We discuss the accuracy requirements for measuring mesoscale (roughly horizontal scales >10 km or 5 to 10 times the planetary boundary-layer (PBL) depth) fluxes in the convective PBL, and the ability of current research aircraft to achieve this accuracy. We conclude that aircraft equipped with inertial nagivation systems capable of < 3 km hr −1 navigational accuracy are able to resolve mesoscale fluctuations in velocity, and thus variances and fluxes on the mesoscale. We then discuss measurements of velocity and scalar spectra, and cospectra of vertical velocity with horizontal velocity components and scalars, obtained from long flight legs with the National Center for Atmospheric Research Electra aircraft over the boreal forest of Canada in summer during the BOreal Ecosystem-Atmosphere Study (BOREAS), over the tropical Pacific Ocean from the Tropical Ocean Global Atmosphere Coupled Ocean-Atmosphere Response Experiment (TOGA COARE), and over the East China Sea during wintertime cold-air outbreaks from the Air Mass Transformation Experiment (AMTEX). Each of these studies has somewhat different forcings and boundary conditions, so we can compare their consequences on the spectra and cospectra. On average, we found no significant scalar or momentum fluxes for horizontal scales >10 km. We also develop a simple model based on observed thermal structure to explain the phase angle between vertical velocity and the along-wind horizontal velocity as a function of height, which shows good agreement with the observed phase angle in AMTEX.