  Spiral shocks are potentially a major source of turbulence in the
interstellar medium. To address this problem quantitatively, we use numerical
simulations to investigate gas flow across spiral arms in vertically
stratified, self-gravitating, magnetized models of galactic disks. Our models
are isothermal, quasi-axisymmetric, and local in the quasi-radial direction
while global in the vertical direction. We find that a stellar spiral potential
perturbation promptly induces a spiral shock in the gas flow. For vertically
stratified gas disks, the shock front in the radial-vertical plane is in
general curved, and never achieves a steady state. This behavior is in sharp
contrast to spiral shocks in two-dimensional (thin) disks, which are generally
stationary. The non-steady motions in our models include large-amplitude
quasi-radial flapping of the shock front. This flapping feeds random gas
motions on the scale of the vertical disk thickness, which then cascades to
smaller scales. The induced gas velocity dispersion in quasi-steady state
exceeds the sonic value for a range of shock strengths, suggesting that spiral
shocks are indeed an important generator of turbulence in disk galaxies.
