A new modelling framework using Lagrangian particle tracking has been developed to assess dynamic and thermodynamic effects of underwater frazil ice. This frazil-ice model treats a Lagrangian particle as a bulk cluster of many frazil crystals, and calculates the thermodynamic growth of each particle and the corresponding budget of latent heat and fresh water. The effective density and viscosity of sea water depend on the mass fraction of underwater frazil ice, and hence affect ocean convection. An idealized experiment using our model successfully reproduces the formation of underwater frazil ice and its transition to grease ice at the surface. Because underwater frazil ice does not reduce the atmosphere/ocean heat exchange, surface heat flux and net sea-ice production in the experiment with frazil ice are relatively high compared with the experiment where surface cooling directly leads to columnar growth of a solid ice cover which effectively insulates the heat flux. These results suggest that large-scale sea-ice models which do not take account of the effects of frazil ice might underestimate atmosphere/ocean heat exchange, particularly at times of active new ice formation.