The Arctic represents a relatively pristine frontier that is vulnerable to pollution. Substances originating at mid latitudes are transported to the Arctic by atmospheric processes, ocean currents and rivers. These pollutants can accumulate in the Arctic environment. Testing of nuclear weapons, dumping of waste and operation of ships, and nuclear power plants also pose threats.

To investigate possible pollutant pathways we used a multi-level primitive-equation ocean model, coupled to a dynamic-thermodynamic sea-ice model. Coupling included conservative transfer of momentum, heat and fresh water. Atmospheric forcing (wind stress, temperature, humidity, radiation and heat fresh-water fluxes) was supplied by datasets or bulk formulae. Open lateral-boundary conditions for the ocean model were supplied either by datasets (temperature and salinity) or from a larger-scale ocean model (momentum). Two integrations were compared — one used a centred-difference advection scheme and viscous damping, while the other used a better representation of an advection scheme and a sub-gridscale eddy parameterization.

Tracer simulations showed (1) the importance of good representation of numerical advection, and (2) the role of eddy interacting with sea-floor topography (the neptune effect).

The Reynolds stress associated with the adjustment of two-dimensional isotropic eddies subject to a large-scale shear flow is examined in a series of initial-value calculations in a periodic channel. Several stages in the temporal evolution of the stress can be identified. Initially, there is a brief period associated with quasi-passive straining of the eddy field in which the net Reynolds stress and the associated eddy viscosity remain essentially zero. In spectral space this is characterized by mutual cancellation of contributions to the Reynolds stress at high and low eddy wavenumbers. Subsequently, eddy–eddy interactions produce a tendency to restore isotropy at higher eddy wavenumbers, leading to an overall positive eddy viscosity associated with the dominant contribution to the Reynolds stress at low eddy wavenumbers. These results are consistent with theoretical predictions of positive eddy viscosity for initially isotropic homogeneous two-dimensional turbulence. Due to the inverse cascade, the accumulation with time of energy at the scale of the channel produces a competing tendency to negative eddy viscosity associated with linear shearing of the disturbances. This finite-domain effect may become dominant if the nonlinearity of the eddy field is relatively weak.

Evaluation of spectral closure theory and direct numerical simulation are used to examine the eddy transport of a passive scalar in barotropic β-plane flow. When a large-scale gradient of scalar concentration is imposed, the implied scale separation between fixed background gradient and eddies supports the concept of ‘eddy diffusion’. The results can be cast in terms of an eddy diffusion tensor K, whose behaviour as a function of mean vorticity gradient β is examined. Earlier theoretical work by Holloway & Kristmannsson (1984) is extended to include cases where strong vorticity–scalar correlations are observed, and corrected in order to restore random Galilean invariance.

The anisotropy of eddy energy and the direct influence of Rossby wave propagation contribute to the overall anisotropy of K, The resulting suppression of meridional diffusivity Kyy, and enhancement of zonal diffusivity Kxx, with increased β is examined. The variation in simulation Kyy is closely reproduced in the closure equations. However, the increased Kxx is the result of zonal jets whose persistence is not accounted for in the statistical theory.

Numerical simulations of geostrophic turbulence above topography are used to compare (a) nonlinear generation of system entropy, S, (b) selective damping of enstrophy and (c) development of vorticity–topography correlation. In the damped cases, S initially increases, approaching a quasi-equilibrium (maximum S subject to the instantaneous, though decaying, energy and enstrophy). When strongly scale-selective damping is applied, onset of the vorticity–topography correlation follows the timescales for enstrophy decay. During the period of decay, it is shown that nonlinear interaction continues to generate S, offsetting in part the loss of S to explicit damping.

Numerical simulations are employed in a detailed test of the statistical mechanical description of topographic turbulence. Predictions of steady flows correlated with topography are given particular attention. Agreement between numerical and statistical mechanical results is demonstrated for a large range of parameter values, and over an ensemble of random choices of topography and initial conditions.

The interaction of eddies with variations in topography, together with a tendency for large-scale wave propagation, generates a systematic stress which acts upon large-scale mean flows. This stress resists the midlatitude tropospheric westerlies, resists the oceanic Antarctic Circumpolar Current, and may be a dominant mechanism in driving coastal undercurrents. Associated secondary circulation provides a systematic upwelling in coastal oceans, pumping deeper water onto continental shelf areas. The derivation rests in turbulence closure theory and is supported by numerical experiments.

