free variation of p0(s), as a function of the tangential coordinate s, the minimum volume is zero under the ideal conditions. Practically, one minimizes a moment rather than the volume, with identical results in the ideal case. The minimization requires an identification of “corresponding points” (endpoints of the same streamline) from the P-conservation; this may become impractical in the presence of strong noise. In such cases an alternative method based on an integral equation expressing the detailed flux balance of P and B is proposed.

A theoretical study is made of a simple mixed-layer model, in the form of a well-mixed constant-depth layer, forced from above by a heat flux kT(TA−T) and salinity flux kS(SA−S), where TA and SA are two reference values and T and S the temperature and salinity of the layer. The layer has a turbulent exchange of heat and salt with underlying water, kept at constant temperature and salinity, which is small in a statically stable case; large in a statically unstable case. If kT>kS, self-sustained oscillations may occur. In one cycle, a fast temperature rise, a slower salinity increase, and a final relaxation when the layer adjusts to the conditions of the underlying water, are observed.

An air-water system coupled by heat and stress is modelled by two interacting fluid loops. When heated from above and cooled from below the system can become unstable and self-sustained oscillations develop, whereas a single fluid system is stable in the same situation. The oscillations are explained by thermal lag between the loops. The water loop oscillates stably under its restoring buoyancy torque but the coresponding air oscillations, generated by heat conduction from the water loop, lag by roughly half a period, and the air stress therefore acts to amplify rather than damp oscillations in the water loop.

Some constraints resulting from a required overall vorticity balance in an ocean forced by a net wind-stress curl are considered. It is pointed out that the Sverdrup balance holds for Ekman-geostrophic flow in an area-averaged sense even in the presence of topography. It is suggested that nonlinear stretching and twisting of vorticity in an inertial boundary current may provide a source of vorticity which may balance a net wind-stress curl, without help of frictional effects at the bottom or sides. It is also suggested that potential vorticity generated by the wind-stress curl can be balanced by other local potential vorticity sources in the top layer. At this stage no proof for the need of bottom or side friction in a generally stratified ocean exists, and a counterexample is also lacking, leaving the question open for further studies.

A three-dimensional regime with a differentially heated mixed layer on top of an ideal fluid interior is considered in a situation which corresponds to the interior of the well-known wind-driven model by Stommel (1948). Although the transport field in this case is continuous and simple, the same is not necessarily true for the density and velocity fields: if the mixed layer is weakly coupled to the atmosphere a front is generated at the line of a maximum downwelling; another front is expected at the line of a zero downwelling.

A theoretical discussion is given of the thermal transients and self-sustained oscillations in a fluid, heated at a constant rate below the surface, and cooled from the top strongly enough to allow freezing. Assuming that the fluid is well mixed and that the thickness of the ice is small compared to the fluid depth, it is shown that the system can have zero, one, or two steady states. The ice-covered steady state is stable for small perturbations; however, the ice-free steady state may be unstable with the impulsive addition of a thin ice sheet. Transient developments may include both ice-covered and ice-free states. In the case where no steady state exists the system exhibits periodic self-sustained oscillations. Application of the theory to a laboratory experiment is considered.

In an experiment where a body of water is heated internally while it is cooled to freezing from above, self-sustained oscillations may appear with ice forming and disappearing periodically. Application to natural systems is being considered.

A previous theoretical study by Welander (1977) on a freshwater-ice oscillator is extended to the saltwater case. The system comprises a deep high-salinity, warm water reservoir (fixed temperature and salinity), and a shallow constant-depth mixed layer with temperature, salinity, and ice thickness varying in time. This layer is cooled by contact with overlaying air kept at a fixed, subzero temperature. The main new feature is the variation of the heat flux through the water interface with the stratification. This variation causes two new phenomena of interest: (a) “false” thermal adjustments to existing ice-covered steady states, and (b) multi-periodic self-sustained oscillations including both ice-covered and ice-free regimes. The usefulness of basic model studies of this type in connection with climate research is pointed out. DOI: 10.1111/j.2153-3490.1977.tb00757.x