A large-eddy simulation study on the diurnally evolving nonlinear trapped lee waves over a two-dimensional steep mountain

The diurnally evolving trapped lee wave over a small-scale two-dimensional steep mountain is investigated in large eddy simulations based on a fully compressible and non-hydrostatic model (ICON) with triangular grids of 50-m-edge length. An idealized atmospheric profile derived from a realistic case is designed to account for influences from the stagnant layer near the surface, the stability of the atmospheric boundary layer (ABL) and the upper-level jet. Firstly, simulations were done to bridge from the linear regime to the nonlinear regime by increasing the mountain height, which showed that larger amplitude lee waves with longer wavelength can be produced in the nonlinear regime than in the linear regime. Secondly, the effects of the stagnant layer near the surface and the ABL stability were explored, which showed that the stagnant layer or the stable ABL can play a similar wave-absorbing role in the nonlinear regime as in linear theories or simulations. Thirdly, the role of the upper-level jet was explored, indicating that a stronger (weaker) upper-level jet can help to produce longer (shorter) lee waves. The stable ABL with a stagnant layer can more (less) efficiently absorb the longer (shorter) lee waves due to the stronger (weaker) jet, so that the wave response is more sensitive to the wave-absorption layer when an upper-level jet is present. Finally, the momentum budget was analyzed to explore the interaction between the upper and lower levels of the troposphere, which showed that the momentum flux due to the upward-propagating waves and trapped waves varies with the upper-level jet strength and low-level stagnancy and ABL stability