A Two-Dimensional Time-Dependent Model of a Wind-Driven Coastal Polynya: Application to the St. Lawrence Island Polynya

M. A. Morales Maqueda Department of Mathematics, Keele University, Keele, Staffordshire, United Kingdom

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A. J. Willmott Department of Mathematics, Keele University, Keele, Staffordshire, United Kingdom

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Abstract

A two-dimensional time-dependent model of a wind-driven coastal polynya is presented. The model combines and extends previous one-dimensional time-dependent and two-dimensional steady-state flux formulations. Given the coastline geometry, and the time-varying surface winds and heat fluxes as free parameters, the model calculates the growth rate, distribution and motion of frazil ice within the polynya, and the mass fluxes of frazil ice and consolidated new ice at the polynya edge. The difference between these two mass fluxes determines the velocity of the polynya edge at all times and, hence, its evolution. Analytical solutions are found for the special case when the coastline is a straight line segment of finite length D (an idealization of an island) and the forcing fields are spatially uniform and constant in time. Two timescales and two spatial scales are shown to be important in characterizing the shape, size, and evolution of the polynya: the consolidated new ice and frazil ice timescales, tce and tfe, respectively, and the offshore and alongshore adjustment length scales, Roe and Rae, respectively. The timescale tce is the time required for the polynya to grow ice of thickness equal to the collection thickness of frazil at the polynya edge. The timescale tfe is the time it takes frazil to cross the equilibrium width of the polynya, which is, in turn, determined by the length scale Roe. In combination, tce and tfe control the timescale for the polynya to respond to variations in the forcing. The length scale Rae is the distance that the angle between the consolidated new ice and frazil ice drifts spans along the equilibrium polynya edge. This length scale measures the sensitivity of the polynya edge to alongshore variations in the coastline geometry and, in particular, to its total extent. It is shown that if Rae is comparable to D, then the offshore dimension of the polynya and the timescale for the polynya to reach equilibrium can be very different from those obtained from a one-dimensional formulation. The model is applied to the study of seasonal and short-term variability of the St. Lawrence Island polynya, in the Bering Sea.

* Current affiliation: Potsdam Institute for Climate Impact Research, Potsdam, Germany.

Corresponding author address: Dr. M. A. Morales Maqueda, Potsdam Institute for Climate Impact Research, P.O. Box 60 12 03, 14412 Potsdam, Germany.

Email: maqueda@pik-potsdam.de

Abstract

A two-dimensional time-dependent model of a wind-driven coastal polynya is presented. The model combines and extends previous one-dimensional time-dependent and two-dimensional steady-state flux formulations. Given the coastline geometry, and the time-varying surface winds and heat fluxes as free parameters, the model calculates the growth rate, distribution and motion of frazil ice within the polynya, and the mass fluxes of frazil ice and consolidated new ice at the polynya edge. The difference between these two mass fluxes determines the velocity of the polynya edge at all times and, hence, its evolution. Analytical solutions are found for the special case when the coastline is a straight line segment of finite length D (an idealization of an island) and the forcing fields are spatially uniform and constant in time. Two timescales and two spatial scales are shown to be important in characterizing the shape, size, and evolution of the polynya: the consolidated new ice and frazil ice timescales, tce and tfe, respectively, and the offshore and alongshore adjustment length scales, Roe and Rae, respectively. The timescale tce is the time required for the polynya to grow ice of thickness equal to the collection thickness of frazil at the polynya edge. The timescale tfe is the time it takes frazil to cross the equilibrium width of the polynya, which is, in turn, determined by the length scale Roe. In combination, tce and tfe control the timescale for the polynya to respond to variations in the forcing. The length scale Rae is the distance that the angle between the consolidated new ice and frazil ice drifts spans along the equilibrium polynya edge. This length scale measures the sensitivity of the polynya edge to alongshore variations in the coastline geometry and, in particular, to its total extent. It is shown that if Rae is comparable to D, then the offshore dimension of the polynya and the timescale for the polynya to reach equilibrium can be very different from those obtained from a one-dimensional formulation. The model is applied to the study of seasonal and short-term variability of the St. Lawrence Island polynya, in the Bering Sea.

* Current affiliation: Potsdam Institute for Climate Impact Research, Potsdam, Germany.

Corresponding author address: Dr. M. A. Morales Maqueda, Potsdam Institute for Climate Impact Research, P.O. Box 60 12 03, 14412 Potsdam, Germany.

Email: maqueda@pik-potsdam.de

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