# Looking for Equation that can describe both scenarios

## Main Question or Discussion Point

Scenario 1: Rocket Exhaust Shock Waves
A wave pattern forms on an exhaust plume. The wave is reflected back and forth between the fluid jet boundary, forming oblique shocks which resemble diamonds.

Scenario 2: Traffic Jams on an open highway
While driving on the interstate traffic comes to a halt or a slow down, then it picks up again, then slows back down. Forming a pattern. ----- - - ----- - - ----- - - (something like that, I would imagine).

I was told these two patterns can be found using the same equation or explained using the same equation (not necessarily found). And I cannot for the life of me locate what equation these could be.

Any help on what topic to look under or the equation itself would be nice.

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Mech_Engineer
Gold Member
It seems quite ridiculous that a single equation would be capable of properly describing those two completely different phenomenea. One is supersonic flow, the other is traffic patterns; the only shared relationship between the two is they have some form of oscillating pattern.

Yes is does seem ridiculous. A colleague of mine said that they read it in a science magazine on an airplane and cannot recall which magazine or the basis of the comparison. I have tried to find any similarities possible, maybe some sort of fluids equation?

You may find the following article of interest. If you don't have a subscription that covers it, please let me know.

Ultimately it attempts to relate the governing equations for the behaviour of shocks when meeting a shear layer (such as at wing tips) to the travel of shock waves in traffic in non uniform flows.

On the Propagation of Shock Waves in Regions of Non-Uniform Density
C. W. Jones

Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 228, No. 1172 (Feb. 15, 1955), pp. 82-99

http://www.jstor.org/stable/99477

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