Observation and simulation of flow in vegetation canopies Roger H. Shaw University of California, Davis

Kinetic energy spectral densities that are strongly peaked Strong correlations between streamwise and vertical velocities Large velocity skewness (Sk u >0; Sk w <0) Transport dominated by organized structures Larger contributions from sweep motions than ejections Canopy turbulence

“We will understand the movement of the stars long before we understand canopy turbulence” Galileo Galilei

Time traces of velocity components

Z=2.4h

Z=0.9h

Scalar ‘ramps’ correlated through the depth of the canopy show wholesale ‘ flushing’ of the canopy airspace by large scale gusts.

Scalar

Vertical velocity

Streamwise velocity

Turbulent kinetic energy budget determined from LES

Large-eddy simulation of surface and canopy layers Based on NCAR code developed by Moeng (1984) Modified to include drag effects on both the resolved-scale flow and SGS motions An experimental tool and framework for investigation of observed phenomena

22 Resolved- and subgrid-scales in large-eddy simulation (LES)

LES resolved- and subgrid-scales

canopy periodic horizontal boundary conditions frictionless lid at upper boundary (no flux) uniform force to drive the flow scalar source through depth of canopy

Canopy specification: Represented at each grid point by element area density a (m 2 /m 3 ) Area density horizontally uniform but a(z) Canopy elements rigid Volume occupied by solid elements is considered to be negligible

Static pressure perturbation

22 Resolved- subgrid- and wake-scales

Mean flow KE Resolved- scale TKE Subgrid-scale TKE Internal energy 12 3

Mean flow KE Resolved- scale TKE Subgrid-scale TKE Wake- scale TKE Internal energy Viscous drag Form drag

Drag parameterization: Blasius solution for flow parallel to a flat plate:

inertial cascade form drag SGS energy pool 

inertial cascade form drag SGS energywake energy ww  sgs

Subgrid-scale energy equation where

Wake-scale energy equation where

Additional variable e w to represent kinetic energy associated with wake motions Dissipation of e w controlled by dimension of canopy elements

Additional variable e w to represent kinetic energy associated with wake motions Dissipation of e w controlled by dimension of canopy elements Rate of conversion of kinetic energy from resolved scales to wake scales is large Effective diffusivity of wake-scale turbulence can be ignored

Additional variable e w to represent kinetic energy associated with wake motions Dissipation of e w controlled by dimension of canopy elements Rate of conversion of kinetic energy from resolved scales to wake scales is large Effective diffusivity of wake-scale turbulence can be ignored Important to include the conversion of resolved and SGS energy to wake-scale kinetic energy

Additional variable e w to represent kinetic energy associated with wake motions Dissipation of e w controlled by dimension of canopy elements Rate of conversion of kinetic energy from resolved scales to wake scales is large Effective diffusivity of wake-scale turbulence can be ignored Important to include the conversion of resolved and SGS energy to wake-scale kinetic energy Viscous drag and direct dissipation in viscous boundary layers of leaves is of little consequence

Conditional sampling of LES output and composite averaging of flow structures 1.Pressure signal at z/h=1 used as detection function 2.Structures aligned according to peak in pressure signal 3.Composite averages of various elements of the structures Approximately 1,600 events extracted from one 30-minute time series (but not all independent)

270 seconds (17 frames)

y/h x/h

The structure of the large-eddy motion as a solution to the eigenvalue problem: Where  ij is the spectral density tensor  i is the eigenvector is the associated eigenvalue