An interpretation of the Navier–Stokes-alpha model as a frame-indifferent Leray regularization

We show in this note that the Leray regularization of the Navier–Stokes equations is almost frame-indifferent but for one second-order term. Neglecting this term, we readily recover the Navier–Stokes-alpha equations introduced by Holm et al. [Adv. Math. 137 (1998) 1; Phys. Fluids 11 (8) (1999) 2343]. Hence, as an alternative to the exposition in [Adv. Math. 137 (1998) 1; Phys. Fluids 11 (8) (1999) 2343], we propose to interpret the Navier–Stokes-alpha model as a frame-indifferent perturbation of the Leray regularization.