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In my lecture notes we making some calculations and all terms [itex]\mathcal O(M^3)[/itex] are to be thrown away. Here M is the Mach number. Now, there is the expression (u denotes the velocity):

[tex]

uu\partial_t \rho \approx \rho_0 uu\nabla u

[/tex]

which in my notes are thrown away because they

**claim**it is [itex]\mathcal O(M^3)[/itex]. But is it really true, I mean the derivative of u will not necessarily be on the same order as Ma, right?