METHODOLOGICAL NOTES

Asymptotic theory of classical tracer transport in inhomogeneous and nonstationary media. Hamilton's formalism

P. S. Kondratenko, L. V. Matveev

Nuclear Safety Institute, Russian Academy of Sciences, Moscow

Abstract: We develop an asymptotic theory of tracer transport due to diffusion and advection, when the diffusivity and advection velocity vary slowly over space and time. The tracer concentration is expressed through a single time integral. The integrand is determined by solving first-order ordinary differential equations, which are similar to Hamilton's equations for a material point in classical mechanics.

Keywords: diffusion, advection, asymptotic form, Hamilton's equations.

PACS: 02.60.Cb, 05.60.Cd, 05.60.-k

Received: June 14, 2024
Revised: September 2, 2024
Accepted: September 13, 2024

DOI: 10.3367/UFNr.2024.09.039764

 English version: Physics–Uspekhi, 2025, 68:6, 627–630

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