Modelling of streaky structures and turbulentspot generation process in wing boundary layer at high free-stream turbulence *

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1 Thermophysics and Aeromechanics, 2008, Vol. 15, No. 4 Modelling of streaky structures and turbulentspot generation process in wing boundary layer at high free-stream turbulence * G.R. Grek, M.M. Katasonov, and V.V. Kozlov Khristianovich Institute of Theoretical and Applied Mechanics SB RAS, Novosibirsk, Russia grek@itam.nsc.ru (Received October 24, 2007) Results of an experimental study of turbulent breakdown in gradient boundary layer at high freestream turbulence are reported. For the first time it is shown that, like the flat-plate boundary layer, the wing boundary layer at high freestream turbulence is modulated with streaky structures. One of possible mechanisms underlying the generation of turbulence spots in wing boundary layer is modelled assuming the interaction of streaky structures with high-frequency waves. Qualitative and quantitative data concerning the evolution of streaky structures in swqpt-wing boundary layer and in swept-wing boundary layer are presented. Certain differences between the evolution of streaky structures in wing boundary layer and in flat-plate boundary layer are revealed. Key words: straight wing, boundary layer, streaky structures, turbulent spot, high turbulence level. INTRODUCTION In recent decades, much interest has been expressed by scientists doing research in fluid dynamics to the problem of laminar-turbulent transition under conditions of high freestream turbulence. This interest has arisen due to both theoretical and applied aspects of the development of state-of-the-art technologies. Among the theoretical aspects here are, first, the recognition of the fact that this transition mechanism cardinally differs from the comprehensively examined mechanism of the transition to turbulence under low-turbulence conditions and, second, the considerable progress made in computers and in the development of new theoretical models and experimental procedures. The applied aspects are related to the development of advanced control methods for developing disturbances, for instance, to the development of MEMS control means. The MEMS technology offers a possibility in principle to control the laminar-turbulent transition by exerting an immediate action on the disturbances developing at any spatial point and at any time using a microprocessor-controlled sensor/actuator array. The current progress in this field offers a better insight into, and a better control of, turbulization mechanisms of com- * This work was supported by the President of the Russian Federation (Grants NSh , MK ), by the Russian Foundation for Basic Research (Grant No ), by the Ministry of Education and Science of the Russian Federation (Grant No. RNP ), and by the Russian Government (State Contract No ). G.R. Grek, M.M. Katasonov, and V.V. Kozlov,

