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Turbulence plays a crucial role in shaping the structure of the interstellar medium. The ratio of the three-dimensional density contrast ($\sigma _{\rho /\rho _0}$) to the turbulent sonic Mach number ($\mathcal {M}$) of an isothermal, compressible gas describes the ratio of solenoidal to compressive modes in the turbulent acceleration field of the gas, and is parameterized by the turbulence driving parameter: $b=\sigma _{\rho /\rho _0}/\mathcal {M}$. The turbulence driving parameter ranges from b = 1/3 (purely solenoidal) to b = 1 (purely compressive), with b = 0.38 characterizing the natural mixture (1/3 compressive, 2/3 solenoidal) of the two driving modes. Here, we present a new method for recovering $\sigma _{\rho /\rho _0}$, $\mathcal {M}$, and b, from observations on galactic scales, using a roving kernel to produce maps of these quantities from column density and centroid velocity maps. We apply our method to high-resolution ${\rm H}\,\rm{\small I}$ emission observations of the Small Magellanic Cloud (SMC) from the GASKAP-HI survey. We find that the turbulence driving parameter varies between b ∼ 0.3 and 1.0 within the main body of the SMC, but the median value converges to b ∼ 0.51, suggesting that the turbulence is overall driven more compressively (b > 0.38). We observe no correlation between the b parameter and ${\rm H}\,\rm{\small I}$ or H α intensity, indicating that compressive driving of ${\rm H}\,\rm{\small I}$ turbulence cannot be determined solely by observing ${\rm H}\,\rm{\small I}$ or H α emission density, and that velocity information must also be considered. Further investigation is required to link our findings to potential driving mechanisms such as star-formation feedback, gravitational collapse, or cloud–cloud collisions.

Filamentary structures have been found nearly ubiquitously in molecular clouds and yet their formation and evolution is still poorly understood. We examine a segment of Taurus Molecular Cloud 1 (TMC-1) that appears as a single, narrow filament in continuum emission from dust. We use the Regularized Optimization for Hyper-Spectral Analysis (ROHSA), a Gaussian decomposition algorithm that enforces spatial coherence when fitting multiple velocity components simultaneously over a data cube. We analyse HC5N (9–8) line emission as part of the Green Bank Ammonia Survey and identify three velocity-coherent components with ROHSA. The two brightest components extend the length of the filament, while the third component is fainter and clumpier. The brightest component has a prominent transverse velocity gradient of 2.7 ± 0.1 km s−1 pc−1 that we show to be indicative of gravitationally induced inflow. In the second component, we identify regularly spaced emission peaks along its length. We show that the local minima between pairs of adjacent HC5N peaks line up closely with submillimetre continuum emission peaks, which we argue is evidence for fragmentation along the spine of TMC-1. While coherent velocity components have been described as separate physical structures in other star-forming filaments, we argue that the two bright components identified in HC5N emission in TMC-1 are tracing two layers in one filament: a lower density outer layer whose material is flowing under gravity towards the higher density inner layer of the filament.