A test of time-dependent theories of stellar convection

Context. In Cepheids close to the red edge of the classical instability strip, a coupling occurs between the acoustic oscillations and the convective motions close to the surface. The best topical models that account for this coupling rely on 1-D time-dependent convection (TDC) formulations. However, their intrinsic weakness comes from the large number of unconstrained free parameters entering into the description of turbulent convection. Aims. We compare two widely used TDC models with the first 2-D non-linear direct numerical simulations (DNS) of the convection-pulsation coupling in which the acoustic oscillations are self-sustained by the κ-mechanism. Methods. The free parameters appearing in the Stellingwerf and Kuhfuß TDC recipes are constrained using a χ2-test with the time-dependent convective flux that evolves in nonlinear simulations of highly-compressible convection with the κ-mechanism. Results. This work emphasises some inherent limits to TDC models, that is, the temporal variability and non-universality of their free parameters. More importantly, within these limits, Stellingwerf’s formalism is found to give better spatial and temporal agreements with the nonlinear simulation than Kuhfuß’s one. It may therefore be preferred in 1-D TDC hydrocodes or stellar evolution codes