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Effects of variable material properties in coldwater convection

Daisuke Noto*

Hugo N. Ulloa

  • *Contact author: dnoto@eng.hokudai.ac.jp
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Phys. Rev. Fluids 11, 063501 – Published 3 June, 2026

DOI: https://doi.org/10.1103/77tz-mg44

Abstract

Thermally driven flows have been extensively studied using the canonical Oberbeck-Boussinesq (OB) approximation, which treats material properties as constant except for the buoyancy force, where small density variations are fundamental to driving motion. Yet the validity of this approximation in coldwater systems remains largely unexplored. In such environments, density variations associated with a given temperature difference are relatively small due to the nonlinear equation of state. In contrast, variation in dynamic viscosity and thermal conductivity remains moderate, comparable to those in warmer systems. Here we numerically investigate the effects of temperature-dependent material properties in two canonical configurations of ice-bounded waterbodies: horizontal and vertical convection. Our results show that variable material properties remain dynamically important and significantly affect global transport quantities in quasi-steady states. In particular, we identify anomalous dynamics under specific conditions, in which the dominance of cold and warm circulations completely reverses. This anomaly leads to up to O(10%) of over- or underestimation in global quantities, including the water-to-ice heat flux, which controls systems' energy and ice melt rates. Although the relative importance of the variable material properties depends on domain size and boundary conditions, their persistent influence in both local dynamics and global quantities underscores their non-negligible and, sometimes, pivotal effects in cold aquatic systems. We therefore conclude that the conventional OB approximation may lead to misinterpretation of the dynamics of cryospheric water bodies by excessively simplifying the underlying thermophysical variability.

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Phys. Rev. Fluids 11, 063501– Published 3 June, 2026
  • Received 29 October 2025
  • Accepted 6 May 2026
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