A simplified 2D model for thermobaricity-driven circulation and water renewal in deep, low-salinity lakes

Stratification strongly influences lake circulation, oxygenation, and biogeochemical exchange. In stably stratified lakes, deep and surface waters can differ markedly in chemical composition. Changes in mixing intensity or overturn events can therefore alter oxygen levels and water quality by redistributing reduced or nutrient-rich deep water.

Accurate modelling of circulation and air-water oxygen exchange in deep, low-salinity lakes requires thermobaric effects, i.e. the pressure-temperature dependence of water density. In such systems, density differences at depth can be small enough that thermobaricity becomes a primary driver of vertical exchange and renewal.

We investigate thermobaricity-driven circulation in a simplified setting using a 2D Boussinesq Navier-Stokes framework in which the buoyancy term is derived from the approximate equation of state for freshwater by Farmer and Carmack (1981). To assess deep water renewal and stratification persistence, we introduce a passive “water age” tracer. We first compute a time-periodic solution for the flow and temperature fields, and then transport the age tracer over many cycles using this periodic state. This approach enables efficient long-term estimates of water renewal time scales and their sensitivity to thermobaric forcing, providing a simplified assessment of physical stability in deep-lake stratification.