最近30从www.hoelymoley.com 2023 - 04 - 04 - t06:01:06z //www.hoelymoley.com/feeds/question/20783 https://creativecommons.org/licenses/by-sa/4.0/rdf //www.hoelymoley.com/q/20783 4 侯 //www.hoelymoley.com/users/21802 2021 - 02 - 09 - t16:38:05z 2021 - 02 - 09 - t17:57:00z

< p >的洛伦茨的论文(我指的是气象学家爱德华·洛伦兹),他说,整个气氛的总势能<跨类= " math-container " > p + I < / span >美元(意味着势能的总和,内部能量)是< / p > < p > <跨类= " math-container " > \{方程}开始p + I = c_p p_ {00} ^ {- x} \ int x p ^ \θdM \结束{方程}< / span > < / p > < p >, < span class = " math-container " > $ p $ < / span >是压力,< span class = " math-container " >美元p_ {00} $ < / span >是一个标准的压力,和<跨类= " math-container " > x < / span >是美元比值<跨类= " math-container " > (c_p - c_v) / c_p美元< / span >, < span class = " math-container " > c_v美元< / span >和<跨类= " math-container " > c_p < / span >是美元的具体加热空气,< span class = " math-container " > \θ< / span >美元是温度和M是质量。< / p > < p >我的知识的基础上,内部的能量应该是一个简单的表单< span class = " math-container " > \{方程}开始我= \ int c_v T dM \{方程}< / span >和势能实际上是重力势能,也就是<跨类= " math-container " > \{方程}开始p = \ int g h dM结束\{方程}< / span > < / p > < p >, < span class = " math-container " > g < / span >美元是重力加速度和<跨类= " math-container " > h < / span >是美元的高度。我的问题是如何洛伦茨派生形式的大气的总势能呢?原来的纸是< em >能源和数值天气预报< / em > < a href = " https://www.tandfonline.com/doi/pdf/10.3402/tellusa.v12i4.9420 " rel = " nofollow noreferrer " >洛伦茨1960 < / >,这个方程是第一个方程。< / p >

//www.hoelymoley.com/questions/20783/-/20784 # 20784 3 BarocliniCplusplus //www.hoelymoley.com/users/704 2021 - 02 - 09 - t17:57:00z 2021 - 02 - 09 - t17:57:00z

< p >首先,让我们承认这一事实:< span class = " math-container " > $ $ c_p = R + c_v \标记{1}$ $ < / span >, < span class = " math-container " >在R < / span >是美元的特定气体常数。< / p > < p >这意味着< span class = " math-container " > $ x = R / c_p $ < / span >。重新排列的方程,我们可以看到,< span class = " math-container " > $ $ P + int I = \ {c_p \离开(\压裂{P} {P_{00}} \右)^ {R / c_p} \θdM} \标记{2}$ $ < / span >注意< span class = " math-container " > \离开美元(\压裂{P} {P_{00}} \右)^ {R / c_p} $ < / span >是< a href = " https://en.wikipedia.org/wiki/Exner_function " rel = " nofollow noreferrer " > < / >报告》功能。推而广之,< span class = " math-container " > $ $ P + int I = \ {c_p T dM} \标记{3}$ $ < / span >如果我们重新排列(1)我们可以得到< / P > < P > <跨类= " math-container " > $ $ P + int I = \ {c_v T + RT dM} \标记{4}$ $ < / span >。你正确地观察到< span class = " math-container " > int I =美元\ {c_v T} dM $ < / span >。这使得< span class = " math-container " > $ $ P = \ int {RT dM} \标记{5}$ $ < / span >。< / p > < p >使用理想气体定律,< span class = " math-container " > $ $ p = \ int {p \αdM} $ $ < / span >, < span class = " math-container " > \α< / span >美元是特定体积。这使得(4)看起来像< span class = " math-container " > $ $ P + int I = \ {c_v T + P \αdM} \标记{4}$ $ < / span >也就是热力学第一定律的重申:< span class = " math-container " > $ \δq = c_v dT + P d \α< / span > < / P >美元

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