Asymptotics of the solution of the turbulent diffusion equation taking into account the polydispersity of the impurity and wind pickup from the underlying surface

TL;DR

This paper develops an asymptotic analysis for a complex turbulent diffusion model that accounts for impurity polydispersity, precipitation, wind pickup, and coagulation-dissociation, using boundary function methods.

Contribution

It introduces a novel asymptotic approach for a singularly perturbed turbulent diffusion equation with non-standard boundary conditions.

Findings

Constructed asymptotics of the solution using boundary functions

Derived main term equations without small parameters

Enhanced understanding of impurity transport in atmospheric models

Abstract

The asymptotics of a singularly perturbed problem is constructed. describing the transport of a polydisperse impurity in the atmosphere, taking into account the processes of precipitation and wind pick-up, as well as the processes of coagulation - dissociation. The mathematical model of this process represents a differential-operator equation of turbulent diffusion with a non-standard boundary condition containing two components - atmospheric and soil. The asymptotics of the solution is constructed by the method of boundary functions. Problems that do not contain small parameters are obtained for the main terms of the asymptotic equation.