That one solution is maximum entropy,
in hydrostatic balance, and in thermal equilibrium.
Kinetic energy at the surface acting via conduction and convection supplies the upward pressure gradient force which offsets the downward force of gravity in order to constantly hold the mass of an atmosphere off the surface
in hydrostatic balance.
As a further exercise, you can ask whether the virial theorem, correctly applied, gives you any further information about an atmosphere
in hydrostatic balance.
Not exact matches
Furthermore, the key global energy
balance consideration for the terrestrial greenhouse that is
in hydrostatic and thermal equilibrium, is that the solar energy that is absorbed by the ground surface and atmosphere must be
balanced by the outgoing LW emission to space.
So, we are now ready to pull all that together
in order to show how a planetary atmosphere uses convective overturning to neutralise the effect of radiatively active materials of any type so that
hydrostatic balance can be maintained whatever fate throws at it.
In order to maintain
hydrostatic balance the necessary kinetic energy can not be radiated away to space hence that «additional» energy must be held at the surface over and above that which is required (by the surface and atmosphere combined) solely to radiate enough energy to space to match energy being received from space.
The
hydrostatic equation is the vertical component of the momentum equation (Newton's equation of motion) for the fluid parcel when the forces are
in perfect
balance and the net acceleration = 0.»
Suppose you prepare the gas
in hydrostatic equilibrium (so it is
in perfect force
balance) but with a thermal lapse.
Hydrostatic equilibrium: «In fact, the gravitational force is almost exactly balanced by the pressure gradient force, a condition known as hydrostatic e
Hydrostatic equilibrium: «
In fact, the gravitational force is almost exactly
balanced by the pressure gradient force, a condition known as
hydrostatic e
hydrostatic equilibrium.
In fact, a gas with a DALR is a fairly special case of the many «equilibria» one can reach in the specific limit of hydrodynamic relaxation (only) to a state of hydrostatic balance neglecting the much slower thermal relaxation that eventually makes the gas isotherma
In fact, a gas with a DALR is a fairly special case of the many «equilibria» one can reach
in the specific limit of hydrodynamic relaxation (only) to a state of hydrostatic balance neglecting the much slower thermal relaxation that eventually makes the gas isotherma
in the specific limit of hydrodynamic relaxation (only) to a state of
hydrostatic balance neglecting the much slower thermal relaxation that eventually makes the gas isothermal.
** http://www.metoffice.gov.uk/learning/science/first-steps/atmosphere/wind
Hydrostatic equilibrium: «In fact, the gravitational force is almost exactly balanced by the pressure gradient force, a condition known as hydrostatic e
Hydrostatic equilibrium: «
In fact, the gravitational force is almost exactly
balanced by the pressure gradient force, a condition known as
hydrostatic e
hydrostatic equilibrium.
You're still not getting
hydrostatic balance, it doesn't mean nothing is happening and you have to bring
in another idea into the system to work out what will happen..., the adiabatic lapse rate will happen, because gases will become more dense and sink when cold and so will find themselves under great pressure at the surface where they will get compressed and heat up, and heated up they will become less dense and rise and
in rising they will cool and
in cooling they will become more dense and sink and so on.
In a neutral, unheated atmosphere, once one waits a very long time, there is no more movement of air; it achieves
hydrostatic equilibrium, force
balance.
All of them are
hydrostatic —
in perfect force
balance — by construction, they satisfy the differential equation above for the
balance of buoyant forces
in a fluid.
The second one is that
in hydrostatic equilibrium, where the vertical gradient of total air is
balanced by gravity, the dynamic power is only produced by horizontal pressure gradients (i.e. q = — u. ∇ p).
William Gray also raised the point about how the models achieve
hydrostatic balance in his presentation that was so roundly dissed by Judith Curry, among others.
As soon as a global climate model readjusts a vertical column to unphysically alter the large scale solution
in order to maintain
hydrostatic balance (overturning due to unrealistic heating parameterizations necessitate this adjustment), there is no mathematical theory that can justify the nature of the ensuing numerical solution.
Regarding the origin, EU is more closely related to the total internal kinetic energy of the atmosphere, which — according to the virial theorem —
in hydrostatic equilibrium
balances the total gravitational potential energy.
People who know about this scratch their heads here, because it is a principle which can be important
in stars, but applied to Earth just describes the
hydrostatic balance of the atmosphere.