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Notes: An experimental study on the development of turbulent spots in plane Poiseuille flow at a Reynolds number of 1600 has been carried out with the aim of achieving a better understanding of the transition to and maintenance of turbulence at low Reynolds numbers. Spots were triggered by a loudspeaker-induced jet of high velocity. The initial disturbance was found to undergo a first stage of rapid expansion, in which sharp internal shear layers form at locations away from the symmetry plane and precede the transition to turbulence. After this initial stage, a nearly self-similar structure develops with the typical features of a turbulent spot. The general features, turbulent properties, and spanwise spreading of the spot were investigated and compared both to previous experimental data and to numerical simulations. High-frequency fluctuations are absent at the front of the spot, whereas the turbulence is apparently self-sustained at the rear and displays features similar to fully turbulent Poiseuille flow at much higher Reynolds numbers. The waves accompanying the wing tips of the spot extend well within the spot, and reach amplitudes far in excess of those previously found outside the spot. The high level of random fluctuations in this part of the spot indicates that the breakdown of the waves is important for the spanwise propagation of the turbulent region.

Notes: Linear theory is used to analyze the stability of two-dimensional boundary layer flows to stationary Görtler vortices. The basic flow profiles in the boundary layer are described by the Falkner–Skan similarity solutions. We approach the problem both with local linear theory (with the streamwise position held fixed) and with a streamwise marching technique (to represent the evolution of the inlet disturbance). Comparisons of solutions obtained by the two methods are presented: The results are consistent in showing that adverse pressure gradients are destabilizing, as in the case of Tollmien–Schlichting waves. This is at odds with recent findings by Otto and Denier and underscores the sensitivity of the results to initial conditions. © 1996 American Institute of Physics.

Notes: Abstract. The steady primary instability of Görtler vortices developing along a curved Blasius boundary layer subject to spanwise system rotation is analysed through linear and nonlinear approaches, to clarify issues of vortex growth and wavelength selection, and to pave the way to further secondary instability studies. A linear marching stability analysis is carried out for a range of rotation numbers, to yield the (predictable) result that positive rotation, that is rotation in the sense of the basic flow, enhances the vortex development, while negative rotation dampens the vortices. Comparisons are also made with local, nonparallel linear stability results (Zebib and Bottaro, 1993) to demonstrate how the local theory overestimates vortex growth. The linear marching code is then used as a tool to predict wavelength selection of vortices, based on a criterion of maximum linear amplification. Nonlinear finite volume numerical simulations are performed for a series of spanwise wave numbers and rotation numbers. It is shown that energy growths of linear marching solutions coincide with those of nonlinear spatially developing flows up to fairly large disturbance amplitudes. The perturbation energy saturates at some downstream position at a level which seems to be independent of rotation, but that increases with the spanwise wavelength. Nonlinear simulations performed in a long (along the span) cross section, under conditions of random inflow disturbances, demonstrate that: (i) vortices are randomly spaced and at different stages of growth in each cross section; (ii) “upright” vortices are the exception in a universe of irregular structures; (iii) the average nonlinear wavelengths for different inlet random noises are close to those of maximum growth from the linear theory; (iv) perturbation energies decrease initially in a linear filtering phase (which does not depend on rotation, but is a function of the inlet noise distribution) until coherent patches of vorticity near the wall emerge and can be amplified by the instability mechanism; (v) the linear filter represents the receptivity of the flow: any random noise, no matter how strong, organizes itself linearly before subsequent growth can take place; (vi) the Görtler number, by itself, is not sufficient to define the state of development of a vortical flow, but should be coupled to a receptivity parameter; (vii) randomly excited Görtler vortices resemble and scale like coherent structures of turbulent boundary layers.

Notes: Abstract The steady primary instability of Görtler vortices developing along a curved Blasius boundary layer subject to spanwise system rotation is analysed through linear and nonlinear approaches, to clarify issues of vortex growth and wavelength selection, and to pave the way to further secondary instability studies. A linear marching stability analysis is carried out for a range of rotation numbers, to yield the (predictable) result that positive rotation, that is rotation in the sense of the basic flow, enhances the vortex development, while negative rotation dampens the vortices. Comparisons are also made with local, nonparallel linear stability results (Zebib and Bottaro, 1993) to demonstrate how the local theory overestimates vortex growth. The linear marching code is then used as a tool to predict wavelength selection of vortices, based on a criterion of maximum linear amplification. Nonlinear finite volume numerical simulations are performed for a series of spanwise wave numbers and rotation numbers. It is shown that energy growths of linear marching solutions coincide with those of nonlinear spatially developing flows up to fairly large disturbance amplitudes. The perturbation energy saturates at some downstream position at a level which seems to be independent of rotation, but that increases with the spanwise wavelength. Nonlinear simulations performed in a long (along the span) cross section, under conditions of random inflow disturbances, demonstrate that: (i) vortices are randomly spaced and at different stages of growth in each cross section; (ii) “upright” vortices are the exception in a universe of irregular structures; (iii) the average nonlinear wavelengths for different inlet random noises are close to those of maximum growth from the linear theory; (iv) perturbation energies decrease initially in a linear filtering phase (which does not depend on rotation, but is a function of the inlet noise distribution) until coherent patches of vorticity near the wall emerge and can be amplified by the instability mechanism; (v) the linear filter represents the receptivity of the flow: any random noise, no matter how strong, organizes itself linearly before subsequent growth can take place; (vi) the Görtler number, by itself, is not sufficient to define the state of development of a vortical flow, but should be coupled to a receptivity parameter; (vii) randomly excited Görtler vortices resemble and scale like coherent structures of turbulent boundary layers.