Averaging equation of three-dimensional tracer transport by a dual approach

Abstract

The conventional method for calculating averaged tracer concentration in three-dimensional tracer transport equation relies on classical averaging, which averages tracer concentration data obtained from the tracer transport equation in turbulent flow. However, the averaging tracer concentration quantity calculated by this method is not precisely the same as the one obtained by the dual approach. To address this issue, the author proposes a more intricate dual approach for averaging the three-dimensional tracer transport equation in turbulent flow. This paper describes how the author performs two integrations: one from time t to t + r (where r < T, T being the repeated period of fluctuating concentration), and another from time t to time t + T. The fluctuating concentration quantity in turbulent flow is modeled using the trigonometric Fourier series. The resulting three-dimensional mathematical model of tracer transport obtained by this dual approach is more comprehensive than the one obtained by the classical method.