2 plex near-wall flows over turbine, compressor and fan blades operated under highturbulence conditions, and also into turbulization mechanisms in boundary layers of concave surfaces, swept wings, etc. In these cases, the transition to turbulence is related not only to the development of instability waves, but also to the presence of localized streamwise stationary and non-stationary vortices and streaky structures. It is known that in many cases the laminar-turbulent (LT) transition at a low level of free-stream turbulence results from the generation and development of instability waves, the so-called Tollmien Schlichting (TSh) waves [1]. For more than half a century, starting from the classical experiments by G.B. Schubauer and H.K. Skramstäd [2], this type of transition has been examined in detail by many workers [3 6] and is still under study [7, 8]. The mechanism of laminar flow breakdown under conditions in which disturbances develop not in the Blasius boundary layer or in a region close to this layer, but in flows spanwise modulated with streamwise vortical structures is a more recondite mechanism. In the latter case, the classical LT-transition scenario related to spatial evolution of TSh waves does not work, and it becomes necessary to identify another mechanism that underlies the formation and dissipation of longitudinal disturbance structures. The formation mechanism of stationary longitudinal vortices such as Gortler vortices or spanwise-flow vortices over swept wings is well known and was examined in sufficient detail. In the former case, Gortler vortices spring up in flows over concave surfaces owing to the action of centrifugal forces. In the latter case, streamwise vortices emerge as a result of the spanwise flow in the swept-wing boundary layer. Presently, one of possible mechanisms causing the breakdown of boundary layers modulated with longitudinal stationary vortices, namely, the mechanism of secondary high-frequency instability, is being studied intensively both by theoretical and experimental methods. The theory of secondary high-frequency instability of such flows [9] was validated by numerical experiments [10 14]. In particular, this theory was also corroborated by experiments performed under controllable conditions for Gortler vortices [15] and spanwiseflow vortices [16]. Certain insight into the transition mechanism at high freestream turbulence has been achieved not long ago, within recent twenty-thirty years. The so-called bypass transition concept, proposed in [17] and implying no involvement of TSh waves in the transition, was confirmed by the experiments performed under natural conditions in [18, 19]. It was shown in those works that TSh wave packets never arise at free-stream turbulence numbers less than one percent. Nonetheless, simultaneously, disturbances with developmental characteristics differing strongly from the developmental characteristics of TSh waves were all the same identified. These disturbances have come to be known as Klebanov instability modes, or K-modes, after P.S. Klebanov, who examined such disturbances in one of his unpublished works. J.M. Kendall [20] examined the bypass transition and visualized the flat-plate boundary transition under conditions with high free-stream turbulence level. According to data obtained, the boundary layer was spanwise modulated with longitudinal structures. Today such disturbances are known as streaky structures. The transversal scale of such structures was correlated to boundary-layer thickness [20 21]. Nonetheless, more subtle developmental characteristics of such structures, and the mechanisms of their production, development and breaking, have remained unstudied. Yet, all authors who examined the bypass transition under natural conditions observed turbulent spots that arose at a late transition stage. The next stage in the study of the LT transition under conditions of high freestream turbulence involves an experimental study of this process under controlled artificial conditions. From such experiments, additional information related to this complex process was gained [22]. It was found that instability waves are generated, exist and develop, and influence the transition, at free-stream turbulence numbers up to 4 percents in flat-plate boundary layer or in swept-wing boundary layer [23 24]. Nonetheless, in the transition process the instability waves play a minor role compared to their major role 550

3 during the transition under conditions with low free-stream turbulence. Experimentally, streaky structures were modelled in flat-plate boundary layer and in straight-/swept-wing boundary layer with the help of time- and space-localized disturbances generated in the free stream and on the walls of the models. The characteristics of developing streaky structures correlated with characteristics of localized disturbances observed under natural experimental conditions. Most comprehensively, one possible mechanism of turbulent-spot generation was investigated, involving the interaction of artificially generated streaky structures with a high-frequency wave. The interaction between the disturbances gave rise to a high-frequency wave packet, whose downstream evolution was accompanied by the production of a turbulent spot [25]. Smoke visualization data for the interaction of an artificial high-frequency wave with natural streaky structures [26] has confirmed the conclusions made in [25]. On the basis of a study performed, in controlled experiments a scenario of the LT transition under conditions with high freestream turbulence was presented [22]. In contrast to stationary longitudinal structures, streaky structures appear as nonstationary disturbances running in the downstream direction and undergoing steady extension along the direction of stream because of the difference between the leading- and trailing-front propagation velocities. In this respect, streaky structures have many features in common, for instance, with Λ disturbance structures observed during the classical breakdown to turbulence. The latter structures also undergo extension as they move with the stream to finally assume the form of hairpin vortices. One of the hypotheses concerning the nature of streaky structures in the viscous sublayer of turbulent boundary layer considers these structures to be spanwise localized non-stationary structures having scales one order of magnitude smaller than the scales in laminar boundary layer [27]. Along with experimental studies of streaky structures, theoretical works attempting a description of these structures within the framework of the linear theory were reported. First of all, the so-called lift-up effect deserves mention here, presenting a mechanism proposed in [28], capable of adequately reproducing the formation process of streaky structures in terms of linear theory. Based on the obtained data concerning the mechanism of turbulence origination in flows modulated with streaky structures, experimental studies of various control methods for the evolution of streaky structures and related secondary disturbances were carried out. These studies showed that riblets, localized or distributed suction [22], and transverse wall vibrations [29] were capable of delaying, and in some cases even preventing, the transition of these flows in a turbulent state. The majority of the above-mentioned studies were carried out on a flat plate presenting the simplest model with zero gradient of pressure. Yet, from the practical standpoint it seems necessary to deeper comprehend regularities in the development of such disturbances in gradient flows, for instance, in wing boundary layer. Various wing configurations provide the basis for many hydrodynamic devices such as turbine, compressor, and fan blades, etc. The main purpose of the present study was to investigate the laminar-turbulent transition under conditions of high free-stream turbulence on a wing model under natural and experimentally modified flow conditions. It was of interest to unveil common and distinguishing features in the mechanisms of flat-plate and wing boundary-layer turbulization. 1. EXPERIMENTAL SETUP. MEASUREMENT AND DATA PROCESSING PROCEDURE The experiments were carried out in the T-324 subsonic, low-turbulence wind tunnel of ITAM SB RAS. The flow turbulence number Tu in the test section of the wind tunnel was lower than 0.04 % of the free-stream velocity U. A high turbulence, Tu = 1.75 % U, was produced by a tripping grid located at the entrance to the test 551

