Recently, it has been discussed whether the mesoscale energy spectra in the upper troposphere and lower stratosphere are generated by weakly or strongly nonlinear dynamics. A necessary condition for weak non- linearity is that the Rossby number Ro vertical bar zeta(z)vertical bar/f << 1, where zeta(z) is the vertical vorticity and f is the Coriolis parameter. First, it is shown that Ro can be estimated by integration of the rotational wavenumber energy spectrum E-r. Then divergence and rotational energy spectra and their ratio, R E-d/E-r, are calculated from the Measurement of Ozone and Water Vapor by Airbus In-Service Aircraft (MOZAIC) dataset, and it is shown that at least 1000 flight segments are needed to obtain converged results. It is found that R < 1 in the upper troposphere, ruling out the hypothesis that the spectra are produced by inertia-gravity waves with frequencies larger than f. In the lower stratosphere R is slightly larger than unity. An analysis separating between land and ocean data shows that E-d and temperature spectra have somewhat larger magnitude over land compared to ocean in the upper troposphere-a signature of orographically or convectively forced gravity waves. No such effect is seen in the lower stratosphere. At midlatitudes the Rossby number is on the order of unity and at low latitudes it is larger than unity, indicating that strong nonlinearities are prevalent. Also the temperature spectra, when converted into potential energy spectra, have larger magnitude than predicted by the weakly nonlinear wave hypothesis.