Journal ArticleDOI
Axial instability of a free-surface front in a partially filled horizontal rotating cylinder
TLDR
In this paper, the axial instability of the free-surface front of a viscous fluid in a horizontal cylinder rotating about its longitudinal axis was investigated and a simplified model equation for the evolution of free surface is derived and includes the effects of gravity, capillarity, inertia, and viscosity.Abstract:
We investigate the axial instability of the free-surface front of a viscous fluid in a horizontal cylinder rotating about its longitudinal axis. A simplified model equation for the evolution of the free surface is derived and includes the effects of gravity, capillarity, inertia, and viscosity. This equation is solved numerically to determine the base state with no axial variation, and a numerical linear stability analysis is carried out to examine the onset of unstable axial modes. Various computational results are presented for the wavelength of the axial instability. Inertia is found to play an important role in the onset of the instability and the wavelength of the instability λ satisfies the power law λ∼γ1/3, where γ is surface tension. Finally some numerical simulations of the simplified evolution equation are presented to show that they can capture the steady shark-teeth patterns observed in recent experiments [R. E. Johnson, in Engineering Science, Fluid Dynamics: A Symposium to Honor T. Y. Wu (Wo...read more
Citations
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Journal ArticleDOI
Fourth order partial differential equations on general geometries
TL;DR: This work extends a recently introduced method for numerically solving partial differential equations on implicit surfaces to fourth order PDEs including the Cahn-Hilliard equation and a lubrication model for curved surfaces and discusses in detail the differences between computing these fourth order equations and computing the first and second order P DEs considered in earlier work.
Journal ArticleDOI
Fingering phenomena for driven coating films
TL;DR: In this article, a theoretical and numerical model is formulated to describe the instability and the long-time evolution of both gravity-driven and surface-shear-stress-driven thin coating films.
Journal ArticleDOI
Complexity, segregation, and pattern formation in rotating-drum flows
Gabriel Seiden,Peter J. Thomas +1 more
TL;DR: The literature related to rotating-drum flows is reviewed in this paper, highlighting similarities and differences between the various flow realizations, and placing an emphasis on pattern formation phenomena, such as reversible transitions and hysteresis.
Journal ArticleDOI
An experimental investigation of the stability of the circular hydraulic jump
TL;DR: In this article, an experimental investigation of the striking flow structures that may arise when a vertical jet of fluid impinges on a thin fluid layer overlying a horizontal boundary is presented.
Journal ArticleDOI
On the instability of a falling film due to localized heating
TL;DR: In this article, the stability of a thin film falling under the influence of gravity down a locally heated plate was analyzed and the dependence of the critical Marangoni number on the associated Bond and Biot numbers, non-dimensional measures of the curvature pressure and heat-conductive properties of the film respectively.
References
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Book
Boundary layer theory
TL;DR: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part, denoted as turbulence as discussed by the authors, and the actual flow is very different from that of the Poiseuille flow.
Book
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
TL;DR: In this article, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
A Reflection on Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
J. Guckenheimer,P. J. Holmes +1 more
TL;DR: In this paper, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
Book Review: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
John Guckenheimer,Philip Holmes +1 more
TL;DR: Guckenheimer and Holmes as discussed by the authors survey the theory and techniques needed to understand chaotic behavior of ODEs and provide a user's guide to an extensive and rapidly growing field.