  We present the first lattice QCD calculation of coupled $\pi\omega$ and
$\pi\phi$ scattering, incorporating coupled $S$ and $D$-wave $\pi\omega$ in
$J^P=1^+$. Finite-volume spectra in three volumes are determined via a
variational analysis of matrices of two-point correlation functions, computed
using large bases of operators resembling single-meson, two-meson and
three-meson structures, with the light-quark mass corresponding to a pion mass
of $m_\pi \approx 391$ MeV. Utilizing the relationship between the discrete
spectrum of finite-volume energies and infinite-volume scattering amplitudes,
we find a narrow axial-vector resonance ($J^{PC}=1^{+-}$), the analogue of the
$b_1$ meson, with mass $m_{R}\approx1380$ MeV and width $\Gamma_{R}\approx 91$
MeV. The resonance is found to couple dominantly to $S$-wave $\pi\omega$, with
a much-suppressed coupling to $D$-wave $\pi\omega$, and a negligible coupling
to $\pi\phi$ consistent with the `OZI rule'. No resonant behavior is observed
in $\pi\phi$, indicating the absence of a putative low-mass $Z_s$ analogue of
the $Z_c$ claimed in $\pi J/\psi$. In order to minimally present the contents
of a unitary three-channel scattering matrix, we introduce an $n$-channel
generalization of the traditional two-channel Stapp parameterization.
