Kinetic Energy Budget for the Madden–Julian Oscillation in a Multiscale Framework

A kinetic energy budget for the Madden–Julian oscillation (MJO) is established in a three-scale framework. The three scales are the zonal mean, the MJO scale with wavenumbers 1–4, and the small scale with wavenumbers larger than 4. In the composite budget, the dominant balance at the MJO scale is between conversion from potential energy and work done by the pressure gradient force (PGF). This balance is consistent with the view that the MJO wind perturbations can be viewed as a quasi-linear response to a slowly varying heat source. A large residual in the upper troposphere suggests that much kinetic energy dissipates there by cumulus friction. Kinetic energy exchange between different scales is not a large component of the composite budget. There is a transfer of kinetic energy from the MJO scale to the small scale; that is, this multiscale interaction appears to damp rather than strengthen the MJO. There is some variation in the relative importance of different terms from one event to the next. In particular, conversion from mean kinetic energy can be important in some events. In a few other events, the influence from the extratropics is pronounced.