Leaf Boundary Layer Resistances and Mass and Momentum Exchange:yy g•Concepts of laminar and turbulentConcepts of laminar and turbulent boundary layers•Induced by laminar or Turbulent Flow•Induced by laminar or Turbulent Flow• Dimensionless Numbers for computing d h t t f ffi i tmass and heat transfer coefficients• Reynolds NumberESPM 129 Biometeorology 1ESPM 129 Biometeorology 2Stokes et al 2006 AgForMetBoundary layers over leaves Grace and Wilson ESPM 129 Biometeorology 3Boundary layers over leaves ESPM 129 Biometeorology 4Grace and WilsonLaminarBoundary LayerTurbulentBoundary LayeryyESPM 129 Biometeorology 5Shf it i tiltth ti fthlllitShear force per unit area is proportional to the negative of the local velocity gradient (kg m-1s-2)FVAZAZThe constant of proportionality is the dynamic viscosity (), kg m-1 s-1.ESPM 129 Biometeorology 6Kinematic viscosity (m2s-1) is defined by normalizing dynamic viscosity by the density of the fluidViscosity is a function of the molecular velocity and its mean free path, so it is dependent upon temperature and pressure.ESPM 129 Biometeorology 7Resistance for Momentum transfer, rmu,murm Cud2dzzz12rgmzz11ESPM 129 Biometeorology 8Resistance/Conductance for the diffusion of heat or materialkgm-2s-1Fxaxs,,()dkg m2s1Frgxxaxsxxxa xs,,,,()rgdzDxxzzz112( m/s)rglDccc1( m/s)ESPM 129 Biometeorology 9If gradients in potential are assessed in terms of mixing ratio (c), resistance must be multiplied by the molar volume Vgiving it r units of mol m-2s-1volume, V, giving it, r, units of mol m2s1rgVlDccc1ESPM 129 Biometeorology 10Conceptual diagram of flux, diffusivity and scalar profiles through dj t l i d t b l t b d ladjacent laminar and turbulent boundary layersTurbulentBoundary LayerFlux ProfileK, eddydiff i itScalarConcentrationdiffusivityConcentrationProfileLaminarBoundary Layermolecular, moleculardiffusivityESPM 129 Biometeorology 11Adapted from OkeDefining whether the flow is turbulent or laminarReynolds NumberDefining whether the flow is turbulent or laminar. Reynolds NumberRe duReis the ratio between inertial and viscous forcesReis the ratio between inertial and viscous forces d, physical dimensionu, fluid velocityRe < 2000 laminar, kinematic viscosityESPM 129 Biometeorology 12Osborne ReynoldsRe < 2000, laminarReynolds number as a function of wind speed and length scaleReynolds number as a function of wind speed and length scale10000Relu luRe1000Re10100d: 1 mm d: 1 cm d: 10 cm u (m s-1)02468101210ESPM 129 Biometeorology 13Summary of Concepts•A laminar sublayer always exists close to the surface of leaves, even when experiencing turbulent flow•The Reynolds’ number quantifies whether a leaf is experiencing turbulent or laminar flow and increases with characteristic leaf size.•The conductance for mass transfer is proportional to the molecular diffusivity and the Sherwood number and is inversely proportional to the characteristic leaf sizethe characteristic leaf size.•A constant flux layer exists for heat and mass transfer through the laminar and turbulent boundary layers. The products of molecular (or turbulent) diffusivities and concentration gradients interact torgdzzz12rgdzzz12(or turbulent) diffusivities and concentration gradients interact to preserve this constancy.rgmzz1rgDxxzz1ESPM 129 Biometeorology 14SummarySummary • A laminar sublayer always exists close to the surface of leaves, even when experiencing turbulent floweven when experiencing turbulent flow• The Reynolds’ number quantifies whether a leaf is experiencing turbulent or laminar flow and increases with characteristic leaf size.• The conductance for mass transfer is proportional to the molecular ppdiffusivity and the Sherwood number and is inversely proportional to the characteristic leaf size.• A constant flux layer exists for heat and mass transfer through the laminar and turbulent boundary layers The products of molecularlaminar and turbulent boundary layers. The products of molecular (or turbulent) diffusivities and concentration gradients interact to preserve this constancy.ESPM 129 Biometeorology