Looking for Equation that can describe both scenarios

[JMac14181]

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.

 

[Mech_Engineer]

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.

 

[JMac14181]

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?

 

[timmay]

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

 

[alphy]

I would suggest looking into the field of fluid dynamics to find an equation that could potentially describe both scenarios. In particular, the Navier-Stokes equations are commonly used to study the behavior of fluids, including gases like the exhaust plume from a rocket and the flow of traffic on a highway.

These equations describe the conservation of mass, momentum, and energy in a fluid, and can be used to model the formation of shock waves and other complex flow patterns. However, it is important to note that the equations may need to be modified or simplified for each specific scenario, as the conditions and variables involved may differ.

Other potential equations to consider could be those related to wave propagation, such as the Euler equations, or equations related to traffic flow, such as the Lighthill-Whitham-Richards model. Ultimately, the best approach would be to consult with experts in these fields for guidance on which equations may be most relevant and applicable to both scenarios.