# Does a shockwave travel with bulk fluid motion

Given the velocity of the fluid is significantly less than the speed of sound, can a shockwave be assumed to be moving with the fluid reference frame?

For example, let’s assume we’re looking at some cross section of a conical shockwave behind a bullet from directly behind the bullet in a ground referenced system(so it looks like a circle to us, the observer), there is a cross wind of 5 m/s left-to-right for the observer and speed of sound is 340 m/s. Will the rightmost wave front appear to be moving at 345 m/s to the right and leftmost at 335 m/s to the left to the observer? How close to the speed of sound would this approximation be valid (if the approximation is valid at low fluid velocities)?

• Depends on what you mean by " fluid". Waves move very well through liquids but not so well for gases. Oct 31, 2022 at 16:18
• Be careful with talking about the speed of sound. The speed of sound in a gas is temperature-dependent, and one of the important things about a shock wave is that the temperature is significantly different on the two sides of it. Nov 4, 2022 at 11:24
• But it wont be a circle! It will be an ellipse if the cross section is perpendicular to the bullet's path over the ground. You have to cut it perpendicular to the bullet's path through the air in the fluid frame to get the circle. And this is because the shockwave only knows what the fluid is. Aug 1, 2023 at 23:42

Longer answer: the usual derivation of the shock Hugoniot proceeds from starting points including the steady flow energy equation. But if there's a moving shock, the flow is not steady, so the derivation is only valid if it's done in a frame of reference in which (at least some locally planar part of) the shock is stationary. To examine a shock that's propagating into a stationary fluid, one has to do the derivation in the frame where (the locally planar part of) the shock is stationary, then transform at the end into a frame where the fluid far upstream/in front of (the locally planar part of) the shock is stationary, and see how the shock is moving in that frame. In the case of interest to OP, that last step would be replaced by transforming into a frame where the fluid far upstream/in front of (the locally planar part of) the shock is moving at $$5\,\mathsf{m}/\,\mathsf{s}$$.