Coupling between turbulence and solar-like oscillations: A combined Lagrangian PDF/SPH approach

Aims. This series of papers aims at building a new formalism specifically tailored to study the impact turbulence on global modes oscillation in solar-like stars. first paper deriving linear wave equation that directly and consistently contains as an input model, therefore naturally information coupling between modes, through stochasticity equations. Methods. We use Lagrangian stochastic model based Probability Density Function methods describe evolution properties individual fluid particles differential then transcribe these equations from frame Eulerian frame, more adapted analysis stellar oscillations. combine this method with Smoothed Particle Hydrodynamics, where all mean fields appearing are estimated set themselves, weighting kernel function allowing filter present any given vicinity. The resulting variables linearised. Results. obtain stochastic, governing time relevant variables, while same containing effect turbulence. generalises classical, unperturbed propagation acoustic waves stratified medium form that, by construction, accounts for mode consistent way. consists non-homogeneous forcing term, responsible driving mode, perturbation homogeneous part equation, both damping modal surface effects.