Modification of the Rankine-Hugoniot relations for shocks in space.

The Rankine-Hugoniot (R-H) equations for hydromagnetic shocks are extended to take into consideration the energy flux and momentum flux due to waves and/or turbulence and/or heat flow in the vicinity of shocks. Eighteen shocks obseved in space were analyzed. It is found that, in order to satisfy the R-H relations with the values of measured parameters in space, waves and/or turbulence and/or heat flow are needed for the shocks with a Mach number of greater than 2, and no waves and/or turbulence are needed to satisfy the R-H equations for the shocks with a Mach number of less than 2. A discussion of the waves, turbulence, and heat flow is given. Fluctuations may considerably affect the time-averaged R-H relations.