The problem of the turbulent boundary layer
01 May 1954-Zeitschrift für Angewandte Mathematik und Physik (Springer Science and Business Media LLC)-Vol. 5, Iss: 3, pp 181-203
TL;DR: In this paper, a simple analysis based on functional similarity in the velocity profile is presented, which is consistent with existing measurements of low-speed turbulent surface friction on a flat plate, in the absence of pressure gradient and roughness.
Abstract: Existing measurements of low-speed turbulent surface friction on a flat plate, in the absence of pressure gradient and roughness, are shown to be consistent with a simple analysis based on functional similarity in the velocity profile. In particular, the fully developed turbulent boundary layer is found to be unique within the accuracy of the experimental data, with uniqueness defined as the existence of a definite correspondence between local friction coefficient and momentum thickness Reynolds number. The relationships known as the law of the wall and the velocity defect law are found to describe the turbulent velocity profiles accurately for a considerable range of Reynolds numbers, and an effort is made to clarify the physical significance of these formulae. Finally, the proper definition of a length Reynolds number is discussed in terms of the asymptotic local properties of the ideal boundary layer, and numerical values for ideal mean and local friction coefficients are tabulated against Reynolds numbers based on momentum thickness and on distance from the leading edge.
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TL;DR: The equations of motion of the rendezvous satellite in a relative coordinate system are derived and used to compute a final injection velocity which would effect collision after a time r.
Abstract: This paper assumes a requirement for an unmanned multiunit satellite to be assembled in orbit. The requirement to be met is to bring the satellites together so tha t they do not collide but actually rendezvous. The equations of motion of the rendezvous satellite in a relative coordinate system are derived and used to compute a final injection velocity which would effect collision after a time r. The velocity is corrected periodically by a command guidance system and just before impact retrothrust is applied. A terminal infrared homing sj^stem is required to actually accomplish physical contact and joining of the satellites. The first satellite placed in orbit is the "control satellite" and controls all the satellites to be assembled and contains the ccmputer, command guidance equipment, precision orientation equipment, and other features necessary to effect rendezvous. The succeeding satellites contain a propulsion system, a rough at t i tude control system, and a command receiver plus whatever scientific equipment they carry to perform their basic mission. This paper presents the following:
1,686 citations
TL;DR: In this paper, the authors proposed to represent the mean-velocity profile by a linear combination of two universal functions, namely the law of the wall and the wake, and compared the results with experimental data.
Abstract: After an extensive survey of mean-velocity profile measurements
in various two-dimensional incompressible turbulent boundary-layer
flows, it is proposed to represent the profile by a linear
combination of two universal functions. One is the well-known
law of the wall. The other, called the law of the wake, is
characterized by the profile at a point of separation or reattachment.
These functions are considered to be established empirically, by
a study of the mean-velocity profile, without reference to any
hypothetical mechanism of turbulence. Using the resulting
complete analytic representation for the mean-velocity field,
the shearing-stress field for several flows is computed from the
boundary-layer equations and compared with experimental data.
The development of a turbulent boundary layer is ultimately
interpreted in terms of an equivalent wake profile, which supposedly
represents the large-eddy structure and is a consequence of the
constraint provided by inertia. This equivalent wake profile is
modified by the presence of a wall, at which a further constraint is
provided by viscosity. The wall constraint, although it penetrates
the entire boundary layer, is manifested chiefly in the sublayer flow
and in the logarithmic profile near the wall.
Finally, it is suggested that yawed or three-dimensional flows
may be usefully represented by the same two universal functions,
considered as vector rather than scalar quantities. If the wall
component is defined to be in the direction of the surface shearing
stress, then the wake component, at least in the few cases studied,
is found to be very nearly parallel to the gradient of the pressure.
1,574 citations
TL;DR: In this paper, the natural transition of boundary layers is investigated for a flat plate in a low-speed wind tunnel with free-stream turbulence intensities ranging from 0.3 to 5 per cent.
Abstract: Natural transition of boundary layers is investigated for a flat plate in a low-speed wind tunnel with free-stream turbulence intensities ranging from 0.3 to 5 per cent, and with pressure-gradient ...
727 citations
TL;DR: In this article, the authors used hot-wire probes to study the flow field near the wall in a turbulent boundary layer using a large digital computer to single out special events (bursting) when large contributions to turbulent energy and Reynolds stress occur.
Abstract: Experimental studies of the flow field near the wall in a turbulent boundary layer using hot-wire probes are reported. Measurements of the product uv are studied using the technique of conditional sampling with a large digital computer to single out special events (bursting) when large contributions to turbulent energy and Reynolds stress occur. The criterion used to determine when the product uv is sampled is that the streamwise velocity at the edge of the sublayer should have attained a certain value. With this simple criterion we find that 60% of the contribution to is made during only 55% of the total time.
629 citations
TL;DR: Schlatter et al. as mentioned in this paper assessed available direct numerical simulation (DNS) data from turbulent boundary layer flows and found that the simulation results showed surprisingly l l l o r...
Abstract: A recent assessment of available direct numerical simulation (DNS) data from turbulent boundary layer flows (Schlatter & Orlu, J. Fluid Mech., vol. 659, 2010, pp. 116-126) showed surprisingly l ...
238 citations
Cites background from "The problem of the turbulent bounda..."
