Nonlinear atmospheric dynamics

Author: Liu Shishi
Publisher:
Publish Date: 2004-01-01
Features: This section is divided into two parts. The first part introduces basic concepts of nonlinear dynamics, such as equilibrium points, stability, bifurcation, catastrophe, and chaos, starting from some physical problems in nonlinear dynamics. Based on the systematic presentation of these concepts, it introduces their applications in fluid mechanics, particularly in atmospheric science, highlighting the analysis of fluid equilibrium states and new perspectives on turbulence. The second part focuses on the physical analysis of nonlinearity, dissipation, and dispersion in nonlinear waves, exploring the analytical traveling wave solutions of nonlinear evolution equations closely related to physical sciences (e.g., Burgers equation, KdV equation, Sine-Gordon equation, nonlinear Schr?dinger equation, nonlinear vorticity equation, etc.), and introducing concepts such as elliptic waves, solitons, and rogue waves. Additionally, it introduces methods for solving nonlinear evolution equations: perturbation methods, series expansion methods, special transformation methods, scattering inversion methods, and Backlund transformation methods. This book can serve as a reference for scientists and engineers in physics, mechanics, applied mathematics, geophysics, and atmospheric science, as well as for faculty and students in relevant university disciplines.