3) Oblique Shockwaves

Oblique shockwaves form at an angle to the direction of a flow. They form around an object inside a supersonic flow as a result of pressure build up around the surface of the body. The impact of the flow onto the object causes the flow direction to bend towards the object, and the familiar inclined shockwave front forms, like around the nose of a supersonic aircraft.

Imagine an aircraft flying at a speed, u, in still air. We know that a boundry layer will form around the aircraft where the speed of the air in this boundry layer will vary from u to zero as distance from the aircraft increases. Now imagine that u becomes greater than the speed of sound. The boundry layer becomes unable to form far ahead of the aircraft as the information about the aircraft can't move ahead fast enough. This means that the supersonic boundry layer will abruptly collide with the still air upstream, and so a shockwave forms. Since the boundry layer forms along the surface of the object, the shape of the shockwave will change depending on the shape of the object travelling through the flow.

You don't have to worry about learning about the maths of the formation of oblique shockwaves; they just help build a clearer image of shockwaves generally.