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L. A. Mysak

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H. Hukuda and L. A. Mysak

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The effect of linear bottom friction on free topographic (second class) waves on a sloping beach is investigated. To handle the coastal singularity in the friction terms, Lighthill's method of strained coordinates is used to find a perturbation solution to the governing equations. Simple expressions for the decay rate are worked out for two classical beach profiles: 1) the uniformly sloping beach, and 2) the exponential depth profile due to Ball (1967). For parameter values characteristic of the north shore of Lake Ontario, which can be modelled by the Ball profile, only the gravest mode will not experience rapid attenuation due to bottom friction.

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H. Bjornsson and L. A. Mysak

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A simple ocean–atmosphere model suitable for long-term paleoclimate studies is presented. It consists of a three-basin zonally averaged ocean model coupled to an energy moisture-balance atmospheric model and a thermodynamic sea-ice model. The model is used to simulate the “present-day” climate conditions and the conditions resembling those of the last glacial maximum (LGM). In the first case, the model has an ocean thermohaline (THC) circulation in which the overturning in the North Atlantic is slightly more than 15 Sv.

Two methods are used to spin up the model to the LGM climate. First, a cool state is obtained by running the coupled model with a reduced model greenhouse effect and increased albedo, but without making any explicit changes to the hydrological cycle. In the second approach, the model is directly set up for LGM conditions, in a manner similar to the method used to simulate the present-day climate. In both cases the computed LGM sea surface temperatures are reasonable, but only in the second case is a realistic ocean THC obtained.

The LGM THC is steady and no self-sustained millennial-scale oscillations are present for conventional values of the diffusivity coefficients. The absence of these oscillations in the model and their presence in other simple climate models is discussed, and it is suggested how a combination of paleoceanographic data and modeling might be used to determine whether the glacial THC indeed exhibited such internal oscillations.

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C. L. Tang and L. A. Mysak

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We show that in the presence of a randomly perturbed stability frequency, a coherent internal wave (f<σ<N 0) or gyroscopic wave (N 0<σ<f) is always attenuated in the direction of energy propagation, where σ and f denote respectively the wave angular frequency and Coriolis parameter, and N 0 denotes the mean stability frequency. For internal waves, the vertical e-folding attenuation scale due to the random perturbations is estimated to be 1–2 km. The effect of the random perturbations on the wave phase and group velocities appears to be insignificant, however.

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L-B. Tremblay and L. A. Mysak

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A dynamic sea ice model based on granular material rheology is presented. The sea ice model is coupled to both a mixed layer ocean model and a one-layer thermodynamic atmospheric model, which allows for an ice albedo feedback. Land is represented by a 6-m thick layer with a constant base temperature. A 10-year integration including both thermodynamic and dynamic effects and incorporating prescribed climatological wind stress and ocean current data was performed in order for the model to reach a stable periodic seasonal cycle. The commonly observed lead complexes, along which sliding and opening of adjacent ice floes occur in the Arctic sea ice cover, are well reproduced in this simulation. In particular, shear lines extending from the western Canadian Archipelago toward the central Arctic, often observed in winter satellite images, are present. The ice edge is well positioned both in winter and summer using this thermodynamically coupled ocean–ice–atmosphere model. The results also yield a sea ice circulation and thickness distribution over the Arctic, which are in good agreement with observations. The model also produces an increase in ice formation associated with the dilatation of the ice medium along sliding lines. In this model, incident energy absorbed by the ocean melts ice laterally and warms the mixed layer, causing a smaller ice retreat in the summer. This cures a problem common to many existing thermodynamic–dynamic sea ice models.

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A. J. Willmott and L. A. Mysak

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In the northeast Pacific eddies are observed in the salinity and, to a lesser extent, in the thermal anomalies. In particular, a pronounced eddy is frequently observed a few hundred kilometers west of Sitka, Alaska, latitude 57°N. This paper investigates a possible mechanism for the production of such eddies. The northeast Pacific ocean is approximated by a quarter-plane region, and a continuously stratified, inviscid linear model is used to study the reflections of wind-driven perturbations by the two boundaries. In the model the perturbations take the form of planetary waves, and by choosing a forcing function which is sinusoidal in time the problem reduces to solving the forced Helmholtz equation in a quarter-plane region. From the solution to this equation, the perturbation density field is derived. In general, it consists of a large number of eddies which result from the superposition of multiply reflected planetary waves. It is found that tilting the quarter-plane from the north-south direction alters the shape of the eddies in the perturbation density field. Furthermore, when the quarter-plane is not rotated the eddies are aligned parallel to the boundary representing the Alaskan peninsula-Aleutian Island chain. As the quarter-plane is tilted, the axis of alignment of the eddies rotates toward the boundary representing the Alaskan-British Columbia coastline.

