Biometeorology ESPM 129 Lecture 24 Leaf Boundary Layers and their Resistances and Mass and Momentum Exchange Part 1 November 1 2010 Instructor Dennis Baldocchi Professor of Biometeorology Ecosystem Science Division Department of Environmental Science Policy and Management 345 Hilgard Hall University of California Berkeley Berkeley CA 94720 Topics to be Covered A Concepts of laminar and turbulent boundary layers B Induced by laminar or Turbulent Flow C Dimensionless Numbers for computing mass and heat transfer coefficients D Reynolds Number L 24 1 Introduction The layer of air adjacent to leaves is called the leaf boundary layer This boundary layer is extremely important for the functioning of life as it is a critical path for the transfer of trace gases momentum and energy between the atmosphere and biosphere Schuepp 1993 Furthermore it is a path that cannot be circumvented by metabolizing organisms The thickness of the boundary layer and the resistance it imposes on mass energy and momentum transfer has many implications on biophysical processes that may be of interest to us A thick leaf boundary layer will retard the transfer of mass heat and energy causing values of temperature humidity and CO2 concentration at the leaf surface to differ markedly with their corresponding value in the free atmosphere The diffusion of gases through the boundary layer causes isotope fractionation So knowledge on leaf boundary layer diffusion is needed if one expects to use isotopes as a tool to study the difference sources and sinks of carbon oxygen nitrogen and hydrogen isotopes in plant canopies An understanding of the properties and behavior of the leaf boundary layer is needed for physiological purposes besides the assessment of flux densities Plants and leaves respond to stimuli that are experienced at their leaf surface not some distance away in the free streaming air Grantz and Meinzer 1990 If we expect to predict how leaves respond to their environment we must compute the environment at that surface This will require an assessment of leaf boundary layers The boundary layer of leaves has an array of attributes Air moving in the leaf boundary layer can be laminar turbulent or a mix Wind speed near a leaf is reduced markedly 1 Biometeorology ESPM 129 as compared to the velocity in the free air due to surface friction At some level near the surface turbulence becomes suppressed so mass and heat transfer eventually occurs by molecular diffusion Finally Fick s Law of Diffusion is applicable in the laminar layer closest to the leaf Most theories that are used to quantify leaf boundary layers are highly idealized The majority of the theories are derived from engineering theory These methods use dimensionless numbers for mass and heat transfer over ideal shapes flat plates spheres cylinders to generate engineering theory for assessing heat and mass transfer resistances Subsequently Fick s Law of Diffusion and Resistance Analog theories are commonly invoked to evaluate fluxes of heat and trace gases between leaves and the air As a word of caution leaves in the natural environment exhibit much variablity in size shape and orientation Consequently heat momentum and mass transfer resistances are affected by leaf orientation and leaf size On the application of theories we will observe that leaf size induced changes in resistance affects leaf temperature and diffusion of water heat and CO2 between leaf surface and atmosphere L24 2 Laminar and Turbulent Flow To begin understanding mass and energy transfer between surfaces and the atmosphere we must start with concepts on the motion of viscous fluids with cases involving laminar and turbulent flow For it is the motion of the fluid that enables material and energy to travel from one location to another As fluids flow over surfaces the velocity of the fluid decreases as one approaches the surface This is a consequence of friction between the surface and fluid and by the viscous forces within the fluid itself The zone between the surface and the free stream fluid flow is the boundary layer it is a zone where the boundary is exerting an influence on the properties of the fluid flow Fluid flow in the boundary layer is either laminar or turbulent In laminar flow the flow is well behaved and the velocity streamlines are parallel to one another In turbulent flow the streamlines are chaotic and seemingly random Whether or not laminar or turbulent flow is occurring is determined by a balance between the inertial forces due to the moving fluid and the viscous forces which tend to stabilize the flow and make it laminar Pouring honey out of a jar is such an example This fluid is highly viscous and its flow tends to be laminar The Reynold s number is a dimensionless number that is used by fluid mechanics to indicate if fluid flow is turbulence or laminar Reynolds Number is defined as the ratio of inertial forces to viscous forces Re 2 lu lu Biometeorology ESPM 129 When viscous forces are large and predominate flow is able to remain laminar as when one pours syrup from a jar For ideal conditions and flat plates a critical Re defines the onset of turbulence ranges between 104 to 105 A typical critical value is Re 20000 Re 10000 1000 d 1 mm 100 d 1 cm d 10 cm 10 0 2 4 6 8 10 12 u m s 1 Figure 1 Reynolds number as a function of wind speed and length scale Surface irregularities of real leaves can cause the critical Re value for the onset of turbulence to be less than 104 Over a natural leaf a laminar flow will start out laminar when it encounters the edge of a leaf but with distance it will start breaking and form a turbulent boundary layer Grace and Wilson Grace and Wilson 1976 made wind measurements over a populus leaf exposed to 1 m s 1 wind The boundary layer was laminar only for a short distance along the adaxial orientation In this case the natural undulations of the leaf caused the transition between laminar and turbulent flow to occur with Re between 400 and 3000 L24 3 Momentum Transfer and Boundary Layers 3 Biometeorology ESPM 129 An understanding of leaf boundary layers requires an examination of momentum transfer as described by Newton s Law of Viscosity the shear force per unit area is proportional to the negative of the local velocity gradient To visualize the process let s consider a fluid between two plates and set lower plate in motion As time proceeds the fluid adjacent to the plate gains speed And fluid at various adjacent layers close to the moving