%0 Unpublished Work %A Caillol, P. %D 2005 %T Nonlinear internal waves in the upper atmosphere %U https://repository.lboro.ac.uk/articles/preprint/Nonlinear_internal_waves_in_the_upper_atmosphere/9381158 %2 https://repository.lboro.ac.uk/ndownloader/files/16992737 %K internal waves %K viscous and stratified shear flow instability %K Prandtl number %K Mathematical Sciences not elsewhere classified %X This paper considers the large-scale dynamics generated in the upper atmosphere by the destabilization of a linear internal gravity wave and its eventual restabilization through nonlinear processes into a coherent pattern. The assumption of a strongly dissipative medium is relevant to wave propagation in the thermosphere range above 100 km. A parametric instability analysis is carried out involving the Froude, Reynolds and Prandtl numbers, and the following parameters: friction, wave incidence and disturbance periodicity. A solution of the motion is sought with the help of a multiscale technique based upon the hypothesis of large-scale flow. The leading-order amplitude equation governing this dynamics contains the Cahn-Hilliard equation, but possesses, as well, a dispersive term depending on the Prandtl number, a large-scale damping proportional to the overall Richardson number and a quadratic term modelling the incidence effects. A numerical and analytical study of this equation is given. An internal-wave stability criterion is obtained which shows the possibility of obtaining coherent structures for large Froude numbers. %I Loughborough University