Each year more than 10 million square kilometres of the polar oceans freeze over, as part of the seasonal evolution of sea ice. This provides key climate feedbacks on the planetary energy budget, and brine rejection from growing ice provides buoyancy forcing to drive ocean circulation and mixing. In this talk I will provide an overview of some of the fluid dynamical processes impacting sea ice growth, before focussing on two selected examples. I will discuss recent work on modelling the initial stages of ice growth in a turbulently-mixed ocean, involving supercooling and convection in suspensions of frazil ice crystals. I will also describe the multiphase properties of consolidated sea ice, which is a chemically reactive porous medium subject to flow localisation as the porosity and permeability evolve.Convective flows and the dissolution of brine channels control the drainage of dense saline brine into the ocean, with modelling work providing insight into the structure and strength of such flows.