非平衡态大气热力学的研究

RESEARCH ON ATMOSPHERIC THERMODYNAMICS OF NON EQUILIBRIUM STATE

概括了建立非平衡态大气热力学的必要性和迫切性。并在考虑到大气系统是以湍涡为基本单元，具有气压梯度力、重力和 Ｃｏｒｉｏｌｉｓ 力的地球大气宏观体系的基础上，直接引入大气动力学方程组，建立了非平衡态大气热力学的熵平衡方程。使熵平衡方程能直接表达大气中发生的湍流粘性热输送、水汽输送、动量输送和水的三种相变等四类不可逆过程以及 Ｎｅｗｔｏｎ 力 Ｆｉ 驱动的气流输送动力可逆过程。利用 Ｐｒｉｇｏｇｉｎｅ 的最小熵源原理证明大气热力学平衡态就是没有任何湍流输送过程；没有任何水的相变过程；大气动力状态处于静力平衡和地转平衡；热力状态处于中性层结，等压面上温度均匀分布的热力学态。利用大气系统 Ｇｉｂｂｓ 关系得到开放系变态方程，它应包含系统变态过程中位温变化和动能变化以及水汽变化。经典大气热力学中的封闭系多元过程只是它的一种特殊情况。开放系大气水汽相变过程也应包括温度变化和动能变化以及水汽的汽、液和固态水比份变化。经典大气热力学中的湿绝热过程和假绝热膨胀过程也只是它的一种特殊情况。利用热力学流以平衡态作为参考态对热力学力作 Ｔａｙｌｏｒ 展开，可能是湍流闭合的一种新途径。它的优点是在不引入新的方程情况下达到闭合目的。

The paper outlined the necessity and stringency to establish the atmospheric thermodynamics in non equilibrium state. The earth atmosphere is a microsystems that includes turbulence eddies as basic cell. The system is forced by air pressure gradient, gravitation and Coriolis force. Dynamical and thermal processes, which are controlled by heat stratification and turbulence, are dominant action. On the base of above basic characteristics, an entropy balance equation of the atmosphere thermodynamics in non equilibrium state is established to introduce directly equation set of the atmosphere dynamics. t(ρ)=-x jJ sj +σ+σ g,(Ⅰ) J sj =ρU j+1θJ θj +ΔμTJ vj -U iTτ ij ,(Ⅱ) σ=J θj x j1θ-J vj x jΔμT-τ ij x jU iT +1θ(λ vw ν vw ω vw +λ vi ν vi ω vi +λ wi ν wi ω wi )-ΔμTm v(ν vw ω vw +ν wi ω wi ),(Ⅲ) σ g=ρU iT1ρpx jδ ij +gδ i3 -f cε ij3 U j. The entropy balance equation can directly express heat transportation, water vapor transportation, momentum transportation and three kinds of water phase transition generated in atmosphere. Above processes are irreversible process. The entropy balance equation includes also a dynamic process to transport air current that is a reversible process to be driven by Newton power F i. Prigogine's minimum principle of entropy production proves that the equilibrium state of atmospheric thermodynamics is a thermodynamics state, which is: (Ⅰ)static equilibrium; (Ⅱ)geostrophic balance; (Ⅲ)without phase change and turbulence transportation process; (Ⅳ)in neutral stratification and uniform temperature distribution on isobaric surface; and (Ⅴ)relative divergences of absolute temperature, vapor and velocity are equal in space. -1ρpx jδ ij -gδ i3 =0, -1ρpx jδ ij +f c ε ij3 U j=0,(Ⅳ)ρC p u ′ jθ ′ +Q * j=0, ρ u ′ jq ′ =0, ρ u ′ iu ′ j =0,(Ⅴ) θx j=0, 1ΔμΔμx j=1U iU ix j=1TTx j.(Ⅵ) The differential equation of transformation process,which is got by Gibbs relation of atmosphere system, proves that the equation of state transformation in open system should include changes of potential temperature, vapor and momentum in the state transformation process. The metamorphosis process of close system in classical atmosphere thermodynamics is a special instance. The water phase transformation processes in open system should include changes of temperature, kinetic energy and ratio of components of vapor, liquid state water and solid state water. Of course, the moist adiabatic process and the pseudo adiabatic process in classical atmosphere thermodynamics are also its special instance. It may be a new way of turbulence close to expand the thermodynamic flow as the thermodynamic powers at equilibrium state that is taken as a reference thermodynamic state. Its advantage is to obtain the turbulence close without introducing new equations.