Ok, assuming a planet that's tidally locked to its sun, but is otherwise roughly similar to earth in gravity and atmosphere. Classic tidally locked planet: one side is covered in ice, the other is a scorched desert. And there's water flowing from the glaciers of the dark hemisphere, towards the zenith pole.
I assume that, because of the intensity of evaporation, on the light hemisphere the "sea" level is much lower than on earth, and there exists very deep sky abysses that are the equivalent of our earth's oceans or even deep sea trenches in depth, but mostly filled with air (as opposed to water on our Earth). (see 1, in the drawing) I guess that at the bottom of these abysses we will find the glacier water flow previously mentioned.
My question is: How might the conditions down these abysses be? Assuming an abyss that's comparable in size to one of Earth's deep sea trench (between five to nine kilometers deep and a few kilometers wide) More specifically:
What might be the atmospheric pressure at these depth? Assuming the pressure at the top of the trench (A) is 1 bar. Water pressure is easy enough to calculate: 10 meters of water amount to 1 bar. But how about air? How many bars of pressure 5000 meters deep? How about 9000 meters deep?
At which point in the trench does it starts to be less like the scorched desert of the surface or the frozen glaciers of the dark hemisphere and more pleasant for life as we know it, to the point where it might even flourish? It it only right around where the light and the shadow meets, or could the convection be powerful enough to allow jungles to grow on the light side (D) nearly all the way up? How about the shadow side (C)? What might live there?
How about the bottom (B)? How might it be? Cool because of the water? Unbearably cold because of the shadow? How about the winds? Should it be subjected to permanent super powerful winds, because of the planetary convection and the increased air density?