We investigate the interaction of concentration fields of passive tracer with velocity fields characterizing geostrophic turbulence. We develop and compare results from equilibrium statistical mechanics, from turbulence-closure theory and from numerical simulation. A consistent account emerges. Among the results we show (1) that velocity fields efficiently scatter tracer variance to all scales, (2) that tracer variance evolves toward an equilibrium spectrum which is different from the equilibrium spectrum for vorticity variance, and (3) that intermittency of the tracer field is characteristic of a cascade of tracer variance across wavenumber space. The greater efficiency of the cascade of tracer variance relative to a vorticity cascade is due to wavenumber-local advective terms which affect tracer but not vorticity. We suggest that the more efficient tracer cascade results in shorter Lagrangian autocorrelation times for tracer than for vorticity.

We investigate the spatial flux of tracer when a uniform gradient of average tracer concentration is imposed. We show (1) that the spatial flux has dominant contributions from fluctuations on scales slightly larger than the dominant energetic scales, (2) that an effective eddy-diffusivity formulation is valid and that the diffusivity agrees with simple mixing-length estimates, and (3) that eddy diffusivity is significantly anisotropic if Rossby-wave propagation occurs. Meridional diffusivity is suppressed relative to zonal diffusivity.

We complement the study of stirring down from a uniform gradient with a numerical investigation of the stirring out of an initially concentrated spot. We see that eddy diffusivity can be a dangerous concept for such problems.

A measure of predictability that has many superior features compared to currently used measures is introduced. Through statistical theory it is demonstrated that in inviscid truncated flow this new predictability measure increases monotonically in time while all initial information about the system decays. Under the influence of forcing and viscosity the behaviour of this measure is shown always to satisfy intuitive expectations.

An extension of the turbulence ‘test-field model’ (Kraichnan 1971 a) is given for two-dimensional flow with Rossby-wave propagation. Such a unified treatment of waves and turbulence is necessary for flows in which the relative strength of nonlinear terms depends upon the length scale considered. We treat the geophysically interesting case in which long, fast Rossby waves propagate substantially without interaction while short Rossby waves are thoroughly dominated by advection. We recover the observations of Rhines (1975) that the tendency of two-dimensional flow to organize energy into larger scales of motion is inhibited by Rossby waves and that an initially isotropic flow develops anisotropy preferring zonal motion. The anisotropy evolves to an equilibrium functional dependence on the isotropic part of the flow spectrum. Theoretical results are found to be in quantitative agreement with numerical flow simulations.

We have applied the methods of classical statistical mechanics to derive the inviscid equilibrium states for one- and two-layer nonlinear quasi-geostrophic flows, with and without bottom topography and variable rotation rate. In the one-layer case without topography we recover the equilibrium energy spectrum given by Kraichnan (1967). In the two-layer case, we find that the internal radius of deformation constitutes an important dividing scale: at scales of motion larger than the radius of deformation the equilibrium flow is nearly barotropic, while at smaller scales the stream functions in the two layers are statistically uncorrelated. The equilibrium lower-layer flow is positively correlated with bottom topography (anticyclonic flow over seamounts) and the correlation extends to the upper layer at scales larger than the radius of deformation. We suggest that some of the statistical trends observed in non-equilibrium flows may be looked on as manifestations of the tendency for turbulent interactions to maximize the entropy of the system.

A method is developed for statistical prediction of turbulent geophysical flows that is more efficient than ensemble integrations. We consider the evolution of low-order moments for inviscid quasi-geostrophic turbulence. Guided by statistical mechanics, equations are developed for predicting the mean and the variance about the mean as functions of position and time. These equations are consistent with the exact moment equations and contain irreversible (entropy producing) fluxes that must be specified in terms of known moments. Using simple choices for these dependences, the resulting scheme, involving just two spatial fields, typically outperforms 100-realization ensembles.

Turbulent stratified flow over topography is studied using layered quasi-geostrophic models. Mean flows develop under random forcing, with lower-layer mean stream-function positively correlated with topography. When friction is sufficiently small, upper-layer mean flow is weaker than, but otherwise resembles, lower-layer mean flow. When lower-layer friction is larger, upper-layer mean flow reverses and can exceed lower-layer mean flow in strength. The mean interface between layers is domed over topographic elevations. Eddy fluxes of potential vorticity and layer thickness act in the sense of driving the flow toward higher entropy. Such behaviour contradicts usual eddy parameterizations, to which modifications are suggested.

The physical basis for parameterizing topographic stress due to unresolved eddies is examined in a quasi-geostrophic barotropic model. Topographic stress parameterization is shown to represent two effects of eddies: attraction of the flow to a statistical equilibrium featuring topographically correlated mean currents, and dissipation of potential enstrophy. Performance is evaluated by comparing parameterized low-resolution models with explicit high-resolution models.