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Constraining the strength of gas turbulence in protoplanetary discs is anopen problem that has relevant implications for the physics of gas accretionand planet formation. In this work, we gauge the amount of turbulence in 6 ofthe discs observed in the DSHARP programme by indirectly measuring the verticaldistribution of their dust component. We employ the differences in the gapcontrasts observed along the major and the minor axes due to projectioneffects, and build a radiative transfer model to reproduce these features fordifferent values of the dust scale heights. We find that (a) the scale heightsthat yield a better agreement with data are generally low ($\lesssim 4$ AU at aradial distance of $100$ AU), and in almost all cases we are only able to placeupper limits on their exact values; these conclusions imply (assuming anaverage Stokes number of $\approx10^{-2}$) low turbulence levels of$\alpha_{\rm SS}\lesssim10^{-3}-10^{-4}$; (b) for the 9 other systems weconsidered out of the DSHARP sample, our method yields no significantconstraints on the disc vertical structure; we conclude that this is becausethese discs have either a low inclination or gaps that are not deep enough.Based on our analysis we provide an empirical criterion to assess whether agiven disc is suitable to measure the vertical scale height.

Constraining turbulence in protoplanetary discs using the gap contrast: an application to the DSHARP sample