Experiments on single oblique laminar-instability waves in a boundary layer: Introduction, growth, and transition

The laminar-turbulent transition in an incompressible flat-plate boundary layer was studied experimentally by using a spanwise array of computer-controlled surface heating elements to generate small disturbances. Oblique Tollmien-Schlichting waves were successfully introduced, and their downstream development into the intermittent region was studied using flush-mounted hot-film wall-shear sensors and dye flow visualization. Comparative studies of the development of single oblique waves were made for various wave angles, frequencies, and amplitudes. As these single oblique waves grew and began to break down, higher harmonics and subharmonics appeared in the wall shear. The amplitude of the subharmonic component decreased rapidly with increasing oblique-wave angle, so that a 10 degrees oblique wave had a subharmonic amplitude an order of magnitude below that for a two-dimensional (2-D) wave. Thus, the nonlinear mechanism that produces the subharmonic is affected by the symmetry of the primary wave. Intermittency measurements, carried out farther downstream, show that a 2-D wave is most effective in moving the transition point upstream, for a given power input

Structure and entrainment in the plane of symmetry of a turbulent spot

Laser-Doppler velocity measurements in water are reported for the flow in the plane of symmetry of a turbulent spot. The unsteady mean flow, defined as an ensemble average, is fitted to a conical growth law by using data at three streamwise stations to determine the virtual origin in x and t. The two-dimensional unsteady stream function is expressed as ψ=U^2_∞tg(ξ,η) in conical similarity co-ordinates ζ = x/U_∞t and η = y/U_∞t. In these co-ordinates, the equations for the unsteady particle displacements reduce to an autonomous system. This system is integrated graphically to obtain particle trajectories in invariant form. Strong entrainment is found to occur along the outer part of the rear interface and also in front of the spot near the wall. The outer part of the forward interface is passive. In terms of particle trajectories in conical co-ordinates, the main vortex in the spot appears as a stable focus with celerity 0·77U_∞. A second stable focus with celerity 0·64U_∞ also appears near the wall at the rear of the spot. Some results obtained by flow visualization with a dense, nearly opaque suspension of aluminium flakes are also reported. Photographs of the sublayer flow viewed through a glass wall show the expected longitudinal streaks. These are tentatively interpreted as longitudinal vortices caused by an instability of Taylor-Görtler type in the sublayer

Transition in circular Couette flow

Two distinct kinds of transition have been identified in Couette flow between concentric rotating cylinders. The first, which will be called transition by spectral evolution, is characteristic of the motion when the inner cylinder has a larger angular velocity than the outer one. As the speed increases, a succession of secondary modes is excited; the first is the Taylor motion (periodic in the axial direction), and the second is a pattern of travelling waves (periodic in the circumferential direction). Higher modes correspond to harmonics of the two fundamental frequencies of the doubly-periodic flow. This kind of transition may be viewed as a cascade process in which energy is transferred by non-linear interactions through a discrete spectrum to progressively higher frequencies in a two-dimensional wave-number space. At sufficiently large Reynolds numbers the discrete spectrum changes gradually and reversibly to a continuous one by broadening of the initially sharp spectral lines

Measurements of Turbulent Friction on a Smooth Flat Plate in Supersonic Flow

Direct measurements of supersonic local skin friction, using the floating-element technique, are presented for Mach Numbers from 2.0 to 4.5 and Reynolds Numbers from 3 X 10^5 to 9 X 10^6. Turbulent flow and transition are emphasized, although some measurements in the laminar regime are included. The observed effect of compressibility is to reduce the magnitude of turbulent skin friction by a factor of two at a Mach Number of 4.5 and a Reynolds number of about 10^7. The boundary-layer momentum-integral equation for constant pressure is verified within a few per cent by two experimental methods. Typical static pressure measurements are presented to show that transition can be detected by observing disturbances in pressure associated with changes in displacement thickness of the boundary layer. It is found that the turbulent boundary layer cannot be defined experimentally for values of u_1 θ/v_1 less than about 2,000, where θ is the momentum thickness. For larger values of u_1 θ/v_1, there is a unique relationship between local friction coefficient and momentum-thickness Reynolds Number at a fixed Mach Number. The Appendix compares the present measurements at M = 2.5 with experimental data from other sources

