Abstract
Turbulent flows over sparse and dense canopies exerting a similar drag force on the flow are investigated using Direct Numerical Simulations. The dense canopies are modelled using a homogeneous drag force, while for the sparse canopy, the geometry of the canopy elements is represented. It is found that on using the friction velocity based on the local shear at each height, the streamwise velocity fluctuations and the Reynolds stress within the sparse canopy are similar to those from a comparable smooth-wall case. In addition, when scaled with the local friction velocity, the intensity of the off-wall peak in the streamwise vorticity for sparse canopies also recovers a value similar to a smooth-wall. This indicates that the sparse canopy does not significantly disturb the near-wall turbulence cycle, but causes its rescaling to an intensity consistent with a lower friction velocity within the canopy. In comparison, the dense canopy is found to have a higher damping effect on the turbulent fluctuations. For the case of the sparse canopy, a peak in the spectral energy density of the wall-normal velocity, and Reynolds stress is observed, which may indicate the formation of Kelvin-Helmholtz-like instabilities. It is also found that a sparse canopy is better modelled by a homogeneous drag applied on the mean flow alone, and not the turbulent fluctuations.
Highlights
Canopy flows are ubiquitous in both natural and artificial settings
We explore the effect of the canopy parameters on the Kelvin–Helmholtz-like instability and propose simplified models based on linear stability analysis to capture them
We have investigated turbulent flows over canopies using direct numerical simulation
Summary
K Permeability tensor Kij (i, j)th element of the permeability tensor K kxkzEuu Premultiplied spectral energy density of streamwise fluctuations kxkzEuv Premultiplied spectral energy density of Reynolds shear stresses kxkzEvv Premultiplied spectral energy density of wall-normal fluctuations kxkzEww Premultiplied spectral energy density of spanwise fluctuations Kx Streamwise permeability kx Streamwise wavenumber xii. ∆z Spanwise grid resolution γk, ζk Runge–Kutta coefficients for the advective term ∇ Gradient operator κBr Equivalent permeability for substrate governed by Brinkman’s equation xiv κDa Equivalent permeability for substrate governed by Darcy’s equation λf Roughness frontal density λp Roughness plan area ratio λx Streamwise wavelength λz Spanwise wavelength ν Kinematic viscosity νT Turbulent eddy viscosity from Cess (1958). Subscripts (·)max Maximum value xv (·)k Runge–Kutta substep index Other Symbols (ˆ·) Variable in Fourier space ⟨(·)⟩ Quantity averaged in x and z (·) Quantity averaged in x, z and t ( ̃·) Element-induced component Acronyms / Abbreviations CFL Courant–Friedrichs–Lewy number DNS Direct Numerical Simulation K–H Kelvin–Helmholtz QS Quasi-streamwise
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