Shock Parameters - Definitions of terms

In general, ValueN corresponds to the value before the shock for N=1 and after the shock for N=2 for forward and reverse shocks. The following apply primarily to forward shocks; reverse shocks are handled in a similar manner.

For forward shocks:

DeltaV = AMIN1( 60., 52. / SQRT( AMIN1(AvgShockNp1, AvgShockNp2) ) )
DeltaV = AMAX1( 19., DeltaV )
Term_Vsw = ( AvgShockVsw2 - AvgShockVsw1 ) / DeltaV

NpRatio = AvgShockNp2 / AvgShockNp1
Term_NV = NpRatio * AvgShockVsw2 / AvgShockVsw1

Term_Mach = ShockMach1 / ShockMach2
Term_Vth = AvgShockVth2 / AvgShockVth1


Phase-1:  10-1-10 and 2-1-2 Tests

An event is a candidate for a forward shock if is passes the 10-1-10 requirements

  1. Term_Vsw1   > 1.21 (rejected if it fails this)
  2. Term_Nv1   > 1.16 (tested for reverse if it fails this)
  3. Term_Mach1   > 0.71 (or 0.60 for high speeds) (tested for reverse if it fails this)
  4. Term_Vth1   > 0.94 (or 0.70 for high speeds) (tested for reverse if it fails this)
  5. Max_PM_Rate / Min_PM_Rate   > 1.175

and passes the 2-1-2 requirements (rejected if it fails any of these)

  1. Term_Vsw2   > 1.21
  2. Term_Nv2   > 1.18
  3. Term_Mach2   > 0.64 (or 0.60 for high speeds)
  4. Term_Vth2   > 0.81 (or 0.70 for high speeds)

Phase-2:  Zones 0-4 Definitions

The Quality of a shock is determined from the above terms as follows:

for forward shocks:
ShockQuality = Term_Vsw * Term_NV/1.19 * Term_Mach*1.04
Term1 = ( 10. * (AvgShockVsw2 - AvgShockVsw1) / AvgShockVsw1 )**2
Term2 = ( AvgShockNp2 / AvgShockNp1 / 1.8 )**3
Quality = ( ShockQuality - 1.0 ) * ( Term1 + Term2 )

The ratio Vsw / StdVsw uses the following definitions of the standard deviation for forward and reverse shocks:

Vsw1StdDev = SQRT( 4. + AvgVsw1Sqr - AvgShockVsw1(1) * AvgShockVsw1(1) )
Vsw2StdDev = SQRT( 4. + AvgVsw2Sqr - AvgShockVsw2(1) * AvgShockVsw2(1) )

VswStdDev = SQRT(Vsw1StdDev*Vsw1StdDev + Vsw2StdDev*Vsw2StdDev)


Plot of forward shocks found in zones 1 to 4

Phase-3:  Zones 1-3 Further Tests

The ratio Np / StdNp uses the following definitions of the standard deviation for forward and reverse shocks:

Np1StdDev = SQRT( 0.25 + AvgNp1Sqr - AvgShockNp1(1) * AvgShockNp1(1) )
Np2StdDev = SQRT( 0.25 + AvgNp2Sqr - AvgShockNp2(1) * AvgShockNp2(1) )

NpStdDev = SQRT(Np1StdDev*Np1StdDev + Np2StdDev*Np2StdDev)

details_2.html last modified on 11/2/11 at 5:29 PM by sel