  Multi-dimensional (magneto-)hydrodynamical simulations of physical processes
in stellar interiors depend on a multitude of uncalibrated free parameters,
which set the spatial and time scales of their computations. We aim to provide
an asteroseismic calibration of the wave and convective Rossby numbers, and of
the stiffness at the interface between the convective core and radiative
envelope of intermediate-mass stars. We deduce these quantities for rotating
dwarfs from the observed properties of their identified gravity and
gravito-inertial modes. We rely on near-core rotation rates and asteroseismic
models of 26 B- and 37 F-type dwarf pulsators derived from 4-year Kepler space
photometry, high-resolution spectroscopy and Gaia astrometry in the literature
to deduce their convective and wave Rossby numbers. We compute the stiffness at
the convection/radiation interface from the inferred maximum buoyancy frequency
at the interface and the convective turnover frequency in the core. We use
those asteroseismically inferred quantities to make predictions of convective
penetration levels, local flux levels of gravito-inertial waves triggered by
the convective core, and of the cores' potential rotational and magnetic
states. Our sample of 63 gravito-inertial mode pulsators covers near-core
rotation rates from almost zero up to the critical rate. The frequencies of
their identified modes lead to models with stiffness values between $10^{2.69}$
and $10^{3.60}$ for the B-type pulsators, while those of F-type stars cover the
range from $10^{3.47}$ to $10^{4.52}$. The convective Rossby numbers derived
from the maximum convective diffusion coefficient in the convective core, based
on mixing length theory and a value of the mixing length coefficient relevant
for these pulsators, vary between $10^{-2.3}$ and $10^{-0.8}$ for B-type stars
and $10^{-3}$ and $10^{-1.5}$ for F-type stars. (abridged)
