A Theorem on the Lapse-rate of Free Atmosphere

[摘要] In this paper an approximate formula is introduced, which describes the change of the lapse-rate.Coordinates: x. y in horizontal, z in vertical plane.Velocity components: u in x axis, in y axis and w in z. Temperature. Pressure: T, P.Assumptions: Geostrophic wind is blowing.Two equations of horizontal motion (geostrophic wind), Laplace's equation, the first Iaw of thermodynamics and the following equation are used:This equation describes the change of the lapse-rate (∂T/∂z) of a fluid element with time (t).(The physical meaning of this equation needs to be examined. d/dt refers to one fluid particle, but ∂/∂z must be calculated from (at least) two particles.And so, it is necessary to consider the physical meaning of the notation d/dt (∂T/∂z)•.As regards this, see also my paper in the previous number of this journal.)If ∂/∂z (dQ/dt) is negligible, we get after some ealculations-where Q is the heat added from outside of the air particle. ρ the density A is a constant of an individual particle, and not a universal one.The formula states:- As regards one individual air element, the lapse-rate is proportional to its density.Particle of geostrophic wind has const. density and const. ∂T/∂z. It must be understood that the change of ∂T/∂z is caused by non-adiabatic changes.

[学科分类] 大气科学