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G. J. Mertz and L. A. Mysak

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Surface wind data for the western region of the Indian Ocean was collated at the University of Miami, in support of certain FGGE/INDEX/MONEX projects, and published in two technical reports by Fernandez-Partagas and Düing and Fernandez-Partagas et al. Data from these reports have been analyzed to show that the 40–50 day oscillation detected in the tropics by Madden and Julian was also present over the Western Indian Ocean during 1976 and 1979.

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J. D. Fuller and L. A. Mysak

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We examine the generation of trapped edge waves on a continental shelf when a long wave from the deep ocean reaches an irregular coast, and alterations in the propagation characteristics of trapped edge waves due to the coastal irregularities. The continental shelf is modeled by a single flat-step model, and the coast is straight except for irregularities represented as a centered stationary random function of distance along the coast. The relevant boundary value problem are thus stochastic, with the randomness introduced through the boundary condition at the coast. We find the power flux into trapped edge waves and into a continuous spectrum of leaky modes, both generated by the scattering of an incident wave from the deep ocean. Numerical results, assuming a Gaussian spectrum for coastal irregularities, indicate that there is less power transferred to the forward traveling trapped wave than the backward one, and less power to the scattered leaky modes than to either the forward or backward traveling trapped modes. We obtain the attenuation coefficient of a trapped edge wave, the “tilting” of the wave toward the coast, and the correction to the dispersion relation due to the coastal irregularities. The results are valid for wave periods much shorter than the period associated with the Coriolis parameter f and for wavelengths much greater than the average size of the coastal irregularities.

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M. S. Darby, A. J. Willmott, and L. A. Mysak

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A nonlinear, steady-state model of the North Water (NOW), the Arctic's largest polynya, is presented. The model follows in the spirit of the recently developed latent and sensible heat polynya model of Mysak and Huang, but extends it in several important ways: finite amplitude displacements of the upper-layer thickness are allowed; the channel walls diverge to the south; the sensible-heat flux from the lower layer is physically well defined in terms of a vertical entrainment velocity; and the free-drifting frazil ice to the north of the NOW ice edge is allowed to move to the right of the northerly winds.

An important result found here is that with the exception of late spring, the asymptotic southern ice edge position of the NOW can be simulated in terms of a latent heat model alone. In this case, the observed equatorward curvature of the ice edge in the region adjacent to the west Greenland coast can be produced by a combination of a channel that widens in the equatorward direction, together with free-drift frazil ice motion that is to the right of the northerly winds. However, in late spring, when the heat loss to the atmosphere is reduced, the sensible heat flux plays an important role in determining the position and shape of the ice edge, particularly in the region adjacent to the west Greenland coast.

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H. Bjornsson, L. A. Mysak, and G. A. Schmidt

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The Wright and Stocker oceanic thermohaline circulation model is coupled to a recently developed zonally averaged energy moisture balance model for the atmosphere. The results obtained with this coupled model are compared with those from an ocean-only model that employs mixed boundary conditions. The ocean model geometry uses either one zonally averaged interhemispheric basin (the “Atlantic”) or two zonally averaged basins (roughly approximating the Atlantic and the Pacific Oceans) connected by a parameterized Antarctic Circumpolar Current. The differences in the steady states and their linear stability are examined over a wide range of parameters.

The presence of additional feedbacks between the ocean circulation and the atmosphere and hydrological cycle in the coupled model produces significant differences between the latter and the ocean-only model, in both the one-basin and two-basin geometries. The two models generally have different (though similar) equilibria and, most importantly for the issue of climate change, the variability in the models near similar steady states is quite different.

In the one-basin case, three different steady states were found with both models, an unstable two-cell circulation with equatorial upwelling, and two stable states with a one-cell (pole-to-pole) circulation. In the one-cell states, there is an interhemispheric oceanic heat transport that cannot affect the implicit atmosphere under mixed boundary conditions, but which changes the surface air temperature in the coupled model, and which also leads to several feedbacks on the ocean circulation. Consequently, the corresponding states in the coupled model are different from those in the ocean-only model.

In the two-basin case, five basic steady states were found in the ocean-only model: a state with two cells in both basins, a conveyor state, a reverse conveyor state, a state with northern sinking circulation in both basins, and a state with southern sinking in both basins. The state with southern sinking in both basins could not be found in the coupled model. In addition, two more steady states, each with a two-cell circulation in one basin and a one-cell circulation in the other, were found for both models during sensitivity tests. The bifurcation structures for the two models are very different, and also, the two-basin conveyor circulation is shown to be more stable to freshwater perturbations in the coupled model.

The authors conclude that due to the effects produced by the feedbacks in the coupled model, they must have serious reservations about the results concerning long-term climate variability obtained from ocean-only models. Thus, to investigate long-term climatic variability a coupled model is necessary.

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