• Question 3b from the 2018 and 2019 past papers — applying the conservation of Riemann invariants along characteristics.
• Please explain why for the sub (elliptic) case the lecture notes say: “If M <1, the partial differential equation (3.112a) is elliptic, and requires a condition on φ to be imposed at infinity” and then for the super case we have “We suppose that the flow upstream of the wing is undisturbed, that is φ→0 as x→-∞”
• If we want to apply shallow water theory to the ocean around the Earth (or a planet covered entirely by water), then how would it be done?
• When a piston is pushing into a tube, the lecture notes directly impose a shock. But what if the piston is pushing with a subsonic speed?
• About the definitions of speed of sound, I found it quite difficult to remember them since different situations have their own different definitions. Are they defined for convenience and happen to be the speed or is something behind these definitions?
• 2021 Q3 part b ii