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At a particular Mach number, a fluid behaves similarly, but many other conditions could be different.

For example, an aircraft flying at Mach .85 at a low altitude will be in denser, warmer air, and actually flying faster, than the same aircraft flying at Mach .85 at a high altitude.

What aerodynamic differences (if any) will the aircraft experience between the two conditions?

As far as flight aerodynamics is concerned, which of Mach number, true airspeed and indicated airspeed are most significant, and when?

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The Mach number only indicates the behavior of compressibility effects, but does not provide any indication about other effects like inertia and viscosity (read turbulence) or heat transfer.

For high subsonic and supersonic aerodynamics one should typically compare both the Mach number (compressibility) and the Reynolds number (turbulence).

So at the same Mach number but different densities, the Reynolds number will be very different and therefore the turbulence effects will differ highly. Only the compressibility effects will be similar (shock waves).

Note that at low subsonic speeds (Mach<0.3), the compressibility effects become negligible and one can get away by only comparing the Reynolds number. And at hypersonic speeds (Mach~>5) more similarity parameters are needed.

More information about dimensionless numbers in fluid mechanics on Wikipedia.

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There are 2 excellent graphs in the question How does maximum speed vary with altitude?

For flight aerodynamics, we can set aside TAS, which is useful calculating time from point A to B, but not the aerodynamic effects.

That leaves us with IAS and Mach number. At lower altitudes, the Never Exceed Speed has a Mach number less than 1, so it is expressed in IAS. Mach number of a given IAS increases with altitude, there for Mach is limiting "never exceed speed" at higher altitudes.

Temperature slightly increases speed of sound, so in warmer air Mach number will be slightly lower for a given IAS.

So the lower flying aircraft in warmer air at Mach .85 (temperature factor much less significant) will have a higher IAS than the one at higher altitude, there for experiencing stronger aerodynamic effects.

The graphs speak volumes in the linked question.

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  • $\begingroup$ "For flight aerodynamics, we can set aside TAS, which is useful calculating time from point A to B, but not the aerodynamic effects." - that's true of ground speed, but surely not of true airspeed. $\endgroup$
    – Daniele Procida
    Commented Jun 2, 2019 at 15:50
  • $\begingroup$ @Daniele Procida thanks for having me go back and double check this. Yes, True airspeed is the actual speed of the aircraft relative to the air mass (excluding wind direction and speed because the plane moves with the airmass). But at higher altitudes the plane has to go faster to "feel" the same IAS, therefore TAS will be greater than IAS at higher altitudes. Notice TAS is linked to MACH, which is why IAS gives higher MACH numbers at higher altitudes. $\endgroup$
    – Robert DiGiovanni
    Commented Jun 2, 2019 at 16:04
  • $\begingroup$ Never exceed speed actually depends on TAS (too)! There are three effects that limit maximum speed: pressures/forces, which depend on dynamic pressure, so IAS, transsonic flow separation, which depends on Mach number, and flutter, which depends on true airspeed. For aircraft that don't get into the transsonic region, but do get to high altitudes, the Vne is usually tabelated as descreasing with altitude due to flutter. $\endgroup$
    – Jan Hudec
    Commented Jun 5, 2019 at 18:20

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