Stability of a compressible two-dimensional vortex under a three-dimensional perturbation

1984 ◽  
Vol 392 (1803) ◽  
pp. 279-299 ◽  
Keyword(s):  
Mach Number ◽  
Velocity Profile ◽  
Incompressible Flow ◽  
Compressible Fluid ◽  
Three Dimensional ◽  
Critical Value ◽  
Two Dimensional ◽  
Rankine Vortex ◽  
The Core ◽  
Critical Boundary

Kelvin showed that a two-dimensional vortex under a two-dimensional disturbance in incompressible flow responds at a discrete set of eigenvalues, which were found by Broadbent & Moore ( Phil. Trans. R. Soc. Lond. A 290, 353-371 (1979) to become unstable in a compressible fluid. It is now shown that three-dimensional perturbations are also unstable provided the wavelength is greater than some critical value that depends on the Mach number of the vortex. A critical boundary dividing stable from unstable modes is defined. Most of the results relate to a Rankine vortex, as in the previous work mentioned above, but some results are also given for a vortex with a different velocity profile within the core; qualitatively the same kind of behaviour is found.

Corrugated SNOM probe with enhanced energy throughput

2008 ◽  
Vol 16 (4) ◽  
Author(s):  
T. Antosiewicz ◽  
T. Szoplik
Keyword(s):  
Near Field ◽  
Three Dimensional ◽  
Energy Output ◽  
Dipolar Field ◽  
Two Dimensional ◽  
The Core ◽  
Dimensional Approximation ◽  
New Type ◽  
Difference Time ◽  
Main Factor

AbstractIn a previous paper we proposed a modification of metal-coated tapered-fibre aperture probes for scanning near-field optical microscopes (SNOMs). The modification consists in radial corrugations of the metal-dielectric interface oriented inward the core. Their purpose is to facilitate the excitation of surface plasmons, which increase the transport of energy beyond the cut-off diameter and radiate a quasi-dipolar field from the probe output rim. An increase in energy output allows for reduction of the apex diameter, which is the main factor determining the resolution of the microscope. In two-dimensional finite-difference time-domain (FDTD) simulations we analyse the performance of the new type of SNOM probe. We admit, however, that the two-dimensional approximation gives better results than expected from exact three-dimensional ones. Nevertheless, optimisation of enhanced energy throughput in corrugated probes should lead to at least twice better resolution with the same sensitivity of detectors available nowadays.

scholarly journals Characterization of the translocon of the outer envelope of chloroplasts

2003 ◽  
Vol 160 (4) ◽  
pp. 541-551 ◽  
Author(s):  
Enrico Schleiff ◽  
Jürgen Soll ◽  
Michael Küchler ◽  
Werner Kühlbrandt ◽  
Roswitha Harrer
Keyword(s):  
Three Dimensional ◽  
Dependent Manner ◽  
Interior Structure ◽  
Two Dimensional ◽  
Outer Envelope ◽  
Core Complex ◽  
The Core ◽  
Precursor Proteins ◽  
Stable Core

The protein translocon of the outer envelope of chloroplasts (Toc) consists of the core subunits Toc159, Toc75, and Toc34. To investigate the molecular structure, the core complex was purified. This core complex has an apparent molecular mass of ∼500 kD and a molecular stoichiometry of 1:4:4–5 between Toc159, Toc75, and Toc34. The isolated translocon recognizes both transit sequences and precursor proteins in a GTP-dependent manner, suggesting its functional integrity. The complex is embedded by the lipids phosphatidylcholine and digalactosyldiacylglyceride. Two-dimensional structural analysis by EM revealed roughly circular particles consistent with the formation of a stable core complex. The particles show a diameter of ∼130 Å with a solid ring and a less dense interior structure. A three-dimensional map obtained by random conical tilt reconstruction of electron micrographs suggests that a “finger”-like central region separates four curved translocation channels within one complex.

Three isostructural solvates of a tetrahydrofurochromenone derivative

2017 ◽  
Vol 73 (5) ◽  
pp. 407-413 ◽  
Author(s):  
Balasubramanian Sridhar ◽  
Jagadeesh Babu Nanubolu ◽  
Krishnan Ravikumar ◽  
Govindaraju Karthik ◽  
Basi Venkata Subba Reddy
Keyword(s):  
Three Dimensional ◽  
Unit Cell ◽  
Multicomponent Systems ◽  
Two Dimensional ◽  
The Core ◽  
Cell Dimensions ◽  
Similarity Indices ◽  
Unit Cell Dimensions ◽  
Similar Unit ◽  
Crystal Packings

Isostructurality is more likely to occur in multicomponent systems. In this context, three closely related solvates were crystallized, namely, benzene (C27H21BrO6·C6H6), toluene (C27H21BrO6·C7H8) and xylene (C27H21BrO6·C8H10) with methyl 3a-acetyl-3-(4-bromophenyl)-4-oxo-1-phenyl-3,3a,4,9b-tetrahydro-1H-furo[3,4-c]chromene-1-carboxylate, and their crystal structures determined. All three structures belong to the same space group (P\overline{1}) and display similar unit-cell dimensions and conformations, as well as isostructural crystal packings. The isostructurality is confirmed by unit-cell and isostructural similarity indices. In each solvate, weak C—H...O and C—H...π interactions extend the molecules into two-dimensional networks, which are further linked by C—H...Br and Br...Br interactions into three-dimensional networks. The conformation of the core molecule is predominantly responsible for governing the isostructurality.

A Comparative Study Between Two-Dimensional and Three-Dimensional Simulation Results of Melting Inside a Container

2020 ◽  
Author(s):  
Nan Hu ◽  
Li-Wu Fan
Keyword(s):  
Velocity Profile ◽  
Heating Temperature ◽  
Three Dimensional ◽  
Detailed Comparison ◽  
Melting Rate ◽  
Two Dimensional ◽  
End Effects ◽  
Wall Superheat ◽  
Simulation Results ◽  
Dimensional Simulation

Abstract Bother two-dimensional (2D) and three-dimensional (3D) simulations on two example melting problems, i.e., melting in a differentially-heated rectangular cavity and constrained melting in a horizontal cylindrical capsule, were carried out to investigate the rationality of 2D simplification. The effects of thermophysical properties of the phase change material, size of the container along the direction perpendicular to the 2D cross-section, as well as wall superheat were taken into consideration for a systematic and detailed comparison. It was shown that a small length of the container perpendicular to 2D plane will result in a confine space to limit the development of velocity distribution (i.e., parabolic velocity profile) due to the end effects, leading to to an almost identical melting rate to that obtained by the 2D simplified case. A larger size indicates stronger thermal convection (bulk uniform velocity profile) and faster melting rate. When fixing a large size of the container perpendicular to the 2D plane, decreasing the heating temperature and increasing the viscosity of liquid PCM (e.g., by adding nanoparticles) reduce the discrepancy between 2D and 3D simulation results.

Solution of three-dimensional incompressible flow problems

1977 ◽  
Vol 82 (2) ◽  
pp. 309-319 ◽  
Author(s):  
S. M. Richardson ◽  
A. R. H. Cornish
Keyword(s):  
Stream Function ◽  
Incompressible Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Flow Problems ◽  
Vector Potentials

A method for solving quite general three-dimensional incompressible flow problems, in particular those described by the Navier–Stokes equations, is presented. The essence of the method is the expression of the velocity in terms of scalar and vector potentials, which are the three-dimensional generalizations of the two-dimensional stream function, and which ensure that the equation of continuity is satisfied automatically. Although the method is not new, a correct but simple and unambiguous procedure for using it has not been presented before.

Analysis of LDMOS for Effect of Fingers, Device-Width and Inductance (Load) on Reverse Recovery

2012 ◽  
Vol 229-231 ◽  
pp. 2077-2081
Author(s):  
Mohammed Sadique Anwar ◽  
Prima Sukma Permata ◽  
Md. Imran Siddiqui ◽  
Jung Ruey Tsai ◽  
Shao Ming Yang ◽  
...  
Keyword(s):  
Pulse Width ◽  
Circuit Simulation ◽  
Three Dimensional ◽  
Failure Criteria ◽  
Critical Value ◽  
Two Dimensional

This work demonstrates the effect of fingers, device-width and inductance on reverse recovery of LDMOS by unclamped inductive switching (UIS) circuit simulation for two dimensional (2D) and three dimensional (3D) devices. All the observations have been done for maximum pulse width at which device pass under UIS test. For UIS simulations the failure criteria is taken as the device temperature reaching a critical value of 650K. It has been shown that reverse recovery charge (Qrr) increased linearly with number of fingers, device width and inductance.

scholarly journals A two-dimensional depth-averaged -rheology for dense granular avalanches

2015 ◽  
Vol 787 ◽  
pp. 367-395 ◽  
Author(s):  
J. L. Baker ◽  
T. Barker ◽  
J. M. N. T. Gray
Keyword(s):  
Velocity Profile ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Theoretical Models ◽  
Quantitative Agreement ◽  
Surface Velocity ◽  
Momentum Balance ◽  
Test Case ◽  
Two Dimensional ◽  
Uniform Solution

Steady uniform granular chute flows are common in industry and provide an important test case for new theoretical models. This paper introduces depth-integrated viscous terms into the momentum-balance equations by extending the recent depth-averaged ${\it\mu}(I)$-rheology for dense granular flows to two spatial dimensions, using the principle of material frame indifference or objectivity. Scaling the cross-slope coordinate on the width of the channel and the velocity on the one-dimensional steady uniform solution, we show that the steady two-dimensional downslope velocity profile is independent of scale. The only controlling parameters are the channel aspect ratio, the slope inclination angle and the frictional properties of the chute and the sidewalls. Solutions are constructed for both no-slip conditions and for a constant Coulomb friction at the walls. For narrow chutes, a pronounced parabolic-like depth-averaged downstream velocity profile develops. However, for very wide channels, the flow is almost uniform with narrow boundary layers close to the sidewalls. Both of these cases are in direct contrast to conventional inviscid avalanche models, which do not develop a cross-slope profile. Steady-state numerical solutions to the full three-dimensional ${\it\mu}(I)$-rheology are computed using the finite element method. It is shown that these solutions are also independent of scale. For sufficiently shallow channels, the depth-averaged velocity profile computed from the full solution is in excellent agreement with the results of the depth-averaged theory. The full downstream velocity can be reconstructed from the depth-averaged theory by assuming a Bagnold-like velocity profile with depth. For wide chutes, this is very close to the results of the full three-dimensional calculation. For experimental validation, a laser profilometer and balance are used to determine the relationship between the total mass flux in the chute and the flow thickness for a range of slope angles and channel widths, and particle image velocimetry (PIV) is used to record the corresponding surface velocity profiles. The measured values are in good quantitative agreement with reconstructed solutions to the new depth-averaged theory.

Another look at unidirectional turbulent flow

1995 ◽  
Vol 287 ◽  
pp. 75-92 ◽  
Author(s):  
A. J. Reynolds ◽  
K. Wieghardt
Keyword(s):  
Variational Principle ◽  
Velocity Profile ◽  
Turbulent Flow ◽  
Three Dimensional ◽  
Core Region ◽  
Flat Channel ◽  
Mean Velocity ◽  
Channel One ◽  
The Core ◽  
The Mean

Here we consider the mean velocity profile in the core region of a unidirectional turbulent flow, that is, a flow in which the turbulent motion is superposed upon parallel time-averaged streamlines. A kinematical variational principle, originally developed for three-dimensional free-turbulent motions, is shown to be applicable to significant parts of the velocity profiles for flows of both Couette and Poiseuille types. In addition to pure plane Couette and pure plane Poiseuille flows, the motions considered include a variety of admixtures produced by blowing through a wide flat channel one of whose walls comprises a belt which moves either in the direction of the blowing or counter to it.

The Compressible Flow Through Cascade Actuator Discs

1958 ◽  
Vol 9 (2) ◽  
pp. 110-130 ◽  
Author(s):  
J. H. Horlock
Keyword(s):  
Shear Flow ◽  
Compressible Flow ◽  
Incompressible Flow ◽  
Three Dimensional ◽  
Approximate Solutions ◽  
Two Dimensional