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D22303YI ET AL.: DRAINAGE FLOW MODELD22303The shear production rate is usually expressed asP s ¼u 0 w 0 @u@z :ð19ÞThe ratio of the wake and shear production rates is thereforeP w¼ u @u0 w 0@zP s u 0 w 0 @u : ð20ÞSubstituting equations (2) and (3) into equation (20), theratio is reduced to@zP w¼u@c D=@zP s c D @u=@z þ 2 : ð21ÞFigure 9. Half-hour average of SF 6 concentrations at fourtowers during the period 0146–0504 LT on 8 August 2002.During the observation period we observed the typicalS-shaped wind profile (see Figure 10) and the meanObukhov stability was calculated as z =(z d)/L 5.87,indicating highly stable atmospheric conditions above thecanopy (at 21.5 m).optimal performance, we made observations of verticaldispersion at all four observation towers (Figure 9). Therewas clear sharp stratification among even the lowest observationlayers on the WT tower only 50 m downslope fromthe release line, indicating the presence of a thin downslopeflow with little upward mixing. By the time the tracer-ladenair reached the lower towers, there was evidence of somevertical mixing to the 6 m layer, but essentially none in thelayers above 8 m, even at the lowermost tower, 200 mdownslope from the release line. At the south tower (ST)and north tower (NT) we only made observations at thelowest vertical levels; however even at these levels, therewas sharp stratification between the lowest and highestlevels.4.4. Wake-to-Shear Production Rate as a PossibleCause of the Within-Canopy Stable Layer[21] We hypothesized that the stable, within-canopy layeris due to a localized region of high wake-to-shear productionratio. We explored this hypothesis using the analyticalmodel. Ignoring the slope-dependent term in equation (1)we can writeThus the ratio can be estimated on the basis of the windprofile presented in Figure 3 and the drag coefficient profilepresented in Figure 4. Qualitatively, the vertical gradient ofthe drag coefficient is almost opposite to that of wind speed.If the wake-to-shear production ratio is physically limited tobe positive, then it should be theoretically less than or equalto 2.[22] The ratio for the upper part of the canopy calculatedby equation (21) based on the wind and drag coefficientprofiles is shown in Figure 11. Calculated values wereindeed less than 2, except in the lowest part of the canopy,where equation (21) may not be valid because @u/@z 0.The maximum wake-to-shear production rate appears nearthe canopy height of maximum leaf density level rather thannear the top of canopy as has been shown in wind tunnelexperiments [Raupach et al., 1986]. The relative wakeproduction rate decreases linearly to zero from near themaximum leaf area density level to the top of canopy;following the decrease in leaf area density that occurs in theupper canopy layers of these conically shaped trees. Weinterpret this pattern as reflecting the fact that wake turbulenceis caused by the small-scale pressure gradient associatedwith canopy elements and hence depends on leaf areadensity.@u 0 w 0@z¼c D ðÞ‘ z ðÞu z2 ðÞ¼f z D :ð17ÞPhysically, the drag force (form drag) f D is a directconsequence of noncommutation of differentiation and areaaveraging over a horizontal plane that intersects numerousplants, producing the pressure force [Wilson and Shaw,1977; Raupach et al., 1986]. The wake turbulent productionrate is the work done by the flow against the form drag andcan be written asP w ¼ uf D ¼ u @u0 w 0: ð18Þ@zFigure 10. Half-hour average of wind speed at the WTtower during the same period as the SF 6 was observed inFigure 9.8of13