Numerical Study Of The Gravity Waves Nonlinear Propagation And Its Interactions With Mean Winds And Tides

Nonlinear interactions between gravity waves (GWs), mean winds and tidesplay an important role in the middle and upper atmospheric research. In thisthesis, we will study this topic by means of numerical simulation. Two aspectsare studied in this thesis, One of them is the study on the numerical model, theother is the study on the nonlinear GWs propagation by using the model.On the study of the numerical models, two models are established in thethesis: a semi-implicit model and an explicit model. The semi-implicit modelis established by using the time splitting method which combined the explicitalgorithm in the horizontal direction and the implicit algorithm in the verticaldirection. The explicit model is established on the unequal step grid system andusing the 3rd order TVD (Total Variation Diminishing) time integration method.The models developed in this thesis have the following characteristics: (1) The 3rdorder TVD Runge-Kutta time integration method increases the precision of timeintegration. (2) The resolving power of the 4th order compact diflerence schemesuperior to other same order schemes and adapt to simulate the process duringGWs breaking into small scale waves. (3) By using the unequal grid system, notonly the interesting domain can be resolved with higher resolution, but also itcan save the computational cost greatly. Compared with the equal grid systemwith same grids, the unequal step grid system can simulate the evolution of GWsfrom instable to breakdown with higher resolution.In addition, we proposed a high order smooth fitting extrapolate boundaryscheme (SFEBS) based on the idea of non-reflection boundary conditions. Thenumerical results indicate that SFEBS is a better numerical boundary schemefor out flow boundary.On the study of the physical mechanism of GWs nonlinear propagation, thefollowing three aspects are studied by using the numerical model developed inthe thesis. 1. The GWs overturn, saturation and breakdown are studied during GWspropagate nonlinearly. The results indicate that, the nonlinear wave-wave inter-action is induced by the breakdown of GWs directly, thus the energy transfers tosmall scale waves. We also explained the saturation mechanism on the point ofthe nonlinear wave-wave and wave-flow interaction. The research also discoveredthat the nonlinear wave-flow interaction produces energy transform from GWs tomean flow before GWs become instable, and induces the mean flow acceleration.2. The process of GWs propagation in diflerent mean winds is studied. Theresults show that, (1) Compared with GWs propagation in the tail wind, thenonlinear interactions between GWs and the dead wind are also strong, so, thecharacteristics of GWs and the structures of mean flow have changed greatly.(2) The dead wind prolongs the vertical wavelength and accelerates GWs prop-agation. Therefore, GWs propagate up to a higher height, become instable in ashort time and eventually induces an inverse jet flow. Then, the vertical wave-length is becoming short due to the nonlinear interactions between GWs and theinverse jet flow. The inverse jet flow traps the upward propagation of GWs inthe dead wind and diflerent from that predicted by the traditional theory thatGWs propagate can freely in the dead wind.3. we study the nonlinear interactions between GWs with diflerent verticalwavelengths and diurnal tide and compare the above results with that of GWspropagation in the windless background. (1) The diurnal tidal wind acceleratesthe development of GWs instability. GWs instable ranges are consistent withthe ranges of the positive wind shear. Consistent with the dispersion relation,the numerical experiments show that tidal wind reduces the vertical wavelengthsof the GWs when it is in the same direction as the wave propagation, and thusincreases the perturbative shear and the likelihood of instability and wave break-ing, especially for waves with shorter vertical wavelengths. (2) In the conditionof the simulation, GWs with diflerent wavelengths not only accelerate the meanwinds, but also increase the amplitudes of the diurnal tide. The results play animportant role in the research and improvement of GWs parametrization scheme.