A Lagrangian relaxation towards equilibrium wall model for large eddy simulation

A large eddy simulation wall model is developed based on a formal interpretation of quasi-equilibrium that governs the momentum balance integrated in wall-normal direction. The substitutes law-of-the-wall velocity profile for smooth surface into balance, leading to Lagrangian relaxation towards equilibrium (LaRTE) transport equation friction vector $\mathbf{u}_\tau(x,z,t)$. This partial differential includes timescale governing rate at which stress can respond imposed fluctuations due inertia fluid layer from wall-model height. A-priori tests channel flow direct numerical (DNS) data show identified ensures self-consistency with assumed conditions. new approach enables us formally distinguish additional, non-equilibrium contributions stress. particular derived, motivated by laminar Stokes dynamics viscous sublayer when applying fast varying pressure gradients. modeling first tested standard order document various properties approach. then applied LES suddenly spanwise gradient (SSPG). resulting mean evolution compared DNS good agreement. At onset SSPG, develops rapidly while LaRTE portion has delayed response its inherent dynamics. Results also highlight open challenges such as near-wall turbulence occurring above and timescales faster than