4 section. Depending on a particular experiment, the free-stream velocity took different values in the interval from 5 to 10 m/s. Data reported in the present study were obtained on a model of wing with variable angle of slide. The vortical disturbances were introduced into the boundary layer in two different ways, as freestream disturbances introduced through a tube with inner diameter 1 mm or as approach-flow disturbances introduced through transverse slits ( and mm), both the tube and the slits being located on the model surface. The disturbances were produced by dynamic loudspeakers operated in the air blowing/suction mode. The electric signal supplied to the loudspeakers to produce, with their help, localized disturbances was a sequence of short pulses that followed at a repetition frequency of Hz. The high-frequency disturbances were produced using a 280-Hz sinusoidal electric signal. The high-frequency and pulsed signals were synchronized with each other. Measurements were performed with the help of a constant-resistance hot-wire anemometer and single-wire probes. To be determined in the experiments were the longitudinal velocity component U and the pulsating component u of this velocity. The signal from the hot-wire sensor was fed to an ADC input to be subsequently transferred to a computer memory used to store raw measurement data. The phase information on boundary-layer disturbances was recorded during the time intervals in which synchronization of the measured sensor signal with the disturbance generator was affected. The data obtained were processed with the help of tailored software, the results being represented in the form of oscillograms, contour diagrams of velocity pulsations, and disturbance spectra. To visualize the flow, smoke was used, which was supplied into the model-surface boundary layer through a narrow mm transverse slit located at a distance of 35 mm from the leading edge of the wing. The free-stream velocity was measured with the help of a Prandtl tube connected to an inclined liquid micromanometer. The coordinate system used in the measurements was as follows: x is the streamwise coordinate reckoned in the downstream direction from the leading edge of the model, y is the coordinate along the normal to the surface of the model, and z is the transversal coordinate along the leading edge of the model. 2. STREAKY STRUCTURES IN WING BOUNDARY LAYER Smoke visualization of the flow in straight-wing boundary layer under conditions of low and high free-stream turbulence was carried out. The experimental diagram is shown in Fig. 1. The wing model was installed vertically in the test section of the wing tunnel. The visualized boundary-layer flow structure was registered on a video camera. The results in Fig. 2 show that streaky structures under high freestream turbulence may also exist in gradient flows, in particular, on a wing model (see Fig. 2, а). Previously, streaky structures were observed at a high freestream turbulence only on a flat plate with zero gradient of pressure [22]. Simultaneously, at a low level of outside disturbances (see Fig. 2, b) streaky structures never emerge. Thus, under conditions with high free-stream turbulence, like the boundary layer with zero gradient of pressure, the gradient boundary layer is also modulated with streaky structures. Fig. 1. Visualization diagram of boundarylayer flow at low (Tu 0.04 % U ) and high (Tu 1.75 % U ) level of free-stream turbulence. 552

