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We investigate possible linear waves and nonlinear wave interactions in a bounded three-layer fluid system using both analysis and numerical simulations. For sharp interfaces, we obtain analytic solutions for the admissible linear mode-one parent/signature waves that exist in the system. For diffuse interfaces, we compute the overtaking interaction of nonlinear mode-two solitary waves. Mathematically, owing to a small loss of energy to dispersive tails during the interaction, the waves are not solitons. However, this energy loss is extremely minute, and because the dispersively coupled waves in the system exhibit the three types of Lax KdV interactions, we conclude that for all intents and purposes the solitary waves exhibit soliton behavior. [ABSTRACT FROM AUTHOR]

Modified axisymmetric, finite-length Taylor–Couette (TC) cells with stationary outer cylinder and rotating inner cylinder are designed in an effort to produce simultaneous onset of toroidal vortices of continuously varying wavelength along the gap. For a given axial variation in the inner radius, the axial variation in the outer radius can be chosen such that at every axial position, the criterion for the onset of Taylor vortices in a corresponding classical TC cell is met. In one scenario, a conical inner cylinder is chosen and the shape of the outer cylinder is then determined by locally satisfying the onset criterion. In another scenario, the inner and outer radii are chosen such that the onset criterion is locally satisfied and the axial rate of change in the classical onset wave number is held constant. In both cases, the modified cells possess a large-scale meridional circulation wrought by the finite Ekman (Bödewadt) pumping on the inner (outer) cylinder walls. Using direct numerical simulation, it is found that for sufficiently large aspect ratio, there exists a critical rotation rate for the simultaneous transition from the base flow to counter-rotating toroidal vortices throughout the varying-radius region. The vortices propagate in the direction of decreasing gap width with a phase speed that decreases with increasing aspect ratio. [ABSTRACT FROM AUTHOR]

The stability of viscous rotating liquid columns and their application to rotating viscous liquid jets aligned under gravity is reviewed. Experiments on stable viscous fluid flow discharged from rotating vertical pipes exhibit very weak contraction. We present an elementary liquid jet analysis to understand this phenomenon. Indeed, our inviscid model of a slender rotating inviscid liquid jet shows that rotation suppresses contraction. Next we study the comparable problem for granular flow. Our model for noncohesive granular flow emanating from a vertical pipe rotating about its central axis, valid for sufficiently large rotation rate, shows that the granular profiles blossom rather than contract. The profiles of both the liquid and granular jets depend on the same dimensionless parameters—an exit Froude number Fr0 and an exit swirl parameter χ0. The limitations of both models are discussed. Experimental data for granular jet profiles compare well with the collision-free granular flow model in its range of applicability. A criterion for the rotation rate at which particles adjacent to the inner wall of the rotating pipe cease to flow is also given and compared to experiment. [ABSTRACT FROM AUTHOR]

The stability of flow in an annulus capped at both ends and bounded by a fixed outer cylinder and a spiraling inner rod is determined in the context of linear theory. For infinite aspect ratio and constant fluid properties the problem is governed by a Taylor number Ta, an axial Reynolds number Re, and the radius ratio η. Linear stability is tested with respect to both axisymmetric (n=0) and nonaxisymmetric (n≠0) disturbances for η=0.2, 0.4, 0.6, 0.8 over the range 0≤Re≤2000. The evolution of axial wave number, axial phase speed, and spiral inclination angle with increasing Re at each η through all mode transitions to an asymptotic state n=N is reported. It is found that N=2, 4, 7, 19 for η=0.2, 0.4, 0.6, 0.8, respectively, and that the asymptotic state is reached at Re[bar_over_tilde:_approx._equal_to]2000 for all radius ratios. The asymptotic state is characterized by critical Taylor numbers and frequencies that approach constant values while critical wave numbers fall off as Re-1. In this same limit the counter-rotating vortex pairs align themselves axially within the annulus. A conjecture is made on the influence of η on stability in the high Reynolds number limit. [ABSTRACT FROM AUTHOR]

In a recent paper by Abbassi and Rahimi (2009, "Nonaxisymmetric Three-Dimensional Stagnation-Point Flow and Heat Transfer on a Flat Plate,'' ASME J. Fluids Eng, 131(7), p. 074501) the existence of a new nonaxisymmetric 3D stagnation-point flow has been reported. The present paper shows, however, that the model of Abbassis and Rahimi is fully equivalent to the classical 3D stagnation-point flow of Howarth (1951, "The Boundary Layer in Three-Dimensional Flow--Part II: The Flow Near a Stagnation Point,'' Philos. Mag., 42, pp. 1433--1440) published more than sixty years ago. Thus their "new'' solution can be recovered from Howarth's known solution by simple transformations, without any additional research effort. Once this flow problem is solved, the solution of the heat transfer problem of Abbassi and Rahimi (2009, "Nonaxisymmetric Three-Dimensional Stagnation-Point Flow and Heat Transfer on a Flat Plate,'' ASME J. Fluids Eng, 131(7), p. 074501) can be calculated by a semi-analytical or by a usual numerical procedure. [ABSTRACT FROM AUTHOR]

The article discusses the result of a study concerning helical instability of a rotating liquid jet. It was found that initial planar disturbances, marked by vertical striations immediately downstream of the rotating tube, quickly transition into helical waves. The droplet formation process involves thin stretching ligaments which are eventually severed.