Centrifugal Mode Research Articles

The nonlinear evolution of centrifugal instabilities in curved, compressible mixing layers

The nonlinear development of Görtler vortices in a curved compressible mixing layer is studied. It has been shown both experimentally and theoretically that the curved mixing layer can support a centrifugal mode, which is believed to be similar to the Görtler vortex. This study follows the corresponding incompressible study of Seddougui & Otto [Proceedings of the IUTAM Symposium on Nonlinear Instability and Transition in Three-Dimensional Boundary Layers, edited by P. W. Duck and P. Hall (Kluwer Academic, Amsterdam, 1995)] and attempts to demonstrate the effect compressibility has on the growth of such modes. The formulation follows that of Hall & Lakin [Proc. R. Soc. London, Ser. A 415, 421 (1988)] for the corresponding incompressible boundary-layer problem, and utilises a stream function formulation to solve the governing equations. We will present the nonlinear structure of the so-called thermal modes, whose linear counterparts were first discovered in Owen, Seddougui & Otto [Phys. Fluids 9, 2506 (1997)]. A brief discussion will be made concerning the effect of the nonlinear modes on the inherent Kelvin–Helmholtz modes of instability, which may have significant ramifications in flows dominated by this form of instability.

The linear evolution of centrifugal instabilities in curved, compressible mixing layers

The linear development of Görtler vortices in a curved compressible mixing layer is studied. It has been shown both experimentally and theoretically that the curved mixing layer can support a centrifugal mode, which is believed to be similar to the Görtler vortex mode. This study follows the corresponding incompressible study of Otto, Jackson, and Hu, and attempts to demonstrate the effects compressibility has on the growth of such modes [J. Fluid Mech. 315, 85 (1996)]. The ultimate downstream fate of the modes is studied in the high Taylor/Görtler number regime. The problem of the third boundary condition inherent to the mixing layer model is addressed using the set of boundary conditions for both subsonic and supersonic flows derived by Ting [J. Math. Phys. 28, 153 (1959)]. A class of modes is discussed that have no counterpart in the uniform temperature incompressible case.

Basic studies of fluctuations, transport and their control

The first experimental study of a mixed slab - toroidal ITG (ion temperature gradient) driven mode in the Columbia linear machine (CLM) is reported. The effects of the modest levels of magnetic curvature are seen to be further destabilization and reduction of the real frequency of the mode. However, with a further increase in the mirror ratio, the mode amplitude decreased. The mode has the appearance of a hybrid ITG-dissipative trapped electron mode. We have measured the reduction of anomalous fluctuation driven particle transport due to feedback via cross-correlation of Langmuir probe and capacitive probe data for a centrifugal mode driven by E×B rotation of the plasma column. The particle flux is obtained from cross power spectra of density and potential fluctuation. The resulting diffusion coefficient clearly indicates that feedback can reduce the transport by up to a factor of three. To investigate the question of non-linear saturation of the mode we have performed a bispectral analysis of fluctuation data. The results clearly indicate strong mode coupling in the spectral width of the mode. Furthermore, we resolve the spectral width to reveal that it is composed of radial harmonics. These observations suggest that the nonlinear mode coupling between these radial harmonics is the saturation mechanism of the instability, as well as the underlying cause of the consequent anomalous transport.

Oscillatory instabilities of the liquid and mushy layers during solidification of alloys under rotational constraint

Linear flow instabilities due to oscillatory disturbances of the liquid and mushy regions during solidification of binary alloys are investigated under a rotational constraint where the rotation axis is inclined to gravity vector. Results of stability analyses and numerical computations for a preferred centrifugal mode of general oscillatory disturbances at zero and non-zero rotation rates are determined which provide information about the preference of oscillatory flow and its role on the solidification system as modified by the rotational effects. The main results are due to a preferred oscillatory mode of convection which is more significant for non-zero rotation case and is restricted mostly to the mushy region. The preferred oscillatory mode of convection is a traveling wave in the presence of rotation, but it is a standing wave in the absence of rotation. The results for different Prandtl numbers indicate that the freckles formation tendency for metallic alloys is less than that for aqueous solutions. Freckles are imperfections that reduce the quality of the solidified materials.

Effect of rotation on flow instabilities during solidification of a binary alloy

Linear flow instabilities of the liquid and mushy regions during solidification of a binary alloy is investigated under a high gravity environment where the rotation axis is inclined to the high gravity vector. Results of stability analyses and numerical computations for a centrifugal mode of disturbance at several different rotation rates are determined which provide information for various flow features in the liquid and the mushy layers including neutral stability curves, streamlines and density plots for solid fraction perturbation in the mushy layer. The results indicate two distinct modes of convection whose dependences with respect to rotation rate suggest a procedure for possible elimination of chimneys formation tendency in the mushy layer. These chimneys are vertical channels of zero solid fraction and are kind of imperfections that reduce the quality of the solidified materials.

Linear stability of a rotating film flow attached inside a circular cylinder

Stability of a rotating film flow attached inside a circular cylinder was analyzed on a linear basis, where the cylinder is at rest and the basic flow is assumed to be kept rotating under the imposition of an artificial body force acting in the azimuthal direction. A traveling-wave mode that is intrinsic for a film flow on a vertical or an inclined flat plate and a centrifugal instability mode are obtained as unstable modes. The effect of a superimposed shear flow in the axial direction was also examined and it was shown that the shear flow exerts a stabilizing effect on the centrifugal instability mode.

Expression of ontogeny in individual nephron segments

Against any factors threatening homeostasis of body fluids, the infant has but a narrow margin of renal functional defense (H. W. Smith). While this fundamental assumption has been proven by clinical and experimental work, kidney during ontogeny is no longer considered an immature system with poor efficiency and imbalanced nephrons. Rather, transient developmental functions represent process of differentiation of specific cell functions. In nephron, functional differentiation also depends on epigenetic factors such as metabolic, hormonal, and dietary stimuli. The ‘plasticity' of embryonic and perinatal kidney, first perceived by Gersh G [1] and Grobstein [2], renders differentiating nephron segments a unique system for study of interdependence of physical, metabolic, and structural factors in transporting epithelia [3]. This study considers in vitro work on individual perfused and nonperfused nephron segments during ontogeny. The use of individual segments (Fig. 1) has served to uncover properties of differentiating nephron epithelia, since ‘Ontogenetic heterogeneity' limits studies by nonspecific techniques such as clearance, tissue slices, or suspensions of undefined tubule fragments. The process determining this heterogeneity is centrifugal mode of development (Fig. 2) [4].