5 Fig. 3. Visualization diagram of natural streaky structures interacting with a high-frequency instability wave. Fig. 2. Smoke visualization of straight-wing boundary-layer flow at high (а) and low (b) level of free-stream turbulence. Fig. 4. Smoke visualization of natural streaky structures interacting with a high-frequency wave in straight-wing boundary layer. а emergence of an incipient turbulent spot (delineated with the dashed line); b relaxation zone in the turbulent spot (delineated with the dashed line). In subsequent experiments, twodimensional TSh waves were generated in the boundary layer of the model, with streaky structures being also present in this layer, by introducing a periodic disturbance through the same slit that was used for injecting smoke into the flow (see Fig. 3). Visualization data obtained under the latter conditions are shown in Fig. 4. It is seen that the interaction between the disturbances gives rise to highfrequency wave packets (incipient turbulent spots, see Fig. 4, а); as these wave packets move farther downstream, they transform in turbulent spots (relaxation zones, see Fig. 4, b). This result also agrees with visualized data on the interaction of streaky structures with an artificial two-dimensional TSh wave in flat-plate boundary layer [22]. Thus, like the flat-plate boundary layer, the straight-wing gradient boundary layer under conditions of high freestream turbulence is spanwise modulated with streaky structures. One of possible mechanisms underlying the formation of turbulent spots in both cases implies the interaction of high-frequency wave disturbances with streaky structures. 3. MODELLING OF STREAKY STRUCTURES At the next stage of the study streaky structures were modelled in straight-wing and swept-wing boundary layers. The modelling followed the procedure used to model streaky structures (puffs) in flat-plate, straight-wing, and swept-wing boundary layers [22, 30]. The experimental conditions used in the present study differed from those used in [22, 30] in terms of the wind-tunnel facility and wing model used, and also in freestream turbulence number. Contour diagrams of velocity pulsations in streaky structures (puffs) produced in straight-wing and swept-wing boundary layers are shown, respec- 553

6 Fig. 5. The straight-wing model (а) and contour diagram of localized-disturbance velocity pulsations in boundary layer (b). Contour lines of positive and negative velocity deviations from unperturbed stream velocity are shown respectively with continuous and dashed lines. Step u /U = 0.25 %, U = 6.6 m/s, x = 71 mm, y = y(u max ). tively, in Figs. 5 and 6. In both cases, the localized vortical disturbances were induced in the boundary layer by controlled free-stream pulsations, this modelling the formation process of such disturbances under natural conditions. It should be noted here that the direction in which the disturbances were introduced into the flow and the free-stream vector in both cases were coincidental (see Figs. 5, а and 6, а). The puff structure in straight-wing boundary layer (see Fig. 5, b) is qualitatively similar to the puff structure in flat-plate boundary layer [22]; typical of both structures are symmetrically located zones with increased and decreased values of flow velocity. A change of sign of the deviation of flow velocity from its unperturbed value is observed when the gas suction gives way to gas blowing, and vice versa. The differences in the structure of a solitary puff in flat-plate boundary layer and in wing boundary layer are related to the presence of oblique waves generated by the puff in the case of zero gradient of pressure on a flat plate [22], and also to the suppression of these waves in the region with favorable pressure gradient on wing (see Fig. 5, b). Fig. 6. The swept-wing model (а) and a contour diagram of localized-disturbance velocity pulsations in boundary layer (b). Contour lines of positive and negative velocity deviations from unperturbed stream velocity are shown, respectively, with solid and dashed lines. Step u /U = 0.25 %, U = 6.6 m/s, x = 71 mm, y = y(u max ). 554

