Appendix to A hydrodynamic instability is used to create aesthetically (original) (raw)
Related papers
A Hydrodynamic Instability Is Used to Create Aesthetically Appealing Patterns in Painting
PLOS ONE, 2015
Painters often acquire a deep empirical knowledge of the way in which paints and inks behave. Through experimentation and practice, they can control the way in which fluids move and deform to create textures and images. David Alfaro Siqueiros, a recognized Mexican muralist, invented an accidental painting technique to create new and unexpected textures. By pouring layers of paint of different colors on a horizontal surface, the paints infiltrate into each other creating patterns of aesthetic value. In this investigation, we reproduce the technique in a controlled manner. We found that for the correct color combination, the dual viscous layer becomes Rayleigh-Taylor unstable: the density mismatch of the two color paints drives the formation of a spotted pattern. Experiments and a linear instability analysis were conducted to understand the properties of the process. We also argue that this flow configuration can be used to study the linear properties of this instability. Fig 7. Correlation length as a function of time. The horizontal dashed line shows the average of the measurement, L c , for 230 < t < 300s. This measurements correspond to the images shown in Fig 5.
Two-dimensional patterns in Rayleigh-Taylor instability of a thin layer
Journal of Fluid Mechanics, 1992
We study experimentally and theoretically the evolution of two-dimensional patterns in the Rayleigh-Taylor instability of a thin layer of viscous fluid spread on a solid surface. Various kinds of patterns of different symmetries are observed, with possible transition between patterns, the preferred symmetries being the axial and hexagonal ones. Starting from the lubrication hypothesis, we derive the nonlinear evolution equation of the interface, and the amplitude equation of its Fourier components. The evolution laws of the different patterns are calculated a t order two or three, the preferred symmetries being related to the non-invariance of the system by amplitude reflection. We also discuss qualitatively the dripping at final stage of the instability. 12-2 350 M . Fermigier, L . Limat, J . E . Wesfreid, P . Boudinet and C . Quilliet \ P I ' P? \ \ \ 13-2
Siquieros accidental painting technique: a fluid mechanics point of view
2012
This is an entry for the Gallery of Fluid Motion of the 65st Annual Meeting of the APS-DFD ( fluid dynamics video ). This video shows an analysis of the 'accidental painting' technique developed by D.A. Siqueiros, a famous Mexican muralist. We reproduced the technique that he used: pouring layers of paint of different colors on top of each other. We found that the layers mix, creating aesthetically pleasing patterns, as a result of a Rayleigh-Taylor instability. Due to the pigments used to give paints their color, they can have different densities. When poured on top of each other, if the top layer is denser than the lower one, the viscous gravity current undergoes unstable as it spread radially. We photograph the process and produced slowed-down video to visualize the process.
Rayleigh-Taylor instability of fluid layers
Journal of Fluid Mechanics, 1987
It is shown that the Rayleigh-Taylor instability of an accelerating incompressible, inviscid fluid layer is the result of pressure gradients, not gravitational acceleration. As in the classical Rayleigh-Taylor instability of a semi-infinite layer, finite fluid layers form long thin spikes whose structure is essentially independent of the initial thickness of the layer. A pressure maximum develops above the spike that effectively uncouples the flow in the spike from the rest of the fluid. Interspersed between the spikes are rising bubbles. The bubble motion is seriously affected by the thickness of the layer. For thin layers, the bubbles accelerate upwards exponentially in time and the layer thins so rapidly that it may disrupt at finite times.
Laboratory experiments on Convective and Rayleigh-Taylor Instabilities
A simple laboratory model of turbulent mixing between two miscible fluids under an initial situation of top heavy stratification in a gravitational field has been performed. The mixing processes are generated by the evolution of a discrete set of unstable forced turbulent plumes. We describe the corresponding turbulent mixing processes measuring the density profiles and the heights of the fluid layers by means of flow visualization. We characterize the partial mixing process and the role of a viscoelastic gel that hampers mixing and controls in a random fashion the initial conditions. The mixing efficiency and the Atwood number (ranging between 9.9 x 10 -3 to 0.13)are related showing an increase up to a level of 10-20% .The evolution of the convective structures produced by bubbles is also discussed comparing the mixing efficiencies in both stable and unstable initial conditions. Other convective mixing situations induced by two phase convective stirring are also compared in order to evaluate the mixing efficiency in different parameter ranges.
The displacement of a more viscous fluid by a less viscous one in a quasi-two dimensional geometry leads to the formation of complex fingering patterns. This fingering has been characterized by a most unstable wavelength, λc, which depends on the viscosity difference between the two immiscible fluids and sets the characteristic width of the fingers. How the finger length grows after the instability occurs is an equally important, but previously overlooked, aspect that characterizes the global features of the patterns. As the lower viscosity fluid is injected, we show that there is a stable inner region where the outer fluid is completely displaced. The ratio of the finger length to the radius of this stable region depends only on the viscosity ratio of the fluids and is decoupled from λc.
Instability of a viscous interface under horizontal oscillation
Physics of Fluids, 2007
The linear stability of superposed layers of viscous, immiscible fluids of different densities subject to horizontal oscillations, is analyzed with a spectral collocation method and Floquet theory. We focus on counterflowing layers, which arise when the horizontal volume-flux is conserved, resulting in a streamwise pressure gradient. This model has been shown to accurately predict the onset of the frozen wave observed experimentally ͓E. Talib, S. V. Jalikop, and A. Juel, J. Fluid Mech. 584, 45 ͑2007͔͒. The numerical method enables us to gain new insights into the Kelvin-Helmholtz ͑KH͒ mode usually associated with the frozen wave, and the harmonic modes of the parametric-resonant instability, by resolving the flow for an exhaustive range of vibrational to viscous forces ratios and viscosity contrasts. We show that the viscous model is essential to accurately predict the onset of each mode of instability. We characterize the evolution of the neutral curves from the multiple modes of the parametric-resonant instability to the single frozen wave mode encountered in the limit of practical flows. We find that either the KH or the first resonant mode may persist when the fluid parameters are varied toward this limit. Interestingly, these two modes exhibit opposite dependencies on the viscosity contrast, which are understood by examining the eigenmodes near the interface.
Nonlinear sinusoidal and varicose instability in a boundary layer
Doklady Physics, 2005
It is well known [1] that the laminar-turbulent transition at a low turbulence level of the free flow is associated with the development of instability waves, the so-called Tollmien-Schlichting waves. When a twodimensional Tollmien-Schlichting wave reaches a certain amplitude at the nonlinear stage of its development, it undergoes three-dimensional distortion and, as a result, characteristic three-dimensional Λ structures arise . Owing to certain features of the appearance and development of these structures, they are not only typical for the classical laminar-turbulent transition, but are also inevitable attributes of a transition to more complex flows, e.g., flows modulated with longitudinal streaky structures, such as Hertler vortices, transverseflow vortices on sliding wings, etc., as well as flows in the viscous sublayer of a turbulent boundary layer. In these cases, they arise in particular due to the secondary high-frequency instability of such flows and may be manifested not only as Λ structures, but also in the form of horseshoe vortices ( Ω structures), hairpin vortices, etc. A characteristic feature of the development of such structures, e.g., on a sliding wing, is the disappearance of one of the counter-rotating vortices due to the transverse flow, whereas the development of a classical Λ structure can be observed on a straight wing [1].