Limit regimes of ice formation in turbulent supercooled water

A study of ice formation in stationary turbulent conditions is carried out in various limit regimes of crystal growth, supercooling, and ice entrainment at the water surface. Analytical expressions for the temperature, salinity, and ice concentration mean profiles are provided, and the role of fluctuations in ice production is numerically quantified. Lower bounds on the ratio of sensible heat flux to latent heat flux to the atmosphere are derived and their dependence on key parameters such as salt rejection in freezing and ice entrainment in the water column is elucidated.

Figure 1

Rise velocity $u_r$ as a function of the particle radius for different values of the aspect ratio: $\epsilon =1/100$ (bottom curve); $\epsilon =1/50$ (middle curve); $\epsilon =1/30$ (top curve).

Figure 2

Sketch of the heat, salinity, and ice fluxes generated during buildup of a grease ice layer. The heat flux to the atmosphere is split into latent heat ${\mathrm{\Phi }}_T^L$ and sensible heat ${\mathrm{\Phi }}_T^B$ contributions. The salinity flux ${\mathrm{\Phi }}_S^B$ is downward directed. The question mark indicates that the sign of the frazil ice flux ${\mathrm{\Phi }}_C^{top}$ is a priori undetermined.

Figure 3

Sketch of the computation domain.

Figure 4

Snapshot of the ice concentration (top) and the supercooling (bottom) for $\langle \mathcal{X}\rangle =-{\mathrm{\Phi }}_C^{\mathrm{top}}=0.1, {\lambda }_{-}=1$, and $\epsilon =1/5$.

Figure 5

Effect of an ice sink at $z=\pm 1$ on the vertical profiles of (a) ice concentration, (b) supercooling, and (c) ice production rate; ${\mathrm{\Phi }}_C^B=0$ in red; ${\mathrm{\Phi }}_C^B=-0.3$ in black. In (a) and (b), solid lines indicate average; in (c), they indicate mean-field result $\overline{\lambda }\overline{C}{\overline{T}}_o$. In (a) and (b), dashed line indicate rms; in (c), they indicate the fluctuation $\overline{{\left(\lambda C{T}_o\right)}_f}$. Values of other parameters: ${\lambda }_{-}=1$; ${\mathrm{\Phi }}_C^{\mathrm{top}}=-0.5$; $\langle \mathcal{X}\rangle =-0.1$; $\epsilon =1/5$.

Figure 6

Vertical profile of $\lambda$. Average solid; rms dashed. Values of the parameters ${\lambda }_{-}=1$; $-{\mathrm{\Phi }}_C^{\mathrm{top}}=\langle \mathcal{X}\rangle =0.1$; $\epsilon =1/5$.

Figure 7

Vertical profiles of the ice production for different values of $\epsilon$. $\epsilon =1$ in red, $\epsilon =1/5$ in black; mean-field contribution $\overline{\lambda }\overline{C}{\overline{T}}_o$ solid line, fluctuation contribution $\overline{{\left(\lambda C{T}_o\right)}_f}$ dashed line. Values of the other parameters: ${\lambda }_{-}=-{\mathrm{\Phi }}_C=\langle \mathcal{X}\rangle =0.1$.

Figure 8

Same as Fig. 7 for different values of $\epsilon$ and $\lambda$. ${\lambda }_{-}=0.02, \epsilon =1/50$ in red; ${\lambda }_{-}=1, \epsilon =1/5$ in black.