In this excellent answer, asked for merlin engines deep throttling in first stage and produced here.
To help you understand where the cross over point is, here is some math for understanding the gas dynamics inside the nozzle. Essentially, the nozzle is an accelerator, turning omnidirectional static pressure into directional velocity. In vacuum, there is nothing pushing against the exhaust, so this expansion can theoretically be taken to a maximum where the static pressure of the exhaust is zero. However, inside the atmosphere, the outside air pushes against the exhaust flow. As long as the static pressure of the exhaust is higher than atmospheric, the flow accelerates, however, once the flow is expanded past atmospheric, the atmospheric pressure begins to slow down the exhaust. This wouldn't matter so much if the flow in the exhaust were uniformly high. However, this doesn't happen because of something called a boundary layer. A boundary layer is a thin layer of fluid along a wall that brings the flow from full exhaust velocity down to zero at the wall. It is here where the problems of exhaust wall separation start, because this flow begins slowing down then reversing after the nozzle flow static pressure drops below atmospheric. This flow reversal then starts lifting the gas flow off of the wall. Now, due to viscosity, this gas flow will feel shear forces, which spin up eddies in the gas layer. These eddies act like scavenging pumps, helping the gas flow claw its way back to the wall. However, because the gas has mass, this clawing will go too far, alternating between hitting the wall and lifting far off the wall each time, causing an oscillation to start. Because the flow velocity to flow viscosity ratio is really high (this is called the Reynolds Number), this oscillation will grow not die out with time.
I am having trouble to understand how the gas flow reversal happens on the boundary layer of the nozzle wall ?
and why does it not happen when the static pressure is higher than atmospheric pressure?
