Physics Student Research

Document Type

Article

Journal/Book Title/Conference

Physics of Fluids

Author ORCID Identifier

Ahmad Talaei https://orcid.org/0000-0003-4603-5666

Timothy J. Garrett https://orcid.org/0000-0001-9277-8773

Volume

37

Issue

10

Publisher

AIP Publishing LLC

Publication Date

10-1-2025

Journal Article Version

Accepted Manuscript

First Page

1

Last Page

12

Abstract

Accurate modeling of hydrometeor dynamics is critical for advancing weather and climate predictions. However, this remains a long-standing challenge in atmospheric science, particularly within the transitional Reynolds number regime, due to the lack of analytical solutions to the Navier–Stokes equations. This study presents two analytical solutions for two-dimensional, incompressible, and viscous flow around a sphere, addressing the gap between low and high Reynolds number regimes. The first framework, an extension of classical expansion methods using hypergeometric, provides a direct analytical relation that characterizes separation angle across the transitional regime. To address post- separation dynamics, a second formulation based on a novel variable transformation is introduced, yielding Bessel function solutions capable of reproducing closed streamline patterns and toroidal vortex rings. These solutions provide a computationally efficient and physically interpretable framework, enhancing the fidelity of hydrometeor fall velocity and drag force parameterizations in large-scale atmospheric models.

Comments

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Ahmad Talaei, Timothy J. Garrett; Analytical solutions for transitional flow around hydrometeors: Implications for particle dynamics and atmospheric modeling. Physics of Fluids 1 October 2025; 37 (10): 107104. https://doi.org/10.1063/5.0288667 and may be found at https://doi.org/10.1063/5.0288667.

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