As in the question statement, I am wondering whether it is possible for Mach number to increase while local flow velocity decreases. I am basing myself on the simple case of an ideal gas, in which:
$$M=\frac{v}{\sqrt{\gamma R T}}\ \tag{*}$$
If we take a diverging supersonic flow ($dA>0, M>1$), for example, the flow velocity must decrease due to the area-velocity relation below:
$$\frac{dv}{v}=\frac{1}{M^2-1}\frac{dA}{A} \ \tag{**}$$
What happens now? Velocity decreased but (from the corresponding temperature relation), the temperature must increase so the Mach number can go either way from equation $(*)$.