7 Drastic changes in the structure of the localized disturbance can be observed as this disturbance develops in swept-wing boundary layer (see Fig. 6, b). First, the disturbance structure becomes asymmetric and, second, the transversal scale of the disturbance almost doubles in comparison with the scale of a similar disturbance developing in straight-wing boundary layer. Apparently, the cause of such changes is related to the presence of spanwise flow in swept-wing boundary layer. On the whole, in spite of the change of experimental conditions in comparison with [22, 30], the results gained in the present study were found to perfectly comply with the results of [22, 30]. 4. INTERACTION OF AN ARTIFICIAL STREAKY STRUCTURE WITH A HIGH-FREQUENCY SECONDARY DISTURBANCE As was noted above, one possible mechanism underlying the generation of turbulent spots under conditions with high freestream turbulence is the interaction of streaky structures with high-frequency secondary disturbances; this was verified by the experiments mentioned in the introduction to [22]. Detailed developmental and interactional characteristics of such disturbances in flat-plate boundary layer were obtained in [25]. In the present study, we examined the development of a streaky structure and its interaction with a high-frequency disturbance in boundary layer of a straight wing installed vertically in the test section of the wind tunnel (Fig. 7). The localized lowfrequency (f 0.5 Hz) streaky structure and the secondary high-frequency (f 280 Hz) wave were generated in the boundary layer by introducing into it disturbances through a narrow ( mm) slit on the surface of the model with the use of the above procedure. The wing model was installed at zero angle of attack; the distribution of flow velocity measured on the upper surface of the wing along its chord outside the boundary layer demonstrates the presence of a favorable pressure gradient in the most part of the examined region (Fig. 8). The rise curves of the localized disturbances and highfrequency oscillations (Fig. 9) show a number of features in the development of these disturbances and oscillations in the case of their separate and joint generation. The intensity of the high-frequency wave (1) rapidly decreases in the downstream direction, its amplitude at the distance of 100 mm from the disturbance source being 0.01 % U, this resulting from the effect due to the favorable pressure gradient. The intensity of the localized disturbance (2) also decreases in the downstream direction with the same damping factor as in the case of flat plate [31]. The interaction between the decaying disturbances (3) (these disturbances are decaying when they are generated separately) results in a growth of the intensity of the emerging high-frequency wave packet (incipient turbulent spot), and its subsequent transformation into a turbulent spot. Fig. 7. Diagram illustrating the experiment on the development and interaction of disturbances in straight-wing boundary layer, U = 8.4 m/s. 555

8 Fig. 8. Straight-wing cross section and the distribution of flow velocity outside the boundary layer. U = 8.4 m/s. On closer inspection of the structure of the localized disturbance (see Fig. 10, I), the following features are observed. Unlike its development on a flat plate at zero pressure gradient, in which case the disturbance is steadily extended downstream because of the difference in the propagation velocity of its fronts, in the latter case no such effect is observed. A solitary streaky structure does not extend; instead, it decays in the spanwise direction into two regions with increased flow velocity, this being distinctly seen in Fig. 10, I at x = 245 mm. Farther downstream, at x = 285 and 315 mm, between these regions there emerges a region with lower velocity, this observation being indicative of two streaky structures formed. One can put forward a hypothesis that this effect results from the action of favorable pressure gradient on the localized disturbance. The pressure gradient acts in two ways. On the one hand, this gradient suppresses the oblique waves generated by the non-stationary streaky structure in the case in which this structure develops in gradientless flow over a flat plate [25]; on the other hand, the favorable pressure gradient stabilizes the longitudinal extension of the streaky structure. Here, instead of extension of the localized disturbance and generation of oblique waves we observe a growth of the transversal scale of the disturbance (from λ z = 9 mm at x = 105 mm to λ z = 16 mm at x = 315 mm) and its transformation in two streaky structures (see Fig. 10, I). It is seen from Fig. 10, I that the integral intensity of the disturbances decreases in the downstream direction. The natural high-frequency wave observed at the leading front of the streaky structure at x = 105 mm is suppressed by the favorable pressure gradient, as well as the oblique waves generated by the localized disturbance developing on a flat plate [22]. The results of the spectral analysis of the disturbance are shown in Fig. 10, II as β-spectra u RMS = f (β). It is seen that the natural two-dimensional high-frequency wave with the transversal wavenumber β max = 0 mm 1 at x = 105 mm turns out to be almost fully suppressed by the favorable pressure gradient already at x = 145 mm and farther downstream. The dominant components of the disturbance spectra are oblique waves in a broad range of transversal wavenumbers from β max = ± mm 1 at x = 145 mm to β max = ± mm 1 at x = 315 mm. In [32] it was found that not only the spectral mode (0, ± β max ) is a component that carries the greatest amount of energy; it is also a mode, at least, the least decaying in comparison with other harmonics of the continuous frequency-wave spectrum. In the case in which the disturbances develop on a wing, in spite of the presence of the pressure gradient, the harmonics (0, ± β max ) forming the streaky structure remain 10, II least decaying ones in comparison with other harmonics except for the harmonics with β max ± mm 1 at x = 245 mm, whose amplitude starts increasing in the downstream direction (see Fig. 10, II). The Fig. 9. Distribution of disturbance intensity in the region with favorable pressure gradient of the straight-wing boundary layer. 1 high-frequency disturbance f = 280 Hz, 2 localized puff disturbance, 3 interaction between the localized disturbance and the highfrequency disturbance, U = 8.4 m/s, y = y(u max ). 556

