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An analytical model is developed to study the tidally induced mean circulation in the frontal zone. Four distinct forcing mechanisms are identified, which result in the generation of the counterclockwise Bernoulli cell, the clockwise Ekman cell, the clockwise frontal cell, and the Stokes drift (facing in the direction with the shallow water to the left). The decomposition of the cross-frontal circulation provides a dynamical framework for interpreting and understanding its complex structure. To illustrate the underlying physics, three model configurations are considered pertaining to a homogenous ocean and winter and summer fronts. For a homogeneous ocean, the circulation is dominated by three cells; for the winter front, the offshore Bernoulli cell is strengthened; and for the summer front, two counterrotating cells are found in the vertical direction, associated with the two branches of the front. The dependence of the cell structure on the Ekman, Burger, and other dimensionless numbers is examined.

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We present a theoretical framework that integrates the dynamics of glaciers with and without the topographic confinement. This Part 1 paper concerns the former, which may exhibit surge cycles when subjected to thermal switches associated with the bed condition. With the topographic trough setting the glacier width and curbing the lateral drainage of the meltwater, the problem falls under the purview of the undrained plastic bed (UPB) formalism. Employing the UPB, we shall examine the external controls of the glacial behavior and test them against observations. Through our non-dimensionalization scheme, we construct a 2-D regime diagram, which allows a ready prognosis of the glacial properties over the full range of the external conditions, both climate- and size-related. We first discern the boundaries separating the glacial regimes of steady-creep, cyclic-surging and steady-sliding. We then apply the regime diagram to observed glaciers for quantitative comparisons. These include the Svalbard glaciers of both normal and surge types, Northeast Greenland Ice Stream characterized by steady-sliding, and Hudson Strait Ice Stream exhibiting cyclic surges. The quantitative validation of our model containing no free parameters suggests that the thermal switch may unify the dynamics of these diverse glaciers.

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The horizontal property flux induced by tides is examined by both analytical and numerical models. It is found that this flux is highly heterogeneous in the vertical and may be directed up the mean gradient near the bottom. This countergradient tidal flux is a consequence of differing boundary conditions satisfied by velocity and property fields, and hence a robust feature. The corresponding tidal diffusivity is substantial where tides are strong and hence potentially important in the mean property balance.* Lamont-Doherty Earth Observatory Contribution Number 6012.

It is hypothesized that tidal mixing may provide a ''diffusivity'' mechanism for frontogenesis. It stems from the fact that tidal diffusivity varies in the opposite sense from the water depth, so the vertically integrated diffusivity may exhibit a minimum at midshelf, thus giving rise to a maximum in the property gradient-even in the absence of flow convergence. An analytical model assuming a tidal diffusivity dominated by shear dispersion is used to elucidate the mechanism, which shows additionally that the front is located at a water depth that is about twice the tidal frictional depth-a prediction not inconsistent with some observed fronts. The proposed frontogenesis is demonstrated by numerical calculations using the Princeton Ocean Model (POM), which show the emergence of a front from an initial field of uniform gradient after tides are switched on, and the diagnosis of the numerical solution and its parameter dependence has corroborated the analytical model. It is suggested moreover that this diffusivity mechanism may be extended to the wind-induced mixing to explain the shelfbreak front off of the northeastern United States.