Abstract
The spectra of the zonal and meridional winds and temperature over the mesoscale range of length‐scales (10^−5^10^−3^rad m^−1^, with k the radian wave number) are examined through a case‐study using measurements and simulations. The measurements include 1 s and 10 min average winds and temperature, from which the temporal spectra are obtained by Fourier transform. The mesoscale Weather Research and Forecasting (WRF) model is used to simulate the weather for four days when gravity waves are observed. The four‐day dataset also includes a period with unstable conditions and free of gravity waves. The simulation provides a possibility to study the spatial spectra and, together with the measurements, it provides an opportunity to examine the validity of the Taylor hypothesis for transforming between temporal and spatial spectra. We examined these issues under stable and unstable conditions, both in the absence and presence of gravity waves. It was found that, in the absence of gravity waves, the spectral behaviour of wind and temperature (in terms of the form of the spectra and the energy distribution) is similar to the literature, and the Taylor hypothesis is valid. When the gravity waves are present, it was found that the Doppler‐shifted frequency has to be taken into account when converting the spectra between time and space. The simulation suggests that, in the presence of gravity waves, the kinetic energy is not evenly distributed between the zonal and meridional winds, rather the wind component along the main wave propagation direction contains larger variance. Copyright © 2011 Royal Meteorological Society