T. Dubos | Searcharxiv

arXiv2025

An energetically and thermodynamically consistent Boussinesq model

The Boussinesq approximation is a cornerstone of geophysical fluid dynamics, yet its thermodynamic and energetic underpinnings have remained ambiguous. In standard formulations, the links with the fully compressible Navier--Stokes equations are obscured, internal energy is only implicit, and the representation of diffusion and irreversibility remains \textit{ad hoc}. Here we derive a new Boussinesq model in a fully traceable way from the two-component compressible Navier-Stokes equations, ensuring exact energy conservation and consistent thermodynamics. Assuming a linear equation of state, our model treats density as a proxy for specific volume, distinguishes in-situ and potential temperature explicitly, and incorporates diffusive fluxes that homogenise the correct thermodynamic potentials, ensuring consistent non-negative entropy production. The result clarifies the status of gravitational potential energy, resolves ambiguities surrounding salinity--entropy coupling, and retains the small terms carriers of key information about thermodynamics. Alongside this, we introduce an exact thermodynamically soundproof (TS) model whose weak diabatic divergence highlights the role of compressibility effects in stratified turbulence. Together, these models provide a transparent framework that reconciles classical approximations with compressible energetics, offering better-defined pathways for analysing stratified mixing, mixing efficiency, and the energy budgets of geophysical flows.

physics.flu-dyn↗

arXiv2019

Idealised simulations of the deep atmosphere of hot jupiters: Deep, hot, adiabats as a robust solution to the radius inflation problem

Context: The anomalously large radii of hot Jupiters has long been a mystery. However, by combining both theoretical arguments and 2D models, a recent study has suggested that the vertical advection of potential temperature leads to an adiabatic temperature profile in the deep atmosphere hotter than the profile obtained with standard 1D models. Aims: In order to confirm the viability of that scenario, we extend this investigation to three dimensional, time-dependent, models. Methods: We use a 3D GCM, DYNAMICO to perform a series of calculations designed to explore the formation and structure of the driving atmospheric circulations, and detail how it responds to changes in both upper and deep atmospheric forcing. Results: In agreement with the previous, 2D, study, we find that a hot adiabat is the natural outcome of the long-term evolution of the deep atmosphere. Integration times of order $1500$ years are needed for that adiabat to emerge from an isothermal atmosphere, explaining why it has not been found in previous hot Jupiter studies. Models initialised from a hotter deep atmosphere tend to evolve faster toward the same final state. We also find that the deep adiabat is stable against low-levels of deep heating and cooling, as long as the Newtonian cooling time-scale is longer than $\sim 3000$ years at $200$ bar. Conclusions: We conclude that the steady-state vertical advection of potential temperature by deep atmospheric circulations constitutes a robust mechanism to explain hot Jupiter inflated radii. We suggest that future studies of hot Jupiters are evolved for a longer time than currently done, and, when possible, include models initialised with a hot deep adiabat. We stress that this mechanism stems from the advection of entropy by irradiation induced mass flows and does not require (finely tuned) dissipative process, in contrast with most previously suggested scenarios.

astro-ph.EP↗