Potential Vorticity in a Moist Atmosphere
Potential Vorticity in a Moist Atmosphere
复制标题
潮湿大气中的潜在涡度
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
H. Kuo
中科院分区：
文献类型：
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作者：
W. Schubert;S. A. Hausman;Matthew Garcia;K. Ooyama;H. Kuo
推导了非静力、潮湿、降水大气的位涡原理。已知的(干)Ertel位涡的适当推广为P5R21(2V1=3u)·=ur，其中r是总密度，由干空气、空气水汽(水汽和云凝结)和降水的密度之和组成，u是干空气和空气水汽的速度；而ur 5Tr是虚势R/c Ap a(p/p)0温度，Tr5p/(Rra)是虚温度，p是总压力(干燥空气和水蒸气的分压之和)，P0是恒定参考压力，Ra是干燥空气的气体常数，Cpa是干燥空气的恒压比热。由于ur只是总密度和总压的函数，它作为热力学变量在P中的使用导致螺线管项的湮没，即=ur·(=r3=p)50。在大气绝对干燥的特殊情况下，P减少到通常的(干燥的)Ertel位涡。对于平衡流，存在一个可逆性原理，它根据P的空间分布确定平衡的质量和风场。正是这种可逆性原理的存在，使P成为一个根本上重要的动力变量。换句话说，P(连同与可逆性原理相关的边界条件)携带了关于缓慢演化的流的平衡部分的所有基本动力学信息。
The potential vorticity principle for a nonhydrostatic, moist, precipitating atmosphere is derived. An appropriate generalization of the well-known (dry) Ertel potential vorticity is found to be P 5 r21(2 V1 = 3 u )· =ur, where r is the total density, consisting of the sum of the densities of dry air, airborne moisture (vapor and cloud condensate), and precipitation; u is the velocity of the dry air and airborne moisture; and ur 5 Tr is the virtual potential R /c aP a (p /p) 0 temperature, with Tr 5 p/(rRa) the virtual temperature, p the total pressure (the sum of the partial pressures of dry air and water vapor), p0 the constant reference pressure, Ra the gas constant for dry air, and cPa the specific heat at constant pressure for dry air. Since ur is a function of total density and total pressure only, its use as the thermodynamic variable in P leads to the annihilation of the solenoidal term, that is, =ur ·( =r 3 =p) 5 0. In the special case of an absolutely dry atmosphere, P reduces to the usual (dry) Ertel potential vorticity. For balanced flows, there exists an invertibility principle that determines the balanced mass and wind fields from the spatial distribution of P. It is the existence of this invertibility principle that makes P such a fundamentally important dynamical variable. In other words, P (in conjunction with the boundary conditions associated with the invertibility principle) carries all the essential dynamical information about the slowly evolving balanced part of the flow.