I have found out that a turbofan engine of say an F-16 is producing zero power when stationary since $Power = Thrust × Velocity$. But assuming that the engine is producing the same thrust, it appears that regardless of whether the F-16 is stationary or moving, the engine is still consuming the same amount of fuel and therefore there is power output that is constant in both cases. I also found that the power I tried to calculate from the equation above is the propulsive power, so there must be something else that is consuming the rest of the power.
To make this simple, I will use some numbers. Let's assume a turbofan engine is capable of producing 100 kN of maximum thrust with no afterburner while consuming 4 kg of fuel per second. For the sake of simplicity I'm gonna use a figure of 30% thermal to mechanical efficiency for the engine that is constant through all of the following cases and which means that there is 30% $×$ 4 kg $×$ 42 MJ/kg = $50 MW$ of mechanical power available at all times. With 43 MJ/kg being the heat value of the jet fuel.
Case 1: The engine is stationary and producing max thrust and therefore the propulsive power is zero so I assume that the 50 MW available is completely used in heating and accelerating the exhaust.
Case 2: The aircraft is accelerating and is now at half its max speed at sea level which is say 200 $m/s$. The propulsive power is now = 100,000 kN × 200 = $20$ $MW$ and so I'm also assuming that the other 30 MW remaining of the 50 MW available are still being consumed in accelerating and heating the exhaust.
Case 3: The aircraft reached its max speed at 400 $m/s$ at sea level. The propulsive power is now = 100,000 kN × 400 = $40$ $MW$ and as before, 10 MW are consumed by the exhaust.
So, if I understand this correctly, the power distribution goes from 0% propulsive power and 100% exhaust power when the engine is stionary to 40% propulsive power and 60% exhaust power when the aircraft is at half full speed and continues to shift the power available to propulsive power at higher speed until it is 80% propulsive power and 20% exhaust power. My question now is: In simple terms and with acceptable approximations, does this shift that redistributes the power from exhaust to the propulsive power as the speed increases really happen?