Abstract
This paper mainly focuses on solitary waves excited by topography with time-dependent variable coefficient. By making use of multiple scale expansion and multiple level approximation method, a variable coefficient KdV equation with variable coefficient topographic forcing term is derived from barotropic and potential vorticity equation on a beta-plane including topography effect. In the derivation, removing y-average trick, a higher order term of stream function including five arbitrary functions and forced topography is introduced. Taking the strict solution of the standard constant coefficient KdV equation as the initial value, the approximate analytical solution of the derived equation is obtained by means of homotopy analysis method. Based on the new equation and its analytical solution, some complicated and changeable atmospheric blocking phenomena might be explained when some functions are selected appropriately.
Highlights
Atmospheric blocking is an important large-scale weather phenomenon
When atmospheric blocking occurs at mid-high latitudes, it often causes extraordinary flood, extreme drought or extreme cold, and other abnormal phenomena
A series of research works about topography forcing effect have been carried out [5,6,7,8], most of which still involved constant coefficient nonlinear equations
Summary
Atmospheric blocking is an important large-scale weather phenomenon. When atmospheric blocking occurs at mid-high latitudes, it often causes extraordinary flood, extreme drought or extreme cold, and other abnormal phenomena. The nonlinear variable coefficient equations can be used to explain atmospheric blocking phenomena. [1] used the derived variable coefficient KdV system to explain well the life cycle of a blocking system. Solving analytical solutions of variable coefficient equation with forced term is a long-standing difficulty. Research into exact analytical solutions of KdV type equation with forced term about variable x or X is almost blank. The main purpose of this paper is to derive a new variable coefficient KdV equation with forced term and investigate the evolution process of atmospheric blocking. A new model is derived from a non-dimensional barotropic and potential vorticity equation on a beta-plane including topography effect in Sect. 3, an approximate analytic solution of the derived equation is obtained by HAM, and the evolution process of stream function field is investigated in different parameters.
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