Peter,
I wasn't going to say anything whilst that stupid semantics argument was raging, but responding to Brian's plea to get back to teasing out a factual explanation of what might be going on and also returning to your original question that related, IIRC, to the effect of afterburner on the secondary induced flow I can offer a explanation based on the Concorde flow set up which, when you look at it closely, is virtually identical to the J58 set up i.e. the intake throat (trap ) bleed flow is passed over the engine as cooling air and then exhausted as an annulus around the primary convergent jet.
I'm no expert on the J58, but I cannot see any reason why the two flows should differ substantially.
For efficiency the secondary flow must be accelerated to supersonic conditions by the time it gets to the final nozzle exit. To my eyes the diagram of the J58 looks to be simplistic in this area because on Concorde at least there wasn't any appreciable mixing of the two flows.
Because it has to be accelerated to supersonic velocity the secondary air must pass through its own aerodynamic 'throat' formed by the expanded primary jet and the solid nozzle surface. The local Mach number at this point will of course be 1.0 and the secondary mass flow will be controlled by the available area at this point. This area will depend on how fast the primary jet expands and this is turn will depend on the pressure ratio between primary and secondary flows at the primary nozzle exit.
The net result (at least for us) was that there was a definite relationship between the corrected secondary mass flow (Ws.sqrt Ts) and the primary jet equivalent Wj.sqrt Tj. as shown on the diagram.
If I have it right, when you light up the afterburner keeping the primary jet exit area the same, the primary jet pressure doesn't change, the mass flow is increased slightly (5% ish?) by the addition of fuel, and the temperature rises substantially. On the cooling side the pressure doesn't change and the temperature will rise a bit because of the hotter jet pipe.
Taken together this means that the corrected mass flow ratio doesn't change much if at all, but because of the increased Tj the secondary mass flow will be increased. I think this is what you were getting at?
OK, if you want to be pedantic the secondary pressure at the nozzle will drop a bit because the starting pressure (intake bleed pressure)and temperature are unchanged but there will be a greater pressure drop through the engine bay as a result of the increased velocity.
If you want to be even more pedantic, when you get to Mach 3 with the spike shock on the lip the total intake capture will be frozen, so any increase in induced cooling flow will be accompanied by a reduction in flow through the engine, so Wj will drop and therefore Ws must drop etc. etc.