The Mean Air Flow as Lagrangian Dynamics Approximation and Its Application to Moist Convection

Abstract

his paper introduces the Mean Airflow as Lagrangian Dynamics Approximation (MAFALDA), a new method designed to extract thermodynamic cycles from numerical simulations of turbulent atmospheric flows. This approach relies on two key steps. First, mean trajectories are obtained by computing the mean circulation using height and equivalent potential temperature as coordinates. Second, thermodynamic properties along these trajectories are approximated by using their conditionally averaged values at the same height and ?e. This yields a complete description of the properties of air parcels that undergo a set of idealized thermodynamic cycles.MAFALDA is applied to analyze the behavior of an atmosphere in radiative?convective equilibrium. The convective overturning is decomposed into 20 thermodynamic cycles, each accounting for 5% of the total mass transport. The work done by each cycle can be expressed as the difference between the maximum work that would have been done by an equivalent Carnot cycle and a penalty that arises from the injection and removal of water at different values of its Gibbs free energy. The analysis indicates that the Gibbs penalty reduces the work done by all thermodynamic cycles by about 55%. The cycles are also compared with those obtained for doubling the atmospheric carbon dioxide, which in the model used here leads to an increase in surface temperature of about 3.4 K. It is shown that warming greatly increases both the energy transport and work done per unit mass of air circulated. As a result, the ratio of the kinetic energy generation to the convective mass flux increases by about 20% in the simulations.