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A technique is developed for obtaining the solution of second order over-damped non-linear systems based on the Krylov-Bogoliubov-Mitropolskii (KBM) method for small ratio of the eigenvalues. The solution is also useful for large ratio of the eigenvalues. The method is illustrated by an example.

A second order nonlinear differential system modeling non-oscillatory processes by over damping is considered. Then second order approximate solution is found by means of an extension of the Krylov-Bogoliubov-Mitropolskii (KBM) method. The method is illustrated by an example. The solutions for different initial conditions show a good agreement with those obtained by numerical solution.

Krylov-Bogoliubov-Mitropolskii (KBM) method has been extended for solving fourth order more critically damped non-linear systems. For different damping forces, the solutions obtained by the present method show good coincidence with numerical solutions. The method is illustrated by an example.

In a large eddy simulation (LES), resolving the wide spectrum of large turbulent eddies from O(m) to O(km) in the atmospheric boundary layer (ABL) requires O(109) computational degrees of freedom; however, these eddies are intermittent in space and time. In this research, we take advantage of the spatial intermittency in a neutrally stratified atmospheric Ekman boundary layer, and study the development of a novel LES methodology. Using the second generation wavelet transform, the proposed model filters the large eddies into distinct groups of significant and insignificant eddies. We show that the significant eddies are sufficient to resolve the physics of the flow. The effects of insignificant eddies are modelled with the proposed multiscale parameterization scheme. The results of the proposed model have been found to be in good agreement with that of an equivalent reference model, experimental data, and asymptotic boundary layer theory. We have found that the number of significant eddies in a neutrally s...

An asymptotic method based on the Krylov-Bogoliubov-Mitropolskii (KBM) method has been developed in this article for obtaining the solutions of a third order over-damped non-linear system. For different sets of initial conditions the solutions obtained by this method are better than the solutions found in [13]. The method is illustrated by an example.