J. HEINLOO

228

(as well as to the related to it earlier idea of G. Mattioli

[18], first suggesting the inclusion of the equation of

moment-of-momentum to the setup of description of tur-

bulent flows). The analysis displays the statement of the

CTM about the evident symmetry of the turbulent stress

tensor erring against the principles of continuum me-

chanics [15], relating the solution of the symmetry prop-

erties of the stress tensor to the context of specification

of the medium internal rotational degrees of freedom.

Within the shortcomings of th e CTM note also its inabil-

ity to propose ph ysically correct explanation to the eddy-

to-mean energy conversion, explained within the PCTM

as the act of turbulence rotational viscosity neglected

within the CTM. The CTM also does not distinguish the

turbulence properties in rotating and non-rotating frames

which by now is verified observationally.

Let us underline that the PCTM does not “discover”

the additional (rotational) viscosity of turbulence—this

type of turbulence viscosity has been foreseen and de-

scribed in a sufficiently complete form by the RK con-

ception—but merely removes the obstacle from the ex-

plicit inclusion of this fundamental property of turbu-

lence into the setup of the TM. Let us highlight also, that

applying all classical motion integrals—of momentum,

of moment-of-momentum and of energy—the PCTM

formulates the turbulence description in mechanically

closed form and as such completes the formulation of the

TM.

We conclude the comments on the PCTM referring to

the paper [35], which utilized the data available within

the Global Drifter Program to estimate the gyrocity and

the spin immediately from observations. The estimated

gyrocity and spin provide the grounding declaration of

the PCTM about the non-vanishing gyrocity and spin of

the turbulent flow with the sense of experimental fact.

Finally, the PDT [11] postulates the conditions of for-

mation of probability distribution properties of momen-

tary states of motion determined as the state of motion

fixed in terms of the TM. These conditions are specified

within the CTM and within the PCTM differently. The

commented role of the TM is emphasized here to stress

the scientific merit of the TM wider than a particular

turbulence description in average terms.

6. Conclusion

The PCTM mandates a critical analysis of the results

following from the CTM. It also mandates the planning

of new tasks and research projects from the position of

the PCTM. The latter mandate is addressed to the initia-

tors of new projects rather than hug e number of scien tists

participating in turbulence-related applied projects and

following firmly established standards. This mandate is

also addressed to the people educating new generation of

specialists in the field of flu id mechanics.

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