Instabilities of three-dimensional viscous falling films

1992 ◽  
Vol 242 ◽  
pp. 529-547 ◽  
Author(s):  
S. W. Joo ◽  
S. H. Davis
Keyword(s):  
Evolution Equation ◽  
Three Dimensional ◽  
Falling Film ◽  
Two Dimensional ◽  
Wave Evolution ◽  
Strongly Nonlinear ◽  
Long Wave ◽  
Threshold Amplitude ◽  
Permanent Wave ◽  
Dimensional Wave

A long-wave evolution equation is used to study a falling film on a vertical plate. For certain wavenumbers there exists a two-dimensional strongly nonlinear permanent wave. A new secondary instability is identified in which the three-dimensional disturbance is spatially synchronous with the two-dimensional wave. The instability grows for sufficiently small cross-stream wavenumbers and does not require a threshold amplitude; the two-dimensional wave is always unstable. In addition, the nonlinear evolution of three-dimensional layers is studied by posing various initial-value problems and numerically integrating the long-wave evolution equation.

Long–Wave Morphologies in Directional Solidification

1990 ◽  
Vol 43 (5S) ◽  
pp. S85-S88
Author(s):  
D. S. Riley
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Stability Limit ◽  
Two Dimensional ◽  
Segregation Coefficient ◽  
Directionally Solidified ◽  
Weakly Nonlinear ◽  
Strongly Nonlinear ◽  
Long Wave

Long–wave instabilities in a directionally–solidified binary mixture may occur in several limits. Sivashinsky identified a small–segregation–coefficient limit and obtained a weakly–nonlinear evolution equation governing subcritical two–dimensional bifurcation. Brattkus and Davis identified a near–absolute–stability limit and obtained a strongly–nonlinear evolution equation governing supercritical two–dimensional bifurcation. In this presentation these previous analyses are set into a logical framework, and a third distinguished (small–segregation–coefficient, large–surface–energy) limit identified. The corresponding strongly–nonlinear, evolution equation equation links both of the previous and describes the change from sub– to super–critical bifurcations.

Two- and three-dimensional locomotion of the nematode Nippostrongylus brasiliensis

Parasitology ◽  
1990 ◽  
Vol 101 (2) ◽  
pp. 301-308 ◽  
Author(s):  
D. L. Lee ◽  
W. D. Biggs
Keyword(s):  
Sodium Alginate ◽  
Intestinal Mucosa ◽  
Three Dimensional ◽  
Viscous Medium ◽  
Nippostrongylus Brasiliensis ◽  
Two Dimensional ◽  
Immune Rejection ◽  
Forward Movement ◽  
Helical Wave ◽  
Dimensional Wave

Locomotion of adult Nippostrongylus brasiliensis has been studied in saline, in 0.6% agar, in sodium alginate of different viscosities and amongst sand grains in these media. In saline the nematode formed two-dimensional waves but there was little forward progression. Amongst sand grains in saline the nematode moved forwards by thrusting against sand grains, but thigmokinetic behaviour later resulted in quiescence. In 0.6% agar and in alginates of weak viscosity the nematode produced two-dimensional waves and sometimes a three-dimensional helical wave which resulted in forward movement. The formation of three-dimensional waves and the distance travelled increased with increasing viscosity up to 4% sodium alginate and also amongst sand gains in these media. In 8% sodium alginate the nematode became coiled like a spring but remained almost stationary. The three-dimensional wave is formed with torsion and obtains thrust from the viscous medium. In the intestine of the host thrust will be obtained from the mucus and villi of the intestinal mucosa. The ability of this nematode to move by two-and three-dimensional undulatory propulsion is probably related to its complex ridged cuticle. Attention is drawn to the role that increased viscosity of mucus may play in entrapping nematodes during their immune rejection.

A three-dimensional supramolecular framework built from two-dimensional wave-shaped layers

2006 ◽  
Vol 59 (8) ◽  
pp. 883-890 ◽  
Author(s):  
Linlin Fan ◽  
Chao Qin ◽  
Yangguang Li ◽  
Enbo Wang ◽  
Xinlong Wang ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Two Dimensional ◽  
Supramolecular Framework ◽  
Dimensional Wave

The development of three-dimensional wave-packets in unbounded parallel flows

1968 ◽  
Vol 32 (4) ◽  
pp. 801-808 ◽  
Author(s):  
M. Gaster ◽  
A. Davey
Keyword(s):  
Wave Packet ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Mean Flow ◽  
Physical Plane ◽  
Parallel Flows ◽  
Flow Velocity Profile ◽  
The Stability ◽  
Special Case ◽  
Dimensional Wave

In this paper we examine the stability of a two-dimensional wake profile of the form u(y) = U∞(1 – r e-sy2) with respect to a pulsed disturbance at a point in the fluid. The disturbed flow forms an expanding wave packet which is convected downstream. Far downstream, where asymptotic expansions are valid, the motion at any point in the wave packet is described by a particular three-dimensional wave having complex wave-numbers. In the special case of very unstable flows, where viscosity does not have a significant influence, it is possible to evaluate the three-dimensional eigenvalues in terms of two-dimensional ones using the inviscid form of Squire's transformation. In this way each point in the physical plane can be linked to a particular two-dimensional wave growing in both space and time by simple algebraic expressions which are independent of the mean flow velocity profile. Computed eigenvalues for the wake profile are used in these relations to find the behaviour of the wave packet in the physical plane.

