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This paper studies the growth rate of reconnection instabilities in thincurrent sheets in the presence of both resistivity and viscosity. In a previouspaper, Pucci and Velli (2014), it was argued that at sufficiently highLundquist number S it is impossible to form current sheets with aspect ratiosL/a which scale as $L/a\sim S^\alpha$ with $\alpha > 1/3$ because the growthrate of the tearing mode would then diverge in the ideal limit$S\rightarrow\infty$. Here we extend their analysis to include the effects ofviscosity, (always present in numerical simulations along with resistivity) andwhich may play a role in the solar corona and other astrophysical environments.A finite Prandtl number allows current sheets to reach larger aspect ratiosbefore becoming rapidly unstable in pile-up type regimes. Scalings withLundquist and Prandtl numbers are discussed as well as the transition tokinetic reconnection

The tearing mode instability of thin current sheets: the transition to fast reconnection in the presence of viscosity