On the effective temperature concept for liquid: Paradox of the similarity?

The problem of vortex shedding behind a heated cylinder for diluted gasses can be solved by reducing to an isothermal case by means of introducing some effective temperature Teff and based on the similarity condition ReC,∞ = ReC,eff. Different situation occurs for liquids. At first sight the similarity should exist since the cylinder cooling stabilizes wake flow. Finding the value of c for liquids represents serious experimental problems therefore, still question remains: there exists a similarity for liquids or not? Here we once and for all give answer that for water the similarity, in aforementioned sense, does not exist. Moreover, more general statement has been formulated based on obtained results: if the kinematic viscosity of a fluid tends to fall as temperature increases the similarity does not exist.