PFM
Not entirly clear what you are asking.
Great circle is always polewards of the rhumb line. From this you can work out what will happen.
If you are in the Northern Hemisphere and are setting out westwards, the GC will be greater (in terms of Track degrees) at the start and less at the end. Thus it will be decreasing as you proceed. Going eastwards from the same starting point the GC will be increasing as you go.