Non-Oberbeck-Boussinesq effects in coldwater

Abstract

Water exhibits an anomalous nonlinear temperature-density ($\rho$-$T$) relation as it approaches freezing, along with an increase in viscosity, and a decrease in thermal conductivity. These departures from the standard Oberbeck--Boussinesq approximation, which assumes constant material properties and a linear $\rho$-$T$ relation, can modify convection in ice-bounded aquatic systems, yet their effects remain unexplored. Here, we examine these effects via the canonical Rayleigh--B\'enard convection framework using direct numerical simulations. We show that non-Oberbeck--Boussinesq effects lower the mean fluid temperature relative to the standard case and break the classical symmetry of the mean temperature profile. The magnitude of this symmetry breaking depends on both the Rayleigh number $Ra$ and the temperature-dependent material properties retained in the governing equations. We further identify a small but measurable shift in the critical Rayleigh number, $Ra_c$. After accounting for this shift, the nondimensional heat transfer rate, $Nu$, follows the classical scaling with supercriticality, while $Re$ remains consistent with the Grossmann--Lohse unifying theory, $Re\propto (Ra-Ra_c)^{1/2}$ for low-$Ra$ convection (regime $\mathrm{I}_u$) and $Re\propto (Ra-Ra_c)^{4/7}$ at high-$Ra$ (regime $\mathrm{III}_u$). Unlike the classical expectation that the latter scaling arises at high Prandtl number, here it is obtained at an intermediate Prandtl number, $Pr\sim 10$. Our results establish how near-freezing material anomalies affect both local and global properties of convection, with implications for heat distribution and mixing in cryospheric liquid waters.