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The drivers of the tidal and residual flows in estuaries can vary spatially and temporally due to geomorphic complexities, fortnightly tides, and climatic influences. In this paper, we explore the mechanisms that give rise to the circulation patterns in Frenchman Bay, Maine, on the Eastern Coast of the USA, under varying freshwater input conditions and fortnightly tidal phases, using idealized simulations from a high-resolution, three-dimensional numerical model. The results of the simulations at the tidal timescale reveal a tidal asymmetry in vorticity, where vorticity generated during flood tide is not spun-down during the subsequent ebb. This asymmetry prompts the investigation of the residual circulation in the bay which is characterized by large tidal residual eddies. These eddies are found to persist in the depth-averaged residual flow regardless of the freshwater input or tidal phase, leading to the conclusion that the eddies are “geomorphically-constrained” in the bay. Analysis of the horizontal momentum terms and a simulation performed without Coriolis forcing demonstrates that the tidal stress terms predominantly balance the barotropic pressure gradient to give rise to the eddy patterns, while the Coriolis force acts to strengthen their vorticity. The eddies create a laterally sheared residual flow structure with depth, however the flow is more vertically sheared during the neap tide when the baroclinic pressure gradient plays a larger role. These findings demonstrate the persistence of tidal residual eddies regardless of freshwater input or fortnightly tidal phase in a geomorphically complex deglaciated coastal bay with low freshwater input. 

We consider sequential stochastic decision problems in which, at each time instant, an agent optimizes its local utility by solving a stochastic program and, subsequently, announces its decision to the world. Given this action, we study the problem of estimating the agent’s private belief (i.e., its posterior distribution over the set of states of nature based on its private observations). We demonstrate that it is possible to determine the set of private beliefs that are consistent with public data by leveraging techniques from inverse optimization. We further give a number of useful characterizations of this set; for example, tight bounds by solving a set of linear programs (under concave utility). As an illustrative example, we consider estimating the private belief of an investor in regime-switching portfolio allocation. Finally, our theoretical results are illustrated and evaluated in numerical simulations.