Ice and Fluid Dynamics

Abstract:

We present studies of the solidification of binary aqueous solutions that undergo time-periodic cooling from below. We develop an experiment for solidification of aqueous NH4Cl solutions, where the temperature of the cooling boundary is modulated as a simple periodic function of time with independent variations of the modulation amplitude and frequency. The thickness of the mushy layer exhibits oscillations about the background growth obtained for constant cooling. We consider the deviation given by the difference between states with modulated and fixed cooling, which increases when the modulation amplitude increases but decreases with increasing modulation frequency. At early times, the deviation amplitude is consistent with a scaling argument for growth with quasi-steady modulation. In situ measurements of the mush temperature reveal thermal waves propagating through the mushy layer, with amplitude decaying with height within the mushy layer, whilst the phase lag behind the cooling boundary increases with height. This also leads to phase lags in the variation of the mushy-layer thickness compared to the boundary cooling. There is an asymmetry of the deviation of mushy-layer thickness: during a positive modulation (where the boundary temperature increases at the start of a cycle) the peak thickness deviation has a greater magnitude than the troughs in a negative modulation mode (where the boundary temperature decreases at the start of the cycle). A numerical model is formulated to describe mushy-layer growth with constant bulk concentration and turbulent heat transport at the mush–liquid interface driven by compositional convection associated with a finite interfacial solid fraction. The model recovers key features of the experimental results at early times, including the propagation of thermal waves and oscillations in mushy-layer thickness, although tends to overpredict the mean thickness.

Abstract:

We report an experimental study of the distributions of temperature and solid fraction of growing NH4Cl–H2O mushy layers that are subjected to periodical cooling from below, focusing on late-time dynamics where the mushy layer oscillates about an approximate steady state. Temporal evolution of the local temperature T(z, t) at various heights in the mush demonstrates that the temperature oscillations of the bottom cooling boundary propagate through the mushy layer with phase delays and substantial decay in the amplitude. As the initial concentration C0 increases, we show that the decay rate of the thermal oscillation with height also decreases, and the propagation speed of the oscillation phase increases. We interpret this as a result of the solid fraction increasing with C0, which enhances the thermal conductivity but reduces the specific heat of the mushy layer. We present a new methodology to determine the distribution of solid fraction φ(z) in mushy layers for various C0, using only measurements of the temperature T(z, t). The method is based on the phase behaviour during thermal modulation, and opens up a new approach for inferring mushy-layer properties in geophysical and engineering settings, where direct measurements are challenging. In our experiments, profiles of the solid fraction φ(z) exhibit a cliff–ramp–cliff structure with large vertical gradients of φ near the mush–liquid interface and also near the bottom boundary, but much more gradual variation in the interior of the mushy layer. Such a profile structure is more pronounced for higher initial concentration C0. For very low concentration, the solid fraction appears to be linearly dependent on the height within the mush. The volume-average of the solid fraction, and the local fluctuations in φ(z) both increase as C0 increases. We suggest that the fast increase of φ(z) near the bottom boundary is possibly due to diffusive transport of solute away from the bottom boundary and the depletion of solute content near the basal region

Abstract:

Sea ice is a reactive porous medium of ice crystals and liquid brine, which is an example of a mushy layer. The phase behaviour of sea ice controls the evolving material properties and fluid transport through the porous ice, with consequences for ice growth, brine drainage from the ice to provide buoyancy fluxes for the polar oceans, and sea-ice biogeochemistry. We review work on the growth of mushy layers and convective flows driven by density gradients in the interstitial fluid. After introducing the fundamentals of mushy-layer theory, we discuss the effective thermal properties including the impact of salt transport on mushy-layer growth. We present a simplified model for diffusively controlled growth of mushy layers with modest cooling versus the solutal freezing-point depression. For growth from a cold isothermal boundary, salt diffusion modifies mushy layer growth by around 5-20% depending on the far-field temperature and salinity. We also review work on the onset, spatial localisation and nonlinear development of convective flows in mushy layers, highlighting recent work on transient solidification and models of nonlinear convection with dissolved solid-free brine channels. Finally, future research opportunities are identified, motivated by geophysical observations of ice growth.