Comparing Transient Noise, Pnoise, and Pnoise with Lorentian approximation of a ring oscillator

I am investigating a ring oscillator (cmos inverters in chain) for its close-in phase noise. My understanding is that the Lorentian spectrum is supposed to approximate the phase noise PSD at small offset frequency so that it does not go to infinity.

I ran 3 simulations with SpectreRF and plotted the phase noise. The way they are obtained are explained below:

Blue: transient noise simulation: The rising edge time of the clock are obtained and the absolute jitter is obtained by comparing with an ideal clock. PSD of the jitter sequence is obtained in matlab and scaled properly in matlab

Red: PSS/pnoise simulation: Pss/pnoise is performed with sampled(jitter) option on the crossing point of the rising edge. Phase noise is then plotted

Green: PSS/pnoise simulation: Pss/pnoise is performed with timeaverage option. Lorentzian option is turned on. Phase noise is then plotted

Please note that it has been confirmed that the integrated Lorentian spectrum matches the power of the clock fundamental signal power. Also, please note that I have confirmed that timeaverage pnoise has the same result as sampled(jitter), as expected for a sqaure-wave clock.

What I don't understand is why the transient noise simulation result is not flattening as the Lorentian noise spectrum is showing. The transient noise PSD (blue) is matching that of the phase noise plot of the Red. I would think that transient noise should have the large signal effect of the circuits so that the close-in phase noise should be bounded as predicted by Lorentian (green).