Mirage is not the same as turbulence blur. They're related, but different optically. Mirage is the wavy, "fun house mirror" image distortion that you usually see at long distance on hot days.
Turbulence blur happens whenever you have a long optical path over flat terrain (i.e. typical shooting range, bean field or desert conditions), It happens at any temperature, night or day (worse case), as long as the ground temp is different than the day temp. Full daylight in the summer is the worse condition for turbulence blur.
Turbulence blur reduces image sharpness and contrast. The blur effect is usually worse than the difference between HD and and non-HD optics. The image blur is worse for larger objective optics.
So, in turbulence blur conditions, the quality of the scope optics does not determine the image quality. A higher mag scope is only making a blurry image larger; it's not providing more detail about the target. If you have good vision, a small 60-65mm HD scope is about right for shooting range work.
For a dual-purpose scope - shorting range and hunting/nature - a 80-85mm HD scope is a good compromise.