- Email: [email protected]
Vapor pressure of ammonium sulfates
0004.6981!78/040148?3 sO?.W/O
Armospherir Enoironmmt Vol. 14, pp. 261-219. Pergamon Press Ltd 1980. Printed in Great Britain.
DISCUSSIONS
that the authors
VAPOR PRESSURE OF AMMONIUM SULFATES*
would reconsider the formation of the H,S04 solution droplets assuming a much lower hydration ratio than I : IO for the saddlepoint composition.
In the meantime, one can only be impressed by the moral example the atmosphere has set for us mortals in this day and age of infidelity. Who but the vilest infidel will not applaud the virtues of a sulfuric acid molecule which stoically withstands millions of collisional invitations by water molecules to condense and waits patiently for its thermodynamically dictated mate, ammonia?
The outstanding paper by Scott and Cattell provides sorely needed data on an atmospheric process of vital importance. Regarding the preferential condensation of H,S04 as (NH,)LS04 rather than as solution droplets, there has been, as the authors state in the introductory section, a lack of general agreement among the earlier workers. I look forward to reading of the forthcoming paper on actual rate calculations by these authors. In as much as kinetic considerations often govern the immediate fate of a reaction system, I hope * Scott W. D. and Cattell Encironmenr 13, 307-3 17.
California Primate Research Center, Unioersity of California. Davis, CA 95616, U.S.A.
F. C. R. (1979) Atmospheric
PURNENTXJK. DASGUPTA
be well-contained by the 17Sm towers at 1OOm. Their comparison with a numerical solution of the two-dimensional gradient diffusion equation showed that the data fell midway between the predictions for K = K, and K = aK,. However, their analysis of the tower data limited the data set to only two runs with L-i less than - 0.05 m-‘, thestability range where the predictions for K, and UK, differ the most. The ground-level, crosswind-integrated tracer concentration measurements provide considerably more vertical diffusion data from the Prairie Grass experiments, not only more runs at IOOm because of fewer restrictions on the analysis but also similar data at 50,200,400 and 800 m. Horst (1979) has used Chaudhry and Meroney’s equation
A NUMERICAL STUDY OF THE VERTICAL DISPERSION OF PASSIVE CONTAMINANTS FROM A CONTINUOUS SOURCE IN THE ATMOSPHERIC SURFACE LAYER* Nieuwstadt and van Ulden (1978) have recently compared the mean dispersion height i measured during the Prairie
Grass diffusion experiments to the predictions of a numerical
solution of the two-dimensional gradient diffusion equation. They examined two choices for the vertical eddy diffusivity, K = Kk the eddy diffusivity for heat and K = aK, where K, di/dx = K(i)/iu(ci), (2) is the eddy diffusivity for momentum and a is the ratio K JK,,, at neutral stability, and found comparable agreement bealong with (1) to predict u,x/Q at z = 1.5m for K = K,, tween measurements and predictions for both alternatives. In K = K,, and s = 1, 1.5 and 2. Here u(ci) is the mean
a companion paper, van Ulden (1978) compared Prairie Grass measurements of the normalized, ground-level, crosswind-integrated tracer concentration x/Q to values predicted by the technique ofchaudhry and Meroney (1973). He assumed K = K,,not K = aK,,,, and used an equation for di/dx slightly different from that of Chaudhry and Meroney. In very similar calculations, Horst (1979) used Chaudhry and Meroney’s equation for di/dx and also found that predictions of x/Q based on K = K, fit the Prairie Grass data quite well. The purpose of this note is to: (1) offer an explanation of why Nieuwstadt and van Ulden found K = K, to be no better than K = aK,, (2) compare the predictions of both Chaudhry and Meroney’s and van Ulden’s equations for d?/dx to the x/Q data, and (3) suggest some additional comparisons between the data and theoretical predictions. Nieuwstadt and van Ulden (1978) very carefully computed Y from the vertical tracer concentration profiles measured 1OOm downwind of the source during Prairie Grass. They required a high correlation between the data and the assumed profile shape x/x0 = expC - WiTI (1) and also that the concentration at the highest measuring level be less than one tenth of the concentration at the lowest level, i.e. they required that the diffusing plume be very regular and *Nieuwstadt
F. T. M. and van Ulden A. P. (1978)
Atmospheric Environment 12, 2119-2124.
horizontal wind speed, n m u(cZ) = X(z/i)dz, u(s)x (z/i@ (3) is 0 s0 and u* is the friction velocity. He found that the best agreement with the Prairie Grass data was for K = K, and s = 1.5 or 2. Using a slightly difdx
different
equation
= K(pf)/piu(pi)
for di/dx,
(4) with p = 1.55, van Ulden (1978) similarly found a good agreement with the Prairie Grass x/Q data for K = K, and s = 1.5. Figure 1 compares the data at 400 m to Horst’s predictions for s = 1.5, K = K, and K = K,, along with the additional prediction for K = aK,.A similar relationship between the data and predictions is found at all distances : the predictions with K = Kh clearly fit the data best. The most unstable data used by Nieuwstadt and van Ulden, runs 15 and 43, are located above the K = K, curve at I!-’ _ - 0.075 m-i and - O.l5m-‘. They have the largest u&Q, and hence the smallest 2 in that stability region. Their location between the K, and aK, curves is found at all distances and is consistent with Nieuwstadt and van Ulden’s fig. 2. Thus the requirement that the plume be well-contained by the height of the towers biases the selection of very unstable runs to those with the smallest Z and largest u&Q, a selection which discriminates against K = KI, and in favor of K = aK,. The more extensive u&Q data show clearly that K, is superior to aK,,,.
267
Armospherir Enoironmmt Vol. 14, pp. 261-219. Pergamon Press Ltd 1980. Printed in Great Britain.
DISCUSSIONS
that the authors
VAPOR PRESSURE OF AMMONIUM SULFATES*
would reconsider the formation of the H,S04 solution droplets assuming a much lower hydration ratio than I : IO for the saddlepoint composition.
In the meantime, one can only be impressed by the moral example the atmosphere has set for us mortals in this day and age of infidelity. Who but the vilest infidel will not applaud the virtues of a sulfuric acid molecule which stoically withstands millions of collisional invitations by water molecules to condense and waits patiently for its thermodynamically dictated mate, ammonia?
The outstanding paper by Scott and Cattell provides sorely needed data on an atmospheric process of vital importance. Regarding the preferential condensation of H,S04 as (NH,)LS04 rather than as solution droplets, there has been, as the authors state in the introductory section, a lack of general agreement among the earlier workers. I look forward to reading of the forthcoming paper on actual rate calculations by these authors. In as much as kinetic considerations often govern the immediate fate of a reaction system, I hope * Scott W. D. and Cattell Encironmenr 13, 307-3 17.
California Primate Research Center, Unioersity of California. Davis, CA 95616, U.S.A.
F. C. R. (1979) Atmospheric
PURNENTXJK. DASGUPTA
be well-contained by the 17Sm towers at 1OOm. Their comparison with a numerical solution of the two-dimensional gradient diffusion equation showed that the data fell midway between the predictions for K = K, and K = aK,. However, their analysis of the tower data limited the data set to only two runs with L-i less than - 0.05 m-‘, thestability range where the predictions for K, and UK, differ the most. The ground-level, crosswind-integrated tracer concentration measurements provide considerably more vertical diffusion data from the Prairie Grass experiments, not only more runs at IOOm because of fewer restrictions on the analysis but also similar data at 50,200,400 and 800 m. Horst (1979) has used Chaudhry and Meroney’s equation
A NUMERICAL STUDY OF THE VERTICAL DISPERSION OF PASSIVE CONTAMINANTS FROM A CONTINUOUS SOURCE IN THE ATMOSPHERIC SURFACE LAYER* Nieuwstadt and van Ulden (1978) have recently compared the mean dispersion height i measured during the Prairie
Grass diffusion experiments to the predictions of a numerical
solution of the two-dimensional gradient diffusion equation. They examined two choices for the vertical eddy diffusivity, K = Kk the eddy diffusivity for heat and K = aK, where K, di/dx = K(i)/iu(ci), (2) is the eddy diffusivity for momentum and a is the ratio K JK,,, at neutral stability, and found comparable agreement bealong with (1) to predict u,x/Q at z = 1.5m for K = K,, tween measurements and predictions for both alternatives. In K = K,, and s = 1, 1.5 and 2. Here u(ci) is the mean
a companion paper, van Ulden (1978) compared Prairie Grass measurements of the normalized, ground-level, crosswind-integrated tracer concentration x/Q to values predicted by the technique ofchaudhry and Meroney (1973). He assumed K = K,,not K = aK,,,, and used an equation for di/dx slightly different from that of Chaudhry and Meroney. In very similar calculations, Horst (1979) used Chaudhry and Meroney’s equation for di/dx and also found that predictions of x/Q based on K = K, fit the Prairie Grass data quite well. The purpose of this note is to: (1) offer an explanation of why Nieuwstadt and van Ulden found K = K, to be no better than K = aK,, (2) compare the predictions of both Chaudhry and Meroney’s and van Ulden’s equations for d?/dx to the x/Q data, and (3) suggest some additional comparisons between the data and theoretical predictions. Nieuwstadt and van Ulden (1978) very carefully computed Y from the vertical tracer concentration profiles measured 1OOm downwind of the source during Prairie Grass. They required a high correlation between the data and the assumed profile shape x/x0 = expC - WiTI (1) and also that the concentration at the highest measuring level be less than one tenth of the concentration at the lowest level, i.e. they required that the diffusing plume be very regular and *Nieuwstadt
F. T. M. and van Ulden A. P. (1978)
Atmospheric Environment 12, 2119-2124.
horizontal wind speed, n m u(cZ) = X(z/i)dz, u(s)x (z/i@ (3) is 0 s0 and u* is the friction velocity. He found that the best agreement with the Prairie Grass data was for K = K, and s = 1.5 or 2. Using a slightly difdx
different
equation
= K(pf)/piu(pi)
for di/dx,
(4) with p = 1.55, van Ulden (1978) similarly found a good agreement with the Prairie Grass x/Q data for K = K, and s = 1.5. Figure 1 compares the data at 400 m to Horst’s predictions for s = 1.5, K = K, and K = K,, along with the additional prediction for K = aK,.A similar relationship between the data and predictions is found at all distances : the predictions with K = Kh clearly fit the data best. The most unstable data used by Nieuwstadt and van Ulden, runs 15 and 43, are located above the K = K, curve at I!-’ _ - 0.075 m-i and - O.l5m-‘. They have the largest u&Q, and hence the smallest 2 in that stability region. Their location between the K, and aK, curves is found at all distances and is consistent with Nieuwstadt and van Ulden’s fig. 2. Thus the requirement that the plume be well-contained by the height of the towers biases the selection of very unstable runs to those with the smallest Z and largest u&Q, a selection which discriminates against K = KI, and in favor of K = aK,. The more extensive u&Q data show clearly that K, is superior to aK,,,.
267