Questions and Answers of Essentials Of Atmospheric

For an infinitesimal volume, informally show thatwhere φ is some (differentiable) property of the fluid. Hence informally deduce that D Dt Do (V) = pV : Dt (P1.1)
Show that the derivative of an integral is given byBy generalizing to three dimensions show that the material derivative of an integral of a fluid property is given bywhere the surface integral
(a) Suppose that a sealed, insulated container consists of two compartments, and that one of them is filled with an ideal gas and the other is a vacuum. The partition separating the compartments is
Why is there no diffusion term in the mass continuity equation? Suppose that a fluid contains a binary mixture of dry air and water vapour. Show that the change in mass of a parcel of air due to the
If it is momentum, not velocity, that responds when a force is applied (according to Newton’s second law), why is the momentum equation given by pDv/Dt -Vp and not D(pv)/Dt = -Vp. =
Using the observed value of molecular diffusion of heat in water, estimate how long it would take for a temperature anomaly to mix from the top of the ocean to the bottom, assuming that molecular
Show that viscosity will dissipate kinetic energy in a compressible fluid.
Show that it follows directly from the equation of state, P = RT/α, that the internal energy of an ideal gas is a function of temperature only.Solution: from (??) and p = RT/α, we haveBut,
Show that it follows directly from the equation of state P = RT/α, that for an ideal gas the heat capacity at constant volume, Cv, is, at most, a function of temperature.
(a) Carry through the derivation of the quasi-geostrophic system starting with the anelastic equations and obtain (5.65).(b) Carry through the derivation of the quasi-geostrophic system in pressure
In realistic calculations of the vertical propagation of Rossby waves one must take into account the vertical variation of density. Carry through the calculation leading to the Charney–Drazin