Not exact matches
«In the real world, convection is intensely variable and clouds have wide
gradients in water vapor density and
vertical velocity,» says Miyamoto.
But I will add that a dependence of the condensation rate on the
vertical velocity component and on the humidity
gradient doesn't strike me as specially contradicting anything I know.
You state ``... [the condensation rate] is proportional to
vertical velocity w (because condensation is due to cooling, hence it is proportional to the
velocity of movement along the temperature
gradient)...» (my emphasis).
Since our atmosphere is horizontally isothermal, the
velocity component that is parallel to temperature
gradient is
vertical velocity w. Please pause at this moment to appreciate that this statement does not in any way follow from the continuity equation.
Actually, in that spirit, approximating a
vertical gradient from the adiabatic rate of change divided by
velocity could work better: just like the
vertical temp.
This relationship determines that in hydrostatic equilibrium any work — w ∂ pi / ∂ z performed by the
vertical partial pressure
gradient per unit time per unit atmospheric volume is compensated exactly by the work — wγiρg performed by the force of gravity that acts on a corresponding molar share γi of the air mass (here w is
vertical velocity).
By averaging over time, you can also get the average
vertical velocity (which should be zero if you aren't in a plume) and average temperature - and
gradients if you measure at more than one height.
As it is, a Hadley cell that conserves angular momentum develops large wind shears and the flow becomes baroclinically unstable (it can be shown through the so - called thermal wind equation that the
vertical gradient of the horizontal wind
velocity is proportional to the horizontal temperature
gradient).
For example, the root system of forest trees facilitates both storage and extraction of moisture from soil; biogenic aerosols produced by trees control the intensity of water vapor condensation over the forest; the large height of trees determines the
vertical temperature
gradient under the canopy, keeping soil evaporation under biotic control; tall trees are also essential for surface friction that does not allow extremely high wind
velocities to develop.
Horizontal temperature
gradients are equivalent to
vertical gradients in wind
velocity, implying implications for the Polar Jet, for example.