  Surface magnetic fields have been detected in 5 to 10% of isolated massive
stars, hosting outer radiative envelopes. They are often thought to have a
fossil origin, resulting from the stellar formation phase. Yet, magnetic
massive stars are scarcer in (close) short-period binaries, as reported by the
BinaMIcS (Binarity and Magnetic Interaction in various classes of Stars)
collaboration. Different physical conditions in the molecular clouds giving
birth to isolated stars and binaries are commonly invoked. In addition, we
propose that the observed lower magnetic incidence in close binaries may be due
to nonlinear tides. Indeed, close binaries are probably prone to tidal
instability, a fluid instability growing upon the equilibrium tidal flow via
nonlinear effects. Yet, stratified effects have hitherto been largely
overlooked. We theoretically and numerically investigate tidal instability in
rapidly rotating, stably stratified fluids permeated by magnetic fields. We use
the short-wavelength stability method to propose a comprehensive (local) theory
of tidal instability at the linear onset, discussing damping effects. Then, we
propose a mixing-length theory for the mixing generated by tidal instability in
the nonlinear regime. We successfully assess our theoretical predictions
against proof-of-concept, direct numerical simulations. Finally, we compare our
predictions with the observations of short-period, double-lined spectroscopic
binary systems. Using new analytical results, cross-validated by a direct
integration of the stability equations, we show that tidal instability can be
generated by nonlinear couplings of inertia-gravity waves with the equilibrium
tidal flow in short-period massive binaries, even against the Joule diffusion.
In the nonlinear regime, a fossil magnetic field can be dissipated by the
turbulent magnetic diffusion induced by the saturated tidal flows. We predict
that the turbulent Joule diffusion of fossil fields would occur in a few
million years for several short-period massive binaries. Therefore, turbulent
tidal flows could explain the observed dearth of some short-period magnetic
binaries.