FREQUENCY DOMAIN RECONSTRUCTION FOR PHOTO- AND THERMOACOUSTIC TOMOGRAPHY WITH LINE DETECTORS

2009 ◽  
Vol 19 (02) ◽  
pp. 283-306 ◽  
Author(s):  
MARKUS HALTMEIER
Keyword(s):  
Wave Equation ◽  
Frequency Domain ◽  
Boundary Data ◽  
Three Dimensional ◽  
Photoacoustic Tomography ◽  
Two Dimensional ◽  
Reconstruction Problem ◽  
Acoustic Data ◽  
Dimensional Wave ◽  
Frequency Domain Reconstruction

This paper is concerned with a version of photoacoustic tomography, that uses line shaped detectors (instead of point-like ones) for the recording of acoustic data. The three-dimensional image reconstruction problem is reduced to a series of two-dimensional ones. First, the initial data of the two-dimensional wave equation is recovered from boundary data, and second, the classical two-dimensional Radon transform is inverted. We discuss uniqueness and stability of reconstruction, and compare frequency domain reconstruction formulas for various geometries.

A novel (3,6)-connected CdII coordination polymer based on an ether-linked tricarboxylate ligand: synthesis, topology and luminescence sensing properties in aqueous solution

2019 ◽  
Vol 75 (12) ◽  
pp. 1666-1674
Author(s):  
Yu'e Yu ◽  
Yuqian Chen ◽  
Xiuna Mi ◽  
Suna Wang ◽  
Jing Lu
Keyword(s):  
Aqueous Solution ◽  
Coordination Polymer ◽  
Three Dimensional ◽  
Isophthalic Acid ◽  
Water Stability ◽  
Two Dimensional ◽  
Carboxylate Ligands ◽  
Strong Luminescence ◽  
Solvothermal Conditions ◽  
Dimensional Wave

A novel three-dimensional coordination polymer, namely, poly[[diaquabis(μ-4,4′-bipyridine)bis{μ3-5-[(2-carboxyphenoxy)methyl]isophthalato}tricadmium(III)] dimethylformamide monosolvate 2.5-hydrate], {[Cd3(C16H9O7)2(C10H8N2)2(H2O)2]·2C3H7NO·5H2O} n , was obtained by the reaction of ether-linked 5-[(2-carboxyphenoxy)methyl]isophthalic acid (H3 L) with CdII salts in the presence of 4,4′-bipyridine (bpy) under solvothermal conditions. In this complex, the CdII centres are connected by the carboxylate ligands to form two-dimensional wave-like layers, which are pillared by bpy ligands and extended into a rare three-dimensional (3,6)-connected sqc27 framework. The complex demonstrated good water stability and strong luminescence emissions. It not only possesses excellent luminescence sensing activities toward Fe3+ and Cr2O7 2− in aqueous solution, but can also distinguish between Cr2O7 2− and CrO4 2− by luminescence. Furthermore, it could be simply and quickly regenerated at least five times. A study of the sensing mechanism indicated that luminescence quenching may be related to the energy competition between the complex and sensing analytes.

Secondary and tertiary excitation of three-dimensional patterns on a falling film

1994 ◽  
Vol 270 ◽  
pp. 251-276 ◽  
Author(s):  
H.-C. Chang ◽  
M. Cheng ◽  
E. A. Demekhin ◽  
D. I. Kopelevich
Keyword(s):  
Solitary Wave ◽  
Three Dimensional ◽  
Wave Structure ◽  
Stationary Wave ◽  
Wave Crest ◽  
Checkerboard Pattern ◽  
Secondary Transition ◽  
Falling Film ◽  
Two Dimensional ◽  
Primary Instability

The primary instability of a falling film selectively amplifies two-dimensional noise down-stream over three-dimensional modes with transverse variation. If the initial three-dimensional noise is weak or if it has short wavelengths such that they are effectively damped by the capillary mechanism of the primary instability, our earlier study (Chang et al. 1993a) showed that the primary instability leads to a weakly nonlinear, nearly sinusoidal γ1 stationary wave which then undergoes a secondary transition to a strongly nonlinear γ2 wave with a solitary wave structure. We show here that the primary transition remains in the presence of significant three-dimensional noise but the secondary transition can be replaced by a selective excitation of oblique triad waves which can even include stable primary disturbances. The resulting secondary checkerboard pattern is associated with a subharmonic mode in the streamwise direction. If the initial transverse noise level is low, a secondary transition to a two-dimensional γ2 solitary wave is followed by a tertiary ‘phase instability’ dominated by transverse wave crest modulations.

