Peter G. Baines

On internal tide generation models

This paper discusses linear generation models for internal tides over large topographic features such as continental slopes, with the objects of making the procedures simpler and more adaptable to oceanic situations than heretofore, providing a unified summary of the mechanics involved, and estimating the global internal tide energy generation at all continental shelf-slope junctions for M2 and S2 frequencies. A ‘composite model’ involving wave generation on a shallow thermocline as well as on the continuously stratified fluid below is developed, together with a discussion of the approximations required. The simple case of a linear slope is discussed in detail; one conclusion is that linear internal tides generated on a shallow thermocline will be small unless T = hL/Lα < 2, where hL is the total depth on the continental shelf, 2πL is a representative wavelength (typically 20 to 30 km) and α is the slope of the continental slope. Such waves propagating seawards are expected to ‘leak’ into the deeper stratified water in one or two wavelengths, whilst those propagating shorewards on the shelf may steepen to form undular bores. The composite model has been applied to all relevant regions of coastline, and the five areas with the largest internal tidal energy production are the European northwest shelf, the East and South China seas, the Guiana Basin region, the Australian northwest shelf, and the Gulf of Maine-Grand Banks region. The summed global barotropic to baroclinic tidal energy conversions by this process in the coastal regions are estimated to be 1.45 × 1010 J s−1 for M2 and 2.73 × 109 J s−1 for S2, on an annual mean basis.

On thermohaline convection with linear gradients

The thermohaline stability problem previously treated by Stern, Walin and Veronis is examined in greater detail. An error in an earlier paper is corrected and some new calculations made. It is shown, for instance, that direct convection can occur for thermal Rayleigh number R much less than 100 R s when R s [gsim ] 0·1, where R s is the salinity Rayleigh number. A graphical presentation is devised to show the relative importance of the different terms in the equations of motion as a function of R and R s . The most unstable mode over all wave-numbers for each R , R s is found and it is shown that where both unstable direct and oscillating modes are present, the most unstable mode is direct in most cases.

Decadal to multidecadal variability and the climate change background

(1) Three prominent quasi-global patterns of variability and change are observed using the Met Offices sea surface temperature (SST) analysis and almost independent night marine air temperature analysis. The first is a global warming signal that is very highly correlated with global mean SST. The second is a decadal to multidecadal fluctuation with some geographical similarity to the El Nino-Southern Oscillation (ENSO). It is associated with the Pacific Decadal Oscillation (PDO), and its Pacific-wide manifestation has been termed the Interdecadal Pacific Oscillation (IPO). We present model investigations of the relationship between the IPO and ENSO. The third mode is an interhemispheric variation on multidecadal timescales which, in view of climate model experiments, is likely to be at least partly due to natural variations in the thermohaline circulation. Observed climatic impacts of this mode also appear in model simulations. Smaller-scale, regional atmospheric phenomena also affect climate on decadal to interdecadal timescales. We concentrate on one such mode, the winter North Atlantic Oscillation (NAO). This shows strong decadal to interdecadal variability and a correspondingly strong influence on surface climate variability which is largely additional to the effects of recent regional anthropogenic climate change. The winter NAO is likely influenced by both SST forcing and stratospheric variability. A full understanding of decadal changes in the NAO and European winter climate may require a detailed representation of the stratosphere that is hitherto missing in the major climate models used to study climate change.

The generation of internal tides by flat-bump topography

Abstract A general procedure for the calculation of the oceanic internal tides generated by the interaction of the surface tide with bottom topography is derived, and applied to typical cases. The formalism is restricted here to essentially two-dimensional topography whose surface is never tangential to the local direction of internal tidal energy propagation, but has otherwise arbitrary shape. The theory is applicable to a wide range of density stratifications which permits a two-parameter fit to any oceanic case. Results have been calculated for certain representative topographic shapes, most notably continental slopes, and these indicate that the rate of conversion of surface tide energy into internal tide energy generally increases rapidly with topographic height, but also depends strongly on the geometry. For instance, for this model, continental slopes are far more effective internal tide generators than, say, the Mid-Atlantic Ridge. For a model ocean with constant Brunt-Vaisala frequency, N, the internal wave energy fluxes on each side of a continental slope (satisfying the above criteria) are approximately equal, but for an ocean with a realistic density profile the energy flux and energy density are larger on the shallow continental shelf than in the deep ocean.