...It is interesting to recall that the classical assessment of experimental data sets by Coles (1954) states that ‘it is not obvious a priori that a state is ever reached in which the dependence of the turbulent boundary layer on its early history is no longer measurable in terms of the local mean…...
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References
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01 Jan 1955
TL;DR: In this article, the results of an experimental investigation of a turbulent boundary layer with zero pressure gradient are presented and the importance of the region near the wall and the inadequacy of the concept of local isotropy are demonstrated.
Abstract: The results of an experimental investigation of a turbulent boundary layer with zero pressure gradient are presented. Measurements with the hot-wire anemometer were made of turbulent energy and turbulent shear stress, probability density and flattening factor of u-fluctuation (fluctuation in x-direction), spectra of turbulent energy and shear stress, and turbulent dissipation. The importance of the region near the wall and the inadequacy of the concept of local isotropy are demonstrated. Attention is given to the energy balance and the intermittent character of the outer region of the boundary layer. Also several interesting features of the spectral distribution of the turbulent motions are discussed.
1,122 citations
01 Jun 1953
TL;DR: In this paper, a hot-wire anemometer was used to measure the turbulent flow in a 10-inch pipe at speeds of approximately 10 and 100 feet per second, and the results include relevant mean and statistical quantities, such as Reynolds stresses, triple correlations, turbulent dissipation, and energy spectra.
Abstract: Measurements, principally with a hot-wire anemometer, were made in fully developed turbulent flow in a 10-inch pipe at speeds of approximately 10 and 100 feet per second. Emphasis was placed on turbulence and conditions near the wall. The results include relevant mean and statistical quantities, such as Reynolds stresses, triple correlations, turbulent dissipation, and energy spectra. It is shown that rates of turbulent-energy production, dissipation, and diffusion have sharp maximums near the edge of the laminar sublayer and that there exist a strong movement of kinetic energy away from this point and an equally strong movement of pressure energy toward it.
1,053 citations
01 Jan 1951
TL;DR: A detailed exploration of the field of mean and fluctuating quantities in a two-dimensional turbulent channel flow is presented in this article, where mean speed and axial-fluctuation measurements were made well within the laminar sublayer.
Abstract: A detailed exploration of the field of mean and fluctuating quantities in a two-dimensional turbulent channel flow is presented. The measurements were repeated at three Reynolds numbers, 12,300, 30,800, and 61,600, based on the half width of the channel and the maximum mean velocity. A channel of 5-inch width and 12:1 aspect ratio was used for the investigation. Mean-speed and axial-fluctuation measurements were made well within the laminar sublayer. The semitheoretical predictions concerning the extent of the laminar sublayer were confirmed. The distribution of the velocity fluctuations in the direction of mean flow u' shows that the influence of the viscosity extends farther from the wall than indicated by the mean velocity profile, the region of influence being approximately four times as wide.
349 citations
01 Oct 1951
TL;DR: In this article, the feasibility of artificially thickening a turbulent boundary layer on a flat plate was investigated and it was shown that it is possible to do substantial thickening and obtain a fully developed turbulent boundary layers, which is free from any distortions introduced by the thickening process.
Abstract: Report gives an account of an investigation conducted to determine the feasibility of artificially thickening a turbulent boundary layer on a flat plate A description is given of several methods used to thicken artificially the boundary layer It is shown that it is possible to do substantial thickening and obtain a fully developed turbulent boundary layer, which is free from any distortions introduced by the thickening process, and, as such, is a suitable medium for fundamental research
172 citations
01 Apr 1951
TL;DR: In this article, the authors investigated the turbulent motion in a boundary layer with zero longitudinal pressure gradient and found that the turbulent energy balance was similar at all three stations and could be described in terms of universal functions, and that the bulk of the eddies are attached to the wall and have very high rates of shear in that region.
Abstract: The nature of the turbulent motion in a boundary layer with zero longitudinal pressure gradient has been investigated with the techniques of hot-wire anemometry which have been developed for the study of shear flow in wakes. Measurements have been made of the intensities of the turbulent velocity components, the turbulent shear stresses, the rates of transport of turbulent energy by diffusive movements, the intensities and flattening factors of the down-stream spatial derivatives of the three velocity components, and spectra of the down-stream component of the velocity fluctuation, at traverses through the boundary layer at three stations where the Reynolds numbers (based on the displacement thickness and free stream velocity) were respectively 3630, 4360 and 5080. Over the range of measurement, which did not include the laminar sublayer, the turbulent motion was similar at all three stations, and could be described in terms of universal functions. By considering the turbulent energy balance, it is shown that, except in the outer part of the layer where the turbulence resembles strongly the turbulence in a wake, there is a strong flow of energy directed toward the wall and transported by the action of turbulent pressure gradients. It is concluded that, most probably in contact with the laminar sublayer, there must be a ‘dissipative layer’ within which most of the turbulent energy dissipation takes place, and that the bulk of the eddies are, in a sense, attached to the wall and have very high rates of shear in that region. In agreement with this view of the structure of the turbulence, length scales derived from the apparent eddy viscosity and the local turbulent intensity are found to be comparable with distance from the wall. Length scales in the direction of the mean stream are much larger, and it is believed that the typical eddy is very elongated in this direction, and has its vorticity directed roughly parallel to the direction of maximum positive mean rate of strain.
127 citations