Abstract
The process of initial ice formation in brine is a highly complex problem. In this paper, we propose a mathematical model that captures the dynamics of nucleation and development of ice inclusions in brine. The primary emphasis is on the interaction between ice growth and salt diffusion, subject to external forcing provided by temperature. Within this setting two freezing regimes are identified, depending on the rate of change of the temperature: a slow freezing regime where a continuous ice domain is formed; and a fast freezing regime where recurrent nucleation appears within the fluid domain. The second regime is of primary interest, as it leads to fractal-like ice structures. We analyse the critical threshold between the slow and fast regimes by identifying the explicit rates of external temperature control that lead to self-similar salt-concentration profiles in the fluid domains. Subsequent heuristic analysis provides estimates of the characteristic length scales of the fluid domains depending on the time-variation of the temperature. The analysis is confirmed by numerical simulations.
Highlights
Sea ice represents an important component of the Arctic and Antarctic ecosystems and forms the habitat for many micro-organisms
Pop through laboratory experiments and numerical simulations Eide & Martin (1975), Allison et al (1985), Worster (1992), Eicken (2003), Vancoppenolle, Fichefet & Bitz (2006), Golden et al (2007), Peppin et al (2007), Notz & Worster (2008), Hunke et al (2011), Wells, Wettlaufer & Orszag (2011), Jones, Ingham & Eicken (2012). These experimental studies provide the basis for the heuristic relationships required when developing computational models, which in their turn are needed for understanding large-scale dynamics
While the mathematical model defined above is stated for arbitrary dimensions, the analysis in the remainder of this manuscript is restricted to the case of one spatial dimension
Summary
Sea ice represents an important component of the Arctic and Antarctic ecosystems and forms the habitat for many micro-organisms. Pop through laboratory experiments and numerical simulations Eide & Martin (1975), Allison et al (1985), Worster (1992), Eicken (2003), Vancoppenolle, Fichefet & Bitz (2006), Golden et al (2007), Peppin et al (2007), Notz & Worster (2008), Hunke et al (2011), Wells, Wettlaufer & Orszag (2011), Jones, Ingham & Eicken (2012) These experimental studies provide the basis for the heuristic relationships required when developing computational models, which in their turn are needed for understanding large-scale dynamics. In addition to identifying self-similar structures for the freezing problem, we derive an estimate for characteristic fluid-region length scales for general freezing regimes Both fractal-forming behaviour and the robustness of fractal patterns with respect to perturbation of the initial conditions are verified numerically.
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