The law of the wake in the turbulent boundary layer

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

Direct Measurement of Supersonic Skin Friction

Recent experiments at the Jet Propulsion Laboratory have established the effect of compressibility on local skin friction for Mach numbers up to 4.5. Friction coefficients were obtained simultaneously at three stations on a flat plate, for both laminar and turbulent boundary-layer flow, for Reynolds numbers from 4 X 10^5 to 1 X 10^7. The floating element technique used is similar to that of Liepmann and Dhawan

Topics in Shear Flow

Unfinished manuscript left by Donald Coles at his death in May of 2013. From the author's draft preface: The fundamental premise for the book is that the only reliable information about turbulent flow is experimental information. This varies greatly in quality and completeness, and needs to be carefully screened. Some additional premises will be self-evident in the text. First, it is advisable to understand thoroughly the laminar version of a particular flow, because some conceptual problems are not peculiar to turbulent flow; e.g., the third boundary condition for the mixing layer, or the integral invariant for the wall jet. Second, the most powerful organizing principle so far available for both laminar and turbulent flow is the principle of similarity. Third, the most important phenomenological concept for many turbulent flows is the concept of entrainment. The need of the user is often likely to be for hard numbers and practical insights, rather than for elegance. I have therefore made some use of mixing-length and eddy-viscosity ideas, and even power-law methods, as primitive links between fundamental and technical problems. Each chapter of the book deals with one of the classical shear flows (mixing layers, jets, plumes, wakes, boundary layers, pipe flow, and so on ) and with its ramifications, or with an important technical problem such as flow management. Wherever possible, the presentation is intended to suggest how various flow problems might be connected analytically and experimentally one to another, using as far as possible a consistent notation and a consistent level of rigor and detail

The Turbulent Boundary Layer in a Compressible Fluid

A transformation is derived from first principles to reduce the boundary-layer equations for a general compressible two-dimensional flow to incompressible form. For the case of boundary-layer flow of a Newtonian fluid past a smooth wall, but with no other restrictions, it is shown that the combination (rho[infinity]µ[infinity]/rhowµw) CfRetheta is an invariant of the transformation. This result is called the law of corresponding stations. In order to apply the transformation to the problem of the turbulent boundary layer on a smooth wall, it is assumed that the sublayer Reynolds number is unaffected by compressibility or heat transfer provided the density and viscosity are evaluated at a mean sublayer temperature defined by the transformation. Explicit formulas are obtained for the effect of Mach number and heat transfer on surface friction when the fluid is a perfect gas, the pressure is constant, and the stagnation temperature is constant or linear in the velocity. An appendix contains a brief critical discussion of the mean-temperature hypothesis, the laminar-film hypothesis, and other analytical ideas related to the idea of a transformation

Coherence measurements in synthetic turbulent boundary layers

Synthetic turbulent boundary layers were constructed on a flat plate by generating systematic moving patterns of turbulent spots in a laminar flow. The experiments were carried out in a wind tunnel at a Reynolds number based on plate length of 1.7 × 10^6. Spots were generated periodically in space and time near the leading edge to form a regular hexagonal pattern. The disturbance mechanism was a camshaft that displaced small pins momentarily into the laminar flow at frequencies up to 80 Hz. The main instrumentation was a rake of 24 single hot wires placed across the flow in a line parallel to the surface. The main measured variable was local intermittency; i.e. the probability of observing turbulent flow at a particular point in space and time. The results are reported in numerous (x, z, t)-diagrams showing the evolution of various synthetic flows along the plate. The dimensionless celerity or phase velocity of the large eddies was found to be very nearly 0.88, independent of eddy scale. All patterns with sufficiently small scales eventually showed loss of coherence as they moved downstream. A novel phenomenon called eddy transposition was observed in several flows that contained appreciable laminar regions. The original large eddies were replaced by new eddies at new positions, intermediate to the original ones, while preserving the hexagonal pattern. The present results, together with some empirical properties of a turbulent spot, were used to estimate the best choice of scales for constructing a synthetic boundary layer suitable for detailed study as a model for a natural flow. The values recommended are: spanwise period/thickness ≈ 2.5, streamwise period/thickness ≈ 8.0