A tree swaying in a turbulent wind: a scaling analysis

Area of Science:

• Fluid dynamics
• Biomechanics
• Forestry

Background:

• Trees are complex structures influenced by wind.
• Understanding tree swaying in turbulent wind is crucial for ecological and structural studies.

Purpose of the Study:

• To develop a tentative scaling theory for tree swaying in turbulent wind.
• To analyze the dynamic bending response of tree branches.
• To investigate the relationship between wind penetration and tree morphology.

Main Methods:

• Development of a tentative scaling theory.
• Analysis of air turbulence within the tree crown, identifying it as the inertial regime.
• Application of a time criterion to model dynamic bending response.
• Use of an energy criterion to assess branch dynamics.
• Discussion of hydrodynamic screening by leaves.

Main Results:

• The air turbulence within the tree crown is characterized as being in the inertial regime.
• An eddy-induced dynamic bending response of branches is described by a time criterion.
• The derived expression for wind penetration depth exponent is consistent with tree branch morphology.
• Branch dynamics are fundamentally passive, as indicated by an energy criterion.

Conclusions:

• The proposed scaling theory provides insights into tree swaying dynamics.
• The findings suggest a passive role for tree branches in response to wind forces.
• Further research can explore the impact of hydrodynamic screening by leaves.