On the spatio-temporal stability of primary and secondary crossflow vortices in a three-dimensional boundary layer

2002 ◽  
Vol 456 ◽  
pp. 85-111 ◽  
Author(s):  
WERNER KOCH
Keyword(s):  
Saddle Point ◽  
High Frequency ◽  
Wave Packets ◽  
Temporal Stability ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Boundary ◽  
Spatio Temporal ◽  
Secondary Instabilities ◽  
Dimensional Wave

To examine possible links between a global instability and laminar–turbulent breakdown in a three-dimensional boundary layer, the spatio-temporal stability of primary and secondary crossflow vortices has been investigated for the DLR swept-plate experiment. In the absence of any available procedure for the direct verification of pinching for three-dimensional wave packets the alternative saddle-point continuation method has been applied. This procedure is known to give reliable results only in a certain vicinity of the most unstable ray. Therefore, finding no absolute instability by this method does not prove that the flow is absolutely stable. Accordingly, our results obtained this way need to be confirmed experimentally or by numerical simulations. A geometric interpretation of the time-asymptotic saddle-point result explains certain convergence and continuation problems encountered in the numerical wave packet analysis. Similar to previous results, all our three-dimensional wave packets for primary crossflow vortices were found to be convectively unstable.Due to prohibitive CPU time requirements the existing procedure for the verification of pinching for two-dimensional wave packets of secondary high-frequency instabilities could not be implemented. Again saddle-point continuation was used. Surprisingly, all two-dimensional wave packets of high-frequency secondary instabilities investigated were also found to be convectively unstable. This finding was corroborated by recent spatial direct numerical simulations of Wassermann & Kloker (2001) for a similar problem. This suggests that laminar–turbulent breakdown occurs after the high-frequency secondary instabilities enter the nonlinear stage, and spatial marching techniques, such as the parabolized stability equation method, should be applicable for the computation of these nonlinear states.

Asymptotic evaluation of three-dimensional wave packets in parallel flows

1991 ◽  
Vol 226 ◽  
pp. 573-590 ◽  
Author(s):  
Feng Jiang
Keyword(s):  
Saddle Point ◽  
Analytic Continuation ◽  
Wave Packets ◽  
Three Dimensional ◽  
Steepest Descent ◽  
Wake Flow ◽  
Two Dimensional ◽  
Asymptotic Evaluation ◽  
Method Of Steepest Descent ◽  
Dimensional Wave

This paper examines the three-dimensional wave packets which are generated by an initially localized pulse disturbance in an incompressible parallel flow and described by a double Fourier integral in the wavenumber space. It aims to clear up some confusion arising from the asymptotic evaluation of this integral by the method of steepest descent. In this asymptotic analysis, the calculation of the eigenvalues can be facilitated by making use of the Squire transformation. It is demonstrated that the use of the Squire transformation introduces branch points in the saddle-point equation that links the physical coordinates to the saddle-point value, regardless of whether the flow is viscous or inviscid. It is shown that the correct branch should be chosen according to the principle of analytic continuation. The saddle-point values for the three-dimensional problem should be considered to be the analytic continuation of those for the two-dimensional case where the saddle-point values can be uniquely determined. The three-dimensional wave packets in an inviscid wake flow are examined; their behaviour at large time is calculated asymptotically by the method of steepest descent in terms of the two-dimensional eigenvalue relation.

Origin of the peak-valley wave structure leading to wall turbulence

1989 ◽  
Vol 208 ◽  
pp. 1-23 ◽  
Author(s):  
Masahito Asai ◽  
Michio Nishioka
Keyword(s):  
Three Dimensional ◽  
Wave Structure ◽  
Wall Turbulence ◽  
Generation Process ◽  
Two Dimensional ◽  
Mean Flow ◽  
S Wave ◽  
Flow Distortion ◽  
Experimental Conditions ◽  
Dimensional Wave

A generation process for the three-dimensional wave which dominates the transition preceded by a Tollmien-Schlichting (T-S) wave is studied both experimentally and numerically in plane Poiseuille flow at a subcritical Reynolds number of 5000. In order to identify the origin of the three-dimensional wave in Nishioka et al.'s laboratory experiment, the corresponding spanwise mean-flow distortion and two-dimensional T-S wave modes are introduced into a parabolic flow as the initial disturbance conditions for a numerical simulation of temporally growing type. Through reproducing the actual wave development into the peak-valley structure, the simulation pinpoints the origin to be the slight spanwise mean-flow distortion in the experimental basic flow. Furthermore, the simulation clearly shows that the growth of the three-dimensional wave requires the vortex stretching effect due to the streamwise vortices, which appear under the experimental conditions only when the amplitude of the two-dimensional T-S wave is above the observed threshold.

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