9 Fig. 10. Contour diagrams of streaky-structure velocity pulsations in the region with favorable pressure gradient of the straight-wing boundary layer (I) and β-spectra corresponding to these diagrams (II). Contour lines of positive and negative velocity deviations from unperturbed stream velocity are shown, respectively, with solid and dashed lines (max and min are the highest positive and negative deviations, step is the step in which the contour lines follow), U = 8.4 m/s, y = y(u max ). 557

10 characteristic transversal scale of the initiated disturbance, a streaky structure, increases in the downstream direction, this being reflected in the evolution of β max (see Fig. 10, I). Simultaneously, in the spectra there appear oblique waves with β max ± mm 1 at x = 245 mm and with β max ± mm 1 at x = 315 mm, this demonstrating a process in which the disturbance transforms in two new streaky structures. In the latter case, there emerges another periodic structure, with the characteristic transversal scale λ z 1/β max of the new disturbance becoming equal approximately to 8 mm instead of the previous 16 mm at x = 315 mm. Oscillograms illustrating the development of a streaky structure and its interaction with a high-frequency wave are shown in Fig. 11, I. These oscillograms were obtained by measuring the disturbance amplitude in the symmetry plane of disturbances. The amplitude of a solitary streaky structure is seen to decay in the downstream direction; yet, the intensity of the interacting disturbances grows in value. The interaction gives rise to a high-frequency wave packet that, as it moves in the downstream direction, trans- z, mm Fig. 11. Oscillograms of flow velocity pulsations in a solitary streaky structure and in a streaky structure interacting with a high-frequency wave in the region with favorable pressure gradient of the straight-wing boundary layer at z = 0 I; contour diagrams of flow velocity pulsations in a solitary streaky structure (а) and in a streaky structure interacting with a high-frequency wave (b) II. Contour lines of positive and negative velocity deviations from unperturbed stream velocity are shown, respectively, with solid and dashed lines, U = 8.4 m/s, y = y(u max ) II. Spanwise distribution of integral velocity pulsations in a streaky structure (1) and during the interaction of the flow disturbances (2) at x = 215 mm, U = 8.4 m/s III. 558

11 forms in a turbulent spot. Contour diagrams of velocity pulsations at x = 215 mm are shown in Fig. 11, II. The amplitude of the interacting disturbances increases by more than eight times (b) compared to the amplitude of a solitary streaky structure (a). The intensity maxima of the high-frequency disturbance (2) are located in regions with maximum transverse velocity gradient in the streaky structure (1), which is indicative of secondary high-frequency instability of the flow modulated with streaky structures, with an inflecting profile of velocity u/ z (see Fig. 11, III). The above result correlates with the data on the interaction between disturbances obtained in the flat-plate experiments of [25]. The β-spectra of the localized disturbance (а) and the evolution of this disturbance during its interaction with a high-frequency wave (b) are shown in Fig. 12. The spectrum of the localized disturbance (a) is dominated by two peaks at f = 0 Hz and β max ± mm 1. This corresponds to a wavelength λ z = 1/β max = 13 mm in the transversal direction; this value fairly well agrees with observation data in the z t plane (see Fig. 10, I). In the case in which the disturbances interact with each other the energy maximum is localized around two peaks at f = 0 Hz and β max ± mm 1 (see Fig. 12, b). Here, the energy is distributed in a broad range of frequencies (from 0 to 300 Hz) and transversal wavenumbers, both at β max ± mm 1 and β max ± mm 1. The spectral peaks at f = 0 Hz and β max ± mm 1 refer to a streaky structure, whereas the nonlinear interaction between the various oblique modes is reflected by the pulsation maxima at the wavenumbers β max ± mm 1 and β max ± mm 1, with the disturbance energy being distributed in a broad frequency interval (from 0 to 300 Hz). The emer- Fig. 12. β-spectra of a solitary streaky structure (a) and a streaky structure interacting with a highfrequency wave (b) in straight-wing boundary layer. The spectra are measured at x = 215 mm, U = 8.4 m/s. F = 2πfν 10 6 /U 2, β * = 2πδ * β (δ * = 1 mm). 559

