Navier-stokes Based Modelling of Airflows in Forest Canopies and Its Influence on Local Climate Dynamics
Ruto Faith Chemwetich *
Department of Mathematics and Computer Science, School of Science, University of Eldoret, P.O Box 1125-30100, Eldoret, Kenya.
Albert Bii
Department of Mathematics and Computer Science, School of Science, University of Eldoret, P.O Box 1125-30100, Eldoret, Kenya.
Maremwa Shichikha
Department of Mathematics and Computer Science, School of Science, University of Eldoret, P.O Box 1125-30100, Eldoret, Kenya.
*Author to whom correspondence should be addressed.
Abstract
Background: Forest canopies strongly influence atmospheric airflow, turbulence generation, heat exchange, water transport, and carbon dioxide distribution, thereby regulating the local climate. However, accurately representing airflow dynamics within forests remains challenging because of vegetation drag and turbulent mixing.
Aims: This study developed a mathematical model based on the Navier–Stokes equations to investigate airflow behaviour within forest canopies and assess its influence on local climate dynamics.
Study Design: This was a computational fluid dynamics (CFD)-based modelling study employing the Reynolds-averaged Navier–Stokes (RANS) equations coupled with the standard k–ε turbulence model.
Place and Duration of Study: Department of Mathematics and Computer Science, University of Eldoret, Kenya, between July 2025 and April 2026.
Methodology: The incompressible Navier–Stokes equations were used to model airflow within and above forest canopies. Vegetation effects were represented using a canopy drag-force term based on leaf area density. Turbulence was simulated using the standard k–ε model, while additional transport equations described temperature, water vapour, and carbon dioxide dynamics. The governing equations were discretised using the Finite Volume Method (FVM) and solved numerically in MATLAB. Simulations were performed for dense, medium, and sparse canopy configurations over a 30 m computational domain.
Results: Airflow velocity increased with height in all canopy configurations, with dense canopies showing the greatest attenuation. At canopy height, velocities were approximately 1.45 m/s, 1.95 m/s, and 2.65 m/s for dense, medium, and sparse canopies, respectively. Turbulent kinetic energy (TKE) peaked near the canopy top, reaching approximately 66 m²/s², 44 m²/s², and 22 m²/s², respectively. Temperature increased with height, while moisture and carbon dioxide concentrations decreased because of enhanced turbulent mixing. Dense canopies retained higher moisture and carbon dioxide levels than medium and sparse canopies.
Conclusion: Forest canopy density significantly influenced airflow structure, turbulence production, and scalar transport. Dense canopies provided stronger microclimatic regulation through enhanced momentum attenuation, moisture retention, and carbon storage. The developed modelling framework provides a useful tool for studying canopy–atmosphere interactions and local climate dynamics.
Keywords: Forest canopy, canopy–atmosphere interaction, navier–stokes equations, reynolds-averaged navier–stokes, k–ε turbulence model, computational fluid dynamics, finite volume method, scalar transport, local climate dynamics, leaf area density