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Turbulence plays a crucial role in shaping the structure of the interstellarmedium. The ratio of the three-dimensional density contrast($\sigma_{\rho/\rho_0}$) to the turbulent sonic Mach number ($\mathcal{M}$) ofan isothermal, compressible gas describes the ratio of solenoidal tocompressive modes in the turbulent acceleration field of the gas, and isparameterised by the turbulence driving parameter:$b=\sigma_{\rho/\rho_0}/\mathcal{M}$. The turbulence driving parameter rangesfrom $b=1/3$ (purely solenoidal) to $b=1$ (purely compressive), with $b=0.38$characterising the natural mixture (1/3~compressive, 2/3~solenoidal) of the twodriving modes. Here we present a new method for recovering$\sigma_{\rho/\rho_0}$, $\mathcal{M}$, and $b$, from observations on galacticscales, using a roving kernel to produce maps of these quantities from columndensity and centroid velocity maps. We apply our method to high-resolution HIemission observations of the Small Magellanic Cloud (SMC) from the GASKAP-HIsurvey. We find that the turbulence driving parameter varies between $b\sim0.3$ and $b\sim 1.0$ within the main body of the SMC, but the median valueconverges to $b\sim0.51$, suggesting that the turbulence is overall driven morecompressively ($b>0.38$). We observe no correlation between the $b$ parameterand HI or H$\alpha$ intensity, indicating that compressive driving of HIturbulence cannot be determined solely by observing HI or H$\alpha$ emissiondensity, and that velocity information must also be considered. Furtherinvestigation is required to link our findings to potential driving mechanismssuch as star-formation feedback, gravitational collapse, or cloud-cloudcollisions.

A new method for spatially resolving the turbulence driving mixture in the ISM with application to the Small Magellanic Cloud