Conservation laws for atmospheric dynamics with clouds

Clouds and rainfall are among the most challenging aspects of weather and climate. In addition to difficulties in observing and simulating clouds, there is a large gap in our theoretical understanding of atmospheric dynamics with clouds versus without clouds (i.e., of moist fluid dynamics versus dry fluid dynamics). Here, I will present some recent work toward closing this gap by defining basic principles of geophysical fluid dynamics (GFD) that hold even in the presence of phase changes of water. In particular, I will present cloudy versions of the conservation principles of energy and potential vorticity, the latter of which is a cloudy extension of the classic Kelvin circulation theorem.