A unified description of two-layer flow over topography

Observations of the flow of a two-layer fluid resulting from the motion of a towed streamlined two-dimensional obstacle are described in some detail. The experiments were designed to further our understanding of the factors governing the nature and magnitude of upstream disturbances in the general flow of stratified fluid over two-dimensional topography, and predictions for arbitrary two-dimensional flows are made from the results of these experiments. In particular, the relationship between uniformly stratified flow and single-layer flow over topography is suggested. Most of the observed features of interest in these experiments are nonlinear in character. Relatively complete descriptions of the observed flows are presented over a wide range of parameter values, and the phenomena observed include upstream undular and turbulent bores, bores with zero energy loss, ‘rarefactions’ (in which the interface height changes monotonically over a transition region of continuously increasing length), and downstream hydraulic drops and jumps. Their properties are shown to be broadly consistent with predictions from a two-layer hydrostatic model based on continuity and momentum considerations, which employs jump criteria and rarefaction equations where appropriate. Bores occur because of nonlinear steepening when the layer containing the obstacle is thinner than the other, and rarefactions occur when this layer thickness is comparable with or greater than that of the other layer. The speed and amplitude of the upstream bores are governed by nonlinear effects, but their character is determined by a balance between nonlinear steepening, wave dispersion and interfacial friction when the bore is non-turbulent. Experimental evidence is presented for two types of hysteresis or ‘multiple equilibria’ - situations where two different flow states may exist for the same external steady conditions. In the first of these hysteresis types, the upstream flow may be supercritical or consist of an upstream bore state. It is analogous to the type anticipated for single-layer flow by Baines & Davies (1980) and described numerically by Pratt (1983), but it is only found experimentally for part of the expected parameter range, apparently because of interfacial stress effects. The second hysteresis type is new, and involves the presence or absence of a downstream hydraulic drop and following jump.

Evidence for a Rapid Global Climate Shift across the Late 1960s

Abstract It is shown that a number of important characteristics of the global atmospheric circulation and climate changed in a near-monotonic fashion over the decade, or less, centered on the late 1960s. These changes were largest or commonest in tropical regions, the Southern Hemisphere, and the Atlantic sector of the Northern Hemisphere. Some, such as the decrease in rainfall in the African Sahel, are well known. Others appear to be new, but their combined extent is global and dynamical linkages between them are evident. The list of affected variables includes patterns of SST; tropical rainfall in the African Sahel and Sudan, the Amazon basin, and northeast Brazil; pressure and SST in the tropical North Atlantic and the west and central Pacific; various branches of the southern Hadley circulation and the southern subtropical jet stream; the summer North Atlantic Oscillation; south Greenland temperature; the Southern Hemisphere storm track; and, quite likely, the Antarctic sea ice boundary. These changes...

Mixing in flows down gentle slopes into stratified environments

Observations of the flow of dense fluid into uniformly density-stratified environments down plane slopes with small inclination to the horizontal ([les ] 20°) are described, and a quantitative model for such flows is presented. In these experiments the dense fluid is released at the top of the slope for a finite period of time. The resulting downslope gravity current, or downflow, has uniform thickness with a distinct upper boundary, until it approaches its level of neutral density where the fluid leaves the proximity of the slope. Turbulent transfers of mass and momentum occur across the upper boundary, causing a continuous loss of fluid from the downflow in most cases, and associated loss of momentum. The flow may be characterized by the local values of the Richardson number Ri , the Reynolds number Re (generally large), and of M = QN 3 / g ′ 2 , where Q is the (two-dimensional) volume flux, N the buoyancy frequency and g ′ the (negative) buoyancy of the dense fluid. The model for the downflow describes the turbulent transfers in terms of entrainment, detrainment and drag coefficients, E e , E d and k respectively, and the observations enable the determination of these coefficients in terms of the local values of M and Ri . The model may be regarded as an extension of that Ellison & Turner (1959) to stratified environments, describing the consequent substantial changes in mixing and distribution of the inflow. It permits the modelling of the bulk properties of these flows in geophysical situations, including shallow and deep flows in the ocean.

