  Galactic fountains driven by star formation result in a variety of kinematic
structures such as ionised winds and thick gas disks, both of which manifest as
complex emission line profiles that can be parametrised by multiple Gaussian
components. We use integral field spectroscopy (IFS) from the SAMI Galaxy
Survey to spectrally resolve these features, traced by broad H$\alpha$
components, and distinguish them from the star-forming thin disk, traced by
narrow components, in 3068 galaxies in the local Universe. Using a matched
sample analysis technique, we demonstrate that the presence of complex emission
line profiles in star-forming galaxies is most strongly correlated with the
global star formation rate (SFR) surface density of the host galaxy measured
within $1R_{\rm e}$ ($\Sigma_{{\rm SFR},R_{\rm e}}$), even when controlling for
both observational biases, including inclination, amplitude-to-noise and
angular scale, and sample biases in parameters such as stellar mass and SFR.
Leveraging the spatially resolved nature of the dataset, we determine that the
presence of complex emission line profiles within individual spaxels is driven
not only by the local $\Sigma_{\rm SFR}$, but by the $\Sigma_{{\rm SFR},R_{\rm
e}}$ of the host galaxy. We also parametrise the clumpiness of the SFR within
individual galaxies, and find that $\Sigma_{{\rm SFR},R_{\rm e}}$ is a stronger
predictor of the presence of complex emission line profiles than clumpiness. We
conclude that, with a careful treatment of observational effects, it is
possible to identify structures traced by complex emission line profiles,
including winds and thick ionised gas disks, at the spatial and spectral
resolution of SAMI using the Gaussian decomposition technique.
