How is Mach related to temperature of the air? How does a sudden change of temperature affects the propulsion of a jet engine?
The term 'Mach' refers to the speed of sound in air, that is corrected for temperature, humidity, and pressure. Temperature and pressure go hand in hand, atmospherically speaking. The warmer the air, the lower the density, thus lower the speed of sound, therefore the higher your speed over the ground to achieve the same Mach number.
There are two kinds of speed we are talking about, one is 'airspeed' - your speed through the air. The other is 'ground speed' - obviously, your speed over the ground. A Mach number is a measure of airspeed, and not of ground speed. Mach is said to change when 1.0 Mach refers to different ground speeds.
A sudden change of temperature will change the propulsion of a jet engine, and more importantly, it will change the way the wing reacts. When jets line up for a formation takeoff, the one in the back is usually sucking hot air from the tailpipe of the ones in front of him. Four things are bad for flying - the four H's: heavy, hot, humid, and high. Heavy is obvious. Hot, humid and high are all related, since any one of these conditions (and worse - more than one) decrease the performance of your airplane.
The worst thing that can happen when you're flying is to tailgate another jet too closely. When that happens you enter a region called the 'jet wash'. Not only is the air hot, and has most of the oxygen burned out of it, but it is also swirling unpredictably. In that case, your jet engines are likely to not get enough clean, cold air, and one (or both) may stall, and flame out. In addition, the unpredictable air can often send your aircraft off tumbling through the sky. So one minute you're flying, remarking on how cool you are, the next, you're upside down, your guts and your head are going different directions, and there's no power. That's no fun. Most modern jet engines are built with computer-controlled fuel control manifolds, which allow the electric brains to figure out what's going on, and at least get the engine running again.
So, in short - the hotter the air, the higher the Mach number, and the faster you must travel over the ground to break the sound barrier. Also - sudden changes of temperature can change the way a jet engine works, but usually that kind of problem is only caused by other jet engines. There are no 'sudden' fluctuations of temperature that occur naturally so fast that the electronic jet engine brains can't deal with it.
Frank DiBonaventuro, B.S., Physics grad, The Citadel, Air Force officer
'One thing I have learned in a long life: that all our science, measured against reality, is primitive and childlike - and yet it is the most precious thing we have.'