From the definition of J , the Mach number increases with density for flow conditions featuring values of J > 0 . Indeed, this is possible only for values of Γ Γ < 1 , that is in the non-ideal regime. However, this is not a sufficient condition for the non-monotone Mach number to appear, since a sufficiently large value of M is also required. In particular, supersonic conditions ( M > 1 ) are necessary.