A numerical study of mountain waves in the Upper Troposphere and Lower Stratosphere (UTLS) is presented for two Intensive Observational Periods (IOPs) of the Terrain-induced Rotor Experiment (T-REX). The simulations use the Weather Research and Forecasting (WRF) model and a microscale model that is driven by the finest WRF nest. During IOP8, the simulation results reveal presence of perturbations with short wavelengths in zones of strong vertical wind shear in the UTLS that cause a reversal of momentum fluxes. The spectral properties of these perturbations and the attendant vertical profiles of heat and momentum fluxes show strong divergence near the tropopause indicating that they are generated by shear instability along shear lines locally induced by the primary mountain wave originating from the lower troposphere. This is further confirmed by results of an idealized simulation initialized with the temperature and wind profiles obtained from the microscale model. For IOP6, we analyse distributions of O3 and CO observed in aircraft measurements. These show small scale fluctuations with amplitudes and phases that vary along the path of the flight. Comparison between these fluctuations and the observed vertical velocity show that the behavior of these short fluctuations is due not only to the vertical motion, but also to the local mean vertical gradients where the waves evolve, which are modulated by larger variations. The microscale model simulation results shows favorable agreement with in situ radiosonde and aircraft observations. The high vertical resolution offered by the microscale model is found to be critical for resolution of smaller scale processes such as formation of inversion layer associated with trapped lee waves in the troposphere, and propagating mountain waves in the lower stratosphere.