A study of clear air turbulence by spontaneous imbalance theory

Emission of inertia–gravity waves (IGWs) through imbalance is a well-known cause of clear air turbulence (CAT) in the upper troposphere. IGWs may initiate CAT by locally modifying the environmental characteristics of the meteorological quantities like static stability and wind shear. CAT is a micro-scale phenomenon for which there are also mechanisms other than IGWs. Accurate forecasting methods using numerical models and CAT diagnostic indices are still being studied and developed (Sharman and Lane, 2016). Following Knox et al. (2008) (hereafter KMW), the current study is focused on detecting CAT by spontaneous imbalance theory and the effect of IGWs on the flow.For this purpose, the lifecycle of the baroclinic waves, including their phases of growth, overturn and decay as well as the generation and propagation of IGWs are investigated by numerical simulation using the Weather Research and Forecasting (WRF) model in a channel of 4000 km length, 10000 km width and 22 km height in respectively the zonal, meridional and vertical directions on the f plane, with a horizontal resolution of 25 km and vertical resolution of 0.25 km. Based on the wave–vortex decomposition (WVD) method, the unbalanced flow, and the dimensional and non-dimensional IGW amplitude have been estimated. In the next step, the non-dimensional wave amplitude has been alternatively determined for reference, based on the Lighthill–Ford theory of spontaneous imbalance in KMW method. Then the turbulent kinetic energy (TKE) dissipation and eddy dissipation rate (EDR) have been calculated to determine the intensity and location of CAT.The results showed that KMW method uses a proportionality constant to make the non-dimensional wave amplitude as order of the Rossby number and determines the constant empirically by matching distributions of pilot reports of turbulence to the pattern of TKE dissipation. For this reason, the EDR has the best fit with the location of observed CAT and the minimum value of Richardson number. This is while most values of the non-dimensional wave amplitudes calculated by the WVD and harmonic divergence analysis are less than unity and have values of the order of the Rossby number itself. On day 8, when the baroclinic wave and IGWs are at their peak of activity, the pattern of distribution of EDR by WVD indicates that there is moderate turbulence all around the jet stream region, and the maximum values of EDR are located below the jet core and in the jet-exit region, which is similar to the location of wave activity and location of CAT in previous studies. Also minimum values of Richardson number are at the jet-exit region where the maxima of EDR reveal moderate turbulence there. The distribution of EDR by KMW, unlike the distribution of EDR by WVD, shows that in most areas of the flow, there is no sign of turbulence except in a few patchy places near the jet region, where moderate turbulence is predicted. Thus making use of an optimal WDV could improve the accuracy of detecting unbalanced parts of the flow and predicting areas of CAT in the upper troposphere in the vicinity of the jet stream.