12 gence of large wavenumbers in the spectrum is related to the generation of harmonics with a short wavelength λ z = mm. On the other hand, a reduction of the transversal wavenumber from β ± mm 1 to β ± mm 1 of the low-frequency streaky structure results in a gr owth of wavelength from λ z 13 mm to λ z 20 mm, probably owing to the influence of regions with relatively low velocity at the boundaries of the localized disturbance (see Fig. 10, b). As a result, during the interaction of the disturbances profound changes in the pulsation spectra are observed. CONCLUSIONS From the results of modelling of the generation of turbulent spots during the interaction of streaky structures and high-frequency disturbances under conditions of high freestream turbulence in gradient boundary layers of straight and swept wings, the following conclusions can be drawn: in the flow over a straight wing, streaky structures arising in the natural way were identified; it is shown that the generation of turbulent spots under natural conditions can result from the interaction of streaky structures with high-frequency waves; it is found that, unlike the case of a straight wing, a streaky structure in the boundary layer of a swept wing becomes asymmetric, with its transversal scale undergoing doubling; the modelling of the streaky structure showed that a favorable pressure gradient suppresses the spreading of the disturbance in the stream direction and, promoting the growth of the transversal scale of the disturbance, results in separation of the solitary streaky structure into two streaky structures; one possible formation mechanism of turbulent spots arising from the interaction of streaky structures with a high-frequency wave is modelled; a favorable pressure gradient is shown to suppress the development of swept waves generated by the streaky structure in the course of its downstream evolution. REFERENCES 1. H. Schlichting, Boundary-Layer Theory, McGraw Hill, New York, G.B. Schubauer and H.K. Skramstäd, Laminar boundary layer oscillations and transition on a flat plate, NASA Rep., No. 909, C.C. Lin, The Theory of Hydrodynamic Stability, Cambridge Univ. Press, Cambridge, P.S. Klebanoff, K.D. Tidstrom, and L.M. Sargent, The three-dimensional nature of boundary layer instability, J. Fluid Mech. Pt. 1, 1962, Vol. 12, Р M.A. Gaster, Theoretical model of a wave packet in the boundary layer on a flat plate, Proc. Roy. Soc. A347, 1975, No. 1649, Р Y.S. Kachanov, V.V. Kozlov, and V.Ya. Levchenko, Turbulent Breakdown in Boundary Layer, Nauka, Novosibirsk, Y.S. Kachanov, On the resonant nature of the breakdown of a laminar boundary layer, J. Fluid Mech., 1987, No. 184, Р U. Rist and H.F. Fasel, Spatial three-dimensional numerical simulation of laminar-turbulent transition in a flat-plate boundary layer, in: Boundary Layer Transition and Control Conf., Cambridge, U.K., Royal Aero. Soc., 1994, Р V.N. Zhigulev, A.N. Kirkinsky, N.V. Sidorenko, and A.M. Tumin, On the mechanism of secondary instability and on the role of this instability in the origination of turbulence, in: Aeromechanics, Nauka, Moscow, 1976, P S.Ya. Gertsenshtein, A.N. Sukhorukov, and E.B. Rodichev, Secondary instability, interaction between disturbances, and scenarios for the onset of turbulence, Izv. vyssh. shkoly: Prikl. nelin. dinamika, 1996, No. 2, P J.D. Swearingen and R.F. Blackwelder, The growth and breakdown of streamwise vortices in the presence of a wall, J. Fluid Mech., 1987, Vol. 182, Р X. Yu and J.T.C. Liu, The secondary instability in Goertler flow, Phys. Fluids A, 1991, Vol. 3, No. 7, Р Y. Kohama, Some expectation on the mechanism of cross-flow instability in a swept wing flow, Acta Mech., 1987, Vol. 66, Р

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