GORTLER VORTICES WITH SYSTEM ROTATION

The steady primary instability of Gortler vortices developing along a curved Blasius boundary layer subject to spanwise system rotation is a nalysed 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 i s carried out for a range of rotation numbers, to yield the (predictab le) result that positive rotation, that is rotation in the sense of th e basic flow, enhances the vortex development, while negative rotation dampens the vortices. Comparisons are also made with local, nonparall el linear stability results (Zebib and Bottaro, 1993) to demonstrate h ow the local theory overestimates vortex growth. The linear marching c ode is then used as a tool to predict wavelength selection of vortices , based on a criterion of maximum linear amplification. Nonlinear fini te 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 pertur bation energy saturates at some downstream position at a level which s eems to be independent of rotation, but that increases with the spanwi se wavelength. Nonlinear simulations performed in a long (along the sp an) cross section, under conditions of random inflow disturbances, dem onstrate that: (i) vortices are randomly spaced and at different stage s of growth in each cross section; (ii) ''upright'' vortices are the e xception in a universe of irregular structures; (iii) the average nonl inear 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 parches of vorticity near the wall emerge and can be amplifie d by the instability mechanism; (v) the linear filter represents the r eceptivity of the flow: any random noise, no matter how strong, organi zes itself linearly before subsequent growth can take place; (vi) the Gortler number, by itself, is not sufficient to define the slate of de velopment of a vortical flow, but should be coupled to a receptivity p arameter; (vii) randomly excited Gortler vortices resemble and scale l ike coherent structures of turbulent boundary layers.