Shock Waves
The Euler equations are nonlinear hyperbolic equations and their general solutions are waves. Much like the familiar oceanic waves, waves described by the Euler Equations 'break' and so-called shock waves are formed; this is a nonlinear effect and represents the solution becoming multi-valued. Physically this represents a breakdown of the assumptions that led to the formulation of the differential equations, and to extract further information from the equations we must go back to the more fundamental integral form. Then, weak solutions are formulated by working in 'jumps' (discontinuities) into the flow quantities – density, velocity, pressure, entropy – using the Rankine–Hugoniot shock conditions. Physical quantities are rarely discontinuous; in real flows, these discontinuities are smoothed out by viscosity. (See Navier–Stokes equations)
Shock propagation is studied – among many other fields – in aerodynamics and rocket propulsion, where sufficiently fast flows occur.
Read more about this topic: Euler Equations (fluid Dynamics)
Famous quotes containing the words shock and/or waves:
“Children demand that their heroes should be fleckless, and easily believe them so: perhaps a first discovery to the contrary is less revolutionary shock to a passionate child than the threatened downfall of habitual beliefs which makes the world seem to totter for us in maturer life.”
—George Eliot [Mary Ann (or Marian)
“The shattered water made a misty din.
Great waves looked over others coming in,
And thought of doing something to the shore
That water never did to land before.”
—Robert Frost (1874–1963)