The generation of internal tides over steep continental slopes

A numerical procedure is presented for the calculation of internal tides generated by the interaction of surface tide with bottom topography which is tangent to the direction of internal tidal energy propagation at some depth. This procedure, together with that of Baines (1973), permits the calculation of internal tides generated by (virtually) arbitrary topography with horizontal scale greater than 1 km, and a wide range of realistic density stratifications. The procedure is applied to continental slopes with simple linear and quartercircle profiles, and constant stratification. For these cases, the largest internal tidal velocities and energy densities occur in regions around characteristics emanating from the tangential corner point; on the shallow shelf side the energy flux is a maximum in this region, but on the deep side it is a minimum and is distributed more evenly with depth. The total energy flux is greater than the maximum for flat-bump topography of comparable height by a factor of order 2-3. It increases nearly exponentially with height but is less sensitive to shape provided the slope is greater than critical, and is greater on the deep than on the shallow side by a factor of order 10. Calculations for more realistic density stratifications yield similar results. The procedure is also applied to a real continental slope for which observations have been made by Wunsch & Hendry (1972), with stratification representing summer and winter conditions. The velocity fields and associated energy fluxes differ significantly from those of simple geometries, and are also sensitive to the seasonal density changes in the upper 50 m. It is suggested that internal tidal generation will give rise to two mixing processes, one associated with the boundary layer near the tangent point and the other with shear instability in the velocity profile. Instability of the theoretical profiles according to the Richardson number criterion may be readily achieved in oceanic conditions. The reflexion of an internal wave from a concave corner is discussed in an appendix, where it is shown that no singularities occur unless the radius of curvature is very large.

On the mechanism of shear flow instabilities

In homogeneous and density-stratified inviscid shear flows, the mechanism for instability that is most commonly invoked and discussed is Kelvin–Helmholtz instability, as it occurs for a simple velocity discontinuity. There is a second mechanism, the wave-interaction mechanism, which is much more general, and is the subject of this paper. This mechanism depends on two free waves that propagate in opposite directions in a stratified shear flow, and which may become stationary relative to each other because of the shear. If this occurs, and their relative phase is suitably chosen, the velocity field of each wave increases the displacement of the other, and so the disturbance grows.We show that this mechanism is responsible for instability in a general class of symmetric but otherwise arbitrary velocity and density profiles, provided that the Richardson number Ri ¼ everywhere, the flow is stable because the free waves described above are absorbed by the critical layer, and hence are heavily damped. The necessary criteria of Rayleigh and Fjortoft for instability in homogeneous fluid are seen to provide a suitable geometry for two interacting waves. Some specific examples are given, including a succinct explanation of Holmboe waves.

Eddy formation by dense flows on slopes in a rotating fluid

Properties of the flow generated by a continuous source of dense fluid on a slope in a rotating system are investigated with a variety of laboratory experiments. The dense fluid may initially flow down the slope but it turns (under the influence of rotation) to flow along the slope, and initial geostrophic adjustment gives it an anticyclonic velocity profile. Some of the dense fluid drains downslope in a viscous Ekman layer, which may become unstable to growing waves. Provided that the viscous draining is not too strong, cyclonic vortices form periodically in the upper layer and the dense flow breaks up into a series of domes. Three processes may contribute to the formation of these eddies. First, initial downslope flow of the dense current may stretch columns of ambient fluid by the ‘Taylor column’ process (which we term ‘capture’). Secondly, the initial geostrophic adjustment implies lower-layer collapse which may stretch the fluid column, and thirdly, viscous drainage will progressively stretch and spin up a captured water column. Overall this last process may be the most significant, but viscous drainage has contradictory effects, in that it progressively removes dense lower-layer fluid which terminates the process when the layer thickness approaches that of the Ekman layer. The eddies produced propagate along the slope owing to the combined effects of buoyancy–Coriolis balance and ‘beta-gyres’. This removes fluid from the vicinity of the source and causes the cycle to repeat. The vorticity of the upper-layer cyclones increases linearly with Γ = L α/ D (where L is the Rossby deformation radius, α the bottom slope and D the total depth), reaching approximately 2 f in the experiments presented here. The frequency at which the eddy/dome structures are produced also increases with Γ , while the speed at which the structures propagate along the slope is reduced by viscous effects. The flow of dense fluid on slopes is a very important part of the global ocean circulation system and the implications of the laboratory experiments for oceanographic flows are discussed.