Non-Oberbeck-Boussinesq effects in coldwater

TL;DR

This study investigates how water's anomalous properties near freezing influence convection patterns, revealing symmetry breaking, a shifted critical Rayleigh number, and scaling behaviors consistent with established theories, with implications for cryospheric systems.

Contribution

It provides the first detailed numerical analysis of non-Oberbeck-Boussinesq effects in near-freezing water, highlighting their impact on convection dynamics and scaling laws.

Findings

Non-Oberbeck-Boussinesq effects lower mean fluid temperature.

Symmetry of mean temperature profile is broken.

Critical Rayleigh number is slightly shifted.

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.