We consider typical area preserving flows on higher genus surfaces and provethat the flow restricted to mixing minimal components is mixing of all orders,thus answering affimatively to Rohlin's multiple mixing question in thiscontext. The main tool is a variation of the Ratner property (a propertyoriginally proved by Ratner for the horocycle flow), i.e. the switchable Ratnerproperty introduced by Fayad and Kanigowski for special flows over rotations.This property, which is of independent interest, provides a quantitativedescription of the parabolic behaviour of these flows and has implications tojoinings classification. The main result is formulated in the language ofspecial flows over interval exchange transformations with asymmetriclogarithmic singularities. We also prove a strengthening of one of Fayad andKanigowski's main results, by showing that Arnold's flows are mixing of allorders for almost every location of the singularities.
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