STATISTICAL ANALYSIS OF WALL
TURBULENCE PHENOMENA
2. ZANk
Department of Thermal Physics
Boris Kidrip Institute. Untwrsity of Belgrade, Yugdslda
1. INTRODUCT~ON
Turbulence is a phenomenon best known for its complexity. Physically, it
represents a mechanical system with an extremely luge number of active
degrees of freedom. The only currcct approad! to the k o b h of turbulence
is, therefore, a statistical one. Staatietical fluid mechanics, however, is still not
marly in a position to provide a theoretical solution to tbe general problem
of turbulence.
From the point of view of engineering predictions, the most successful
were the so-called phenomenological theories of turbukna, bascd on the
longtime averaging of the Navicr-Stokes equations, introduaxi by Reynolds. The resulting system of equations is an uncbed one, as the equations
for the statistical moments of order n contain unkmwns in the form of
statistical moments of order n + 1. Phenomenologbtal theories provide semiempirical relations between the moments of order n + 1 and the moments
of order n. Despite their sums in a great numbor of flow configurations,
they all fail to be general enough
Therefore, a physical insight into turbuIence a d aspacially into the
mechanism of turbulence production is greatly IIc66cd. Until recently, experimental research bas been handicapped by not behq appropriate enough in
dealing with a kicafly statistical phenomenon. The work8 of Frenl;iel and
Klcbanoff (1967) have marked the w i d e s p d 0s6 of digital computers,
indispensable in statistical turbulence ramarch. it bcoarne, however, apparent that the conventional statistical analysis, aduqrtetc for Gaussian
processes, is insufficient in revealing the details of ttre turbulence transport
mechanism. The departures from Gaussianity, howevar small, appear to be
the real feature of turbulence. They are detected by an averaging process
over a long period of time, but in order to find their cause$ a different type of
statistical analysis is naded.
Recent visualization studies by the group in StankmJ (KPne et a/., 1967;
24 9
TURBULENCE PHENOMENA
2. ZANk
Department of Thermal Physics
Boris Kidrip Institute. Untwrsity of Belgrade, Yugdslda
1. INTRODUCT~ON
Turbulence is a phenomenon best known for its complexity. Physically, it
represents a mechanical system with an extremely luge number of active
degrees of freedom. The only currcct approad! to the k o b h of turbulence
is, therefore, a statistical one. Staatietical fluid mechanics, however, is still not
marly in a position to provide a theoretical solution to tbe general problem
of turbulence.
From the point of view of engineering predictions, the most successful
were the so-called phenomenological theories of turbukna, bascd on the
longtime averaging of the Navicr-Stokes equations, introduaxi by Reynolds. The resulting system of equations is an uncbed one, as the equations
for the statistical moments of order n contain unkmwns in the form of
statistical moments of order n + 1. Phenomenologbtal theories provide semiempirical relations between the moments of order n + 1 and the moments
of order n. Despite their sums in a great numbor of flow configurations,
they all fail to be general enough
Therefore, a physical insight into turbuIence a d aspacially into the
mechanism of turbulence production is greatly IIc66cd. Until recently, experimental research bas been handicapped by not behq appropriate enough in
dealing with a kicafly statistical phenomenon. The work8 of Frenl;iel and
Klcbanoff (1967) have marked the w i d e s p d 0s6 of digital computers,
indispensable in statistical turbulence ramarch. it bcoarne, however, apparent that the conventional statistical analysis, aduqrtetc for Gaussian
processes, is insufficient in revealing the details of ttre turbulence transport
mechanism. The departures from Gaussianity, howevar small, appear to be
the real feature of turbulence. They are detected by an averaging process
over a long period of time, but in order to find their cause$ a different type of
statistical analysis is naded.
Recent visualization studies by the group in StankmJ (KPne et a/., 1967;
24 9