Looking for Equation that can describe both scenarios

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Discussion Overview

The discussion revolves around the search for an equation that can describe two seemingly unrelated scenarios: shock waves in rocket exhaust and traffic patterns on highways. The inquiry explores whether a common mathematical framework exists to explain both phenomena, which involve oscillating patterns.

Discussion Character

  • Exploratory
  • Debate/contested

Main Points Raised

  • One participant describes the formation of oblique shock waves in a rocket exhaust plume and compares it to traffic jams on highways, suggesting a potential connection through a common equation.
  • Another participant expresses skepticism about the feasibility of a single equation adequately describing both scenarios, noting the significant differences between supersonic flow and traffic patterns.
  • A third participant mentions a colleague's claim about reading a comparison in a science magazine, indicating a search for similarities and possibly a fluid dynamics equation.
  • A later reply references an article that attempts to relate shock wave behavior in non-uniform flows to traffic patterns, suggesting a potential avenue for further exploration.

Areas of Agreement / Disagreement

Participants generally express skepticism about the existence of a single equation that can describe both scenarios, indicating a lack of consensus on the matter. Multiple competing views remain regarding the relationship between the two phenomena.

Contextual Notes

The discussion highlights the complexity of relating different physical phenomena and the potential limitations of existing equations in capturing the nuances of both scenarios. There is an acknowledgment of the need for further exploration into the governing equations involved.

JMac14181
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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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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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