Group 1 Includes the Reports:

Amorim, J.H., Miranda, A.I., and Borrego, C., " Air Pollutants Dispersion Disturbance Due to Urban Vegetation: a Porous Media Modeling Approach to Lisbon City Centre," in NATO Advanced Study Institute-980064, Institute of Hydromechanics, Kiev, pp. 46-47, 2004.

Here we see the convincing case of influence of trees (treated as a porous medium) on the concentration levels of pollutant in the city's URL environment.

There are obvious inhomogeneous pollutant's distributions in the streets of Lisbon. The strong inhomogeneity of spatial distribution on the adsorbing surfaces of the buildings testifies in favor of interfacial concentration transport on the Upper scale of modeling spaces.

The modeling experiments brought some features untreatable in the One scale Urban Modeling - those I would like to discuss in the below subsection related to the Experimental efforts demonstrated.

Baklanov, A.A., "Modelling of Urban Air Flows with Application to Air Pollution, Emergency Preparedness and Weather Prediction," in NATO Advanced Study Institute-980064, Institute of Hydromechanics, Kiev, pp. 15-19, 2004.

On page 15 we read - "The main objectives of the current European FUMAPEX project: "Integrated Systems for Forecasting Urban Meteorology, Air Pollution and Population Exposure" (web-site: http://fumapex.dmi.dk) are to improve meteorological forecasts for urban areas, the connection of numerical weather prediction models to urban air pollution and exposure models, build improved Urban Air Quality Information and Forecasting Systems, and demonstrate their application in cities subject to various European climates."

Page 16 - "Accordingly, considering the mentioned above features, the following aspects of the urban effects in the improved urban-scale NWP models should realized:.....

Calculation of effective urban roughness ;"

Page 17 - "1. Simple corrections of the surface roughness for urban areas, e.g., following Mestayer et al., (2003), and heat fluxes (adding the albedo changes and additional urban heat flux, e.g. via heat producion in the city) within the existing non-urban physical parameterizations of the surface layer in the model with higher resolution and improved land-use classification. It is realized in the DMI-HIRLAM model. ........

Increased resolution and surface data-bases for the roughness length calculation in operational NWP models are considered and tested in DMI-HIRLAM, LM, MM5, and RAMS models, used by the FUMAPEX partners."

On page 18 we can read that - "

Modified parameterizations and algorithms for roughness parameters in urban areas based on the morphologic methods are developed. ??....

Improved models for urban roughness sublayer simulation, including

(i) Effective roughness and flux aggregation technique,

(ii) Effect of stratification on the surface resistance over very rough surfaces,

(iii) Roughness for momentum, heat, and moisture, are suggested."

No questions, but ?

What a waste, What a cost of this "Roughness Science" ?
For more than 60 years since the time of Nikuradze and Schlichting the "science" of the roughness oust height, the displacement height (d₀) is just only the second after the Turbulence Theory in terms of time wasted and money spent for it. And when for the first 40 years that was somehow justified, then nowadays ?

The progress now is that few groups in Australia, USA, France and the UK seems have stopped to use this language as the only possible one.
~~~

Hunt, J.C.R., "Discrete and Continuum Models of Flow and Dispersion Through Canopies," in NATO Advanced Study Institute-980064, Institute of Hydromechanics, Kiev, pp. 30-32, 2004.

Page 30: "2) spatially averaged properties determined by average drag forces on the obstacles and their volume to displacements." The averaging assumed as in a one huge volume to include everything in it.

Page 31 we read that - "The effect of the canopy on the mean flow can be modeled as a distributed drag force (which depends on the wind speed in the canopy and therefore has to be determined interactively)."

These two sentences above show that author does not know that these tools have been already developed for 15-20 something years before. And that these wishful ideas have been already studied and published.

The references are on the paper of 2003 - by Belcher, S.E., Jerram, N., and Hunt, J.C.R., "Turbulence Structure Around a Columnar Vortex; Rapid Distortion Theory and Vortex Wave Excitation," Journal of Fluid Mechanics, Vol. Vol. 448, pp. 369-398, 2003.

and few more including:

Hunt, J.C.R. and Eames, I., "The Disappearance of Laminar and Turbulent Wakes in Complex Flows," Journal of Fluid Mechanics, Vol. 457 ??, pp. 111-132, 2003.

Eames, I., Roig, V., Belcher, S.E., and Hunt, J.C.R., "General Theory of Inviscid Flow Through and Around Clouds of Obstacles," in NATO Advanced Study Institute-980064, Institute of Hydromechanics, Kiev, pp. 73, 2004.

This is the study which should not exist if authors used to know that the averaging mathematics have been developed long ago.

On page 73 we can read: "However, in the near body region the drag coefficient required to fit experimental data is generally unrealistic. Physically, the essential component which is generally ignored is the role of blocking - the fact that the flow must go around bodies as a kinematic constraint, rather than a dynamical constraint in terms of forces."

"Despite the fact that the theoretical analysis relies on an inviscid description, we will show that a number of fundamental and general physical processes suggest that this approach gives practical estimates for average flow properties for closely packed bodies - such as the urban terrain - contrary to our general assumptions."

In reality the proper averaging either inviscid or viscous flow dynamics equations just remove the all worries and questions mentioned above in the authors abstract.

Nepf, H. M., White, B., Lightbody, A., Ghisalberti, M., Tanino, Y., "Transport in Aquatic Canopies," in NATO Advanced Study Institute-980064, Institute of Hydromechanics, Kiev, pp. 38-40, 2004.

Despite that in the text mentioned the volumetric averaging - the characteristics (properties) of the flow inside of aquatic canopies were being derived using the dimensional general analysis fluid mechanics considerations. As it was found in the written text in the paper by White and Nepf (White, B., and Nepf, H. M., "Scalar Transport in Random Cylinder Arrays at Moderate Reynolds Number," J. Fluid Mech., Vol. 487, pp. 43-79, 2003) the modeling equations are also incorrect, that is why there is no direct interconnection between the model and derived parameterized estimations of characteristics.

On page 47 of that paper we can read - "the two-dimensional incompressible Navier-Stokes equation" momentum equation will be after "averaging" as

which instantly qualifies this equation as the non-averaged equation - see this website sections on "Fluid Mechanics"

and "Fundamentals of ...."

and papers by Whitaker, Slattery, Gray, and other researchers those who established the science of averaging in heterogeneous media.

Meanwhile, on page 48 one can find that the averaged diffusion equation (11) is

meaning that the and are constants? All other theoretical considerations in the paper covers the different assumptions used for parameterization of some effects.
~~~

Van Liefferinge, R., Soulhac, L., Mejean, P., Perkins, R.J., and Salizzoni, P., "Modeling the Urban Canopy as a Porous Medium," in NATO Advanced Study Institute-980064, Institute of Hydromechanics, Kiev, pp. 128-129, 2004.

Page 129 - "The porosity Model.
The influence of a group of obstacles on the flow in the boundary layer can be modelled as a distributed drag force varying in all three dimensions in space. A physical analogy of such a spatially-varying drag force would be the influence of an inhomogeneous porous layer and such a drag force can be incorporated into existing codes through porous modules. The fundamental problem which must be resolved in order to exploit such an approach is the estimation of an appropriate permeability, which will depend on the size, spacing and organisation of the obstacles, and on the properties of the wind flow."

This is the undergraduate level text, and the seniors might be not paid attention.

Group 2 Includes the Reports:

Coceal, O., Thomas, T.G., Castro, I.P., and Belcher, S.E., "Turbulent Flow Over Groups of Urban-Like Obstacles," in NATO Advanced Study Institute-980064, Institute of Hydromechanics, Kiev, pp. 62-63, 2004.

This is the very much awaited study - with the simulation experiment aimed to calculate the some part (stress tensor components) in the averaged Upper scale equation of turbulent momentum for inside and above the porous layer. The porous layer was taken as the regular network of straight square pin fins.

The authors did attempt to make averaging of the flow dynamics characteristics as the Reynolds stress in usual sence, and of the dispersive stress one component (vertical) as via using the equation (following Raupach and Shaw, 1982)
with the spatial fluctuation given as
where the averaging done as the surface-plane 2D averaging
This momentum averaged equation is incorrect equation - see the analysis above in the http://travkin-hspt.com/urbp/turbpart/Turbpart.htm

I consider this is the good experiment, with errors but still a good experiment, and I would like to comment on it below in the subsection of this website -

Finnigan, J.J., "Turbulent Flow in Canopies on Complex Topography and the Effects of Stable Stratification," in NATO Advanced Study Institute-980064, Institute of Hydromechanics, Kiev, pp. 20-24, 2004.

These four lectures by Profs. J.J.Finnigan and R.H.Shaw have the common basis and we would like to comment on it as soon as it is the ground for numerous publications of few groups of meteorologists from Australia, US, England and France.
~~~

Finnigan, J.J. and Shaw, R.H., "Large-Eddy Structure and Low Dimensional Modeling of Canopy Turbulence," in NATO Advanced Study Institute-980064, Institute of Hydromechanics, Kiev, pp. 80-81, 2004.

Few remarks regarding this report were placed below into the "experimental" subsection -

Finnigan, J.J., "Turbulent Fine Structures and Spectra in Canopies ," in NATO Advanced Study Institute-980064, Institute of Hydromechanics, Kiev, p. 79, 2004.

Here is the good research, but with the flawed foundation - averaged equations of turbulent transport, including the TKE and Dissipation rate equations are incorrect.

In the slide of presentation one can read - "Non-Local Transport leads to failure of K-Theory".

Of coarse - because among other reasons, these are the different spaces! We can not compare the both equations budgets using the same one scale !

Page 79 - "Both effects, which are together responsible for the enhanced rate of dissipation observed in canopies, can be equated to the rate that the turbulent flow does work against the total aerodynamic drag (pressure plus viscous) of the foliage."

The problem with this statement is that those effects for the dissipation in the canopy "porous" medium are more than those two only mentioned by author. The TKE and the dissipation rate equations averaged over the fluid phase in suggested by author forms have no integral terms in both equations, at least in the second one the integral terms specified incorrectly.

There is no sense (logic) to study the budgets in both equations and parameterize some effects in them, when the whole body of very important terms just is missing from those equations !

I had a difficult task after this NATO ASI to select the points, the arguments those are obvious to me for more then 20 years.

Since the middle of 80-th I have been talking to students and at some conferences, including that 1986 WMO conference - Shcherban, A.N., Primak, A.V., and Travkin, V., "Turbulent Transfer in Urban Agglomerations on the Basis of Experimental Statistical Models of Roughness Layer Morphological Properties", in Proc. World Meteorological Organization Conf. on Air Pollution Modelling and its Application, Transactions, Geneva, Vol. 2, pp.259-266, (1986), (see this paper in the above subsection with the rules of averaging (4), and the VAT averaged Upper scale turbulent governing equations (5) - (7)), where I firstly spoke to a wide meteorological audience about the scaled turbulent transport in the URL, porous media, that some other advancements in the same direction are unfound, simply incorrect.

Well, after near 20 years I saw that people in other fields using those incorrect governing equations as the basis, referring to those publications now accounting for more then 20 years of printing. Primarily in meteorological journals, as "Boundary Layer Meteorology," and others.

Now, the events at this NATO ASI shown that people completely don't understand mathematical basics, those standing behind all of these averaging procedures and governing equations.

Researchers using those rules without knowing what kind of conditions, restrictions were applied while they were derived ? What kind of equations are conditioned with these theorems and rules. All of this is given in the literature on fluid mechanics (not meteorological studies), chemical technology and thermal physics related VAT publications. I never saw the complete paths of derivations as S.Whitaker, and W.Gray have done regarding the laminar, half-linear governing equations?

If any of this kind of publications would be done in meteorology - the publications should inevitably contain the VAT theorems used to derive that or those formulae, or the rule. That means these studies; these mentioned publications in the meteorology by said groups of meteorologists would not stand apart of the other fluid mechanics areas where the scaled VAT tasks began to find accomplishments since 80-th!

It is the good reason to speak openly about those basics for claimed turbulent models theory by few groups of meteorologists, associated with Profs. Shaw, Finnigan, Raupach and their collaborators in Australia, US, England, and France.

Among a number of their publications I had selected this one.

Here we need to talk about this paper below which was published in 2000 and pretty much serving as a summarizing paper for publications by groups of authors using the same methodology for Turbulent (and Laminar regime) Governing Equations (GE) for canopy (obstructed volumes) development.

Finnigan, J., "Turbulence in Plant Canopies," in Annu. Rev. Fluid Mech. 2000, Vol. 32, pp. 519--571, 2000.

There are on the page 521-522 the definitions of the decomposed general variable as

and

The question is - What are the connections between both? If is the instant value of a variable, then

If is the mean turbulent variable then according to (2.2) (2.4) that should be

Which is correct? The second path probably ?

Page 521 - "where the averaging volume V, which excludes solid plant parts, consists of a horizontal slab, extensive enough in the horizontal to eliminate plant-to-plant variations in canopy structure but thin enough to preserve the characteristic variation of properties in the vertical."

On page. 522 we see the equality

where " is the unit normal vector pointing away from into ". And the is the volume of fluid only, not all the volume of the two-phase (or more phases inside of the real 3D volume, if any exist more than 2 phases).

This equality is incorrect, instead of it should be in the VAT notations used the consequence of the WSAM theorem

or it should be as

in notations of the paper by Finnigan. And this is the fundamental difference.

Then, the another equality (2.6) in the paper by Finnigan (2000) for the time derivative averaging had been made as

where " is the velocity of a point on the plant element surface.

Meanwhile, the VAT's averaging "transport" theorem says that this should be the formula

we have the discrepancy with the sign before the second r.h. term, because the vector then it means that the time derivative fluid phase averaging in notations of Finnigan & Raupach & Shaw and et al. should be as

But the worse thing is that this formula is also incorrect, because this theorem if written for the then in the VAT's notations will looks like

while using the Finnigan's notations it should be as

with the variable time dependent fluid phase volume fraction and of the fluid volume itself

Then, on the same page 522 we see the momentum turbulent equation averaged as

where

while these last two terms are incorrect. These and should be different according to the WSAM theorem for the averaging of type see the explanation above.

Then the next mistake is - that in the averaged momentum equation there is no term which would reflect the integral part of the WSAM theorem when applied to the term ?

Should be the last integral term from the WSAM theorem written for the stress term (in paper's notations)

which is also would be incorrect if writing via the intrinsic fluid phase averaged variables due to averaging mistake- see the remarks above.

The reason why in this development should be used the phase averages but not the intrinsic phase averages as in this and other works by said meteorologists is that the vectorial variables at the boundaries between the "porous" medium and the homogeneous fluid volume medium should be conserving their values - as, for example, the velocity, the mass flux, etc.

Then we see on page 523 the second moments equation written as the "averaged" one in the form

with the exact notation as in (2.11) in the paper. The last two terms probably should read the instead of etc. ?.

This equation can not be called as the averaged one, few issues prevent doing this:

1) the intrinsic phase averaging should not be applied to vectorial (tensor) variables equation;

2) here the intrinsic phase averaging is only designated, but only two terms had been averaged. The first one - the time derivative term, and only with an assumption that the foliage is unmovable. The second term is the "pressure fluctuations drag" term #VIII

still the averaging done incorrectly. The example - the pair of terms

are not the averaged l.h.s. term

and the same can be said about other terms.

And I seems to know why these terms are not averaged. Because some averaging mathematics techniques were not widely known in 80th. And they are not known even today to the most of the community who do the Linear Operators averaging.

3) The intrinsic phase averaging applied with incorrect formulae.

Page 524 we read that - "The application of the volume average operator has removed the dependence of the flow equations on the stochastic distribution of the foliage." ?

Of coarse, not. This action just transformed the lower scale problem into the other one - the Upper space problem, but the morphology plays the vital role in any space into which it is taken as a part of the problem.

Then we see on the page 561 the kinetic energy equation written as the "averaged" in the form

which also is not the averaged equation. All remarks above regarding the second moments equation applicable to this one also.

The important thing is - that even in these forms the equations (2.11) (7.1) can not be solved, because they used to be written in the forms which include the new unknown variables. That means, they were developed without a meaning to be solved? The calculation of these equations budgets has no sence - because the terms are not complete, and the problems still being considered as the Lower scale problem.

Also, there is no one reference in the list of references to the publications on the same topic from other fields, which is like raising the question - author doesn't know or doesn't want to show to reader that there is the huge literature exists on the same or close AVERAGING topics?

More of that, there are no references to the publications of the real pioneers in the scaling description of physical processes - Volume Averaging Theory and techniques, I mean first of all - by Whitaker, Slattery, Gray, with their co-authors regarding the first time developments in this science. Then, when we talk about the nonlinear and turbulent transport two scale advancements - then, I am sorry, my work is of the first of this kind. I am sorry, that I saying like this, but I just have mentioned few dramatic errors in the mentioned meteorologists studies.

I actually spoke openly and published about this situation with averaged equations in the USSR in 80th, and since 1990 in the US. If the concerned people didn't pay attention, or didn't understand this mathematics, or if meteorologists do not read other then "Boundary-Layer Meteorology" magazines and publications! Then What?

All of that had brought the situation to the present state of affairs with this drastic "deflection" of studies of these groups of meteorologists from others developments!! This is the grim situation - and I would like suggesting the cooperation in search for the ways out?
~~~

Shaw, R.H., "Observation and Simulation of Flow in Vegetation Canopies ," in NATO Advanced Study Institute-980064, Institute of Hydromechanics, Kiev, pp. 41-43, 2004.

On page 41 author writes: "Mathematical models of flow through canopies range from ensemble-average models that employ mixing length hypotheses (Wilson and Shaw, 1977) to large-eddy simulation (Shaw and Schumann, 1992). Such models include mathematical descriptions of the drag of foliage elements (Raupach and Shaw, 1982), and of exchangers of heat and mass according to local conditions and appropriate coefficients."

It's need to be said that the "ensemble-average models" if correctly performed are the Upper scale models - the very different from the one scale LES models. So - those two are not the consecutive rungs in the ladder of improving models. They are from different spaces.

"The problems associated with the overall complexity of plant canopy morphology, the large dynamic range of physical scales of the canopy and its components, the flexibility of canopy elements, and mutual shading of foliage parts are generally dealt with in only the most rudimentary fashion."

The author speaks only about situation within the meteorology field, he does not refer to other areas, sciences because he apparently does not have information what's going on in other fluid mechanics, thermal physics, chemical technology, etc. areas, of coarse we are referring to the VAT.

It seems that this author disregarding and stop believing in his own efforts starting in 80th related to averaging ABL governing equations in canopies.
~~~

Shavit, U. and Rosenzweig, R., " Theoretical, Numerical, and Experimental Study of the Macroscopic Velocity Profile Near Permeable Interfaces," in NATO Advanced Study Institute-980064, Institute of Hydromechanics, Kiev, pp. 172-173, 2004.

On page 173 we can read - "The theoretical part of the work includes a description of the averaging procedure for the Navier-Stokes equations over a representative elementary volume (REV). The result of the mathematical formulations is the MRE (Modified Brinkman Equation). The MBE is composed of three differential equations that provide the average velocity profile above, within and below the interface region. The first equation, which describes the flow at the free fluid, is similar to the Stokes equation. The third equation, far below the interface, resembles the Brinkman equation. The second equation, which describes the velocity around the interface region, is more complex and involves terms accounted for the porosity variation across the interface."

This text speaks out obviously about incorrect approach to the averaging process, and to closure of the equations in different areas. This is the kind of equation which can not be derived unless the goal was to make it up.
Authors probably had not read the papers by Whitaker (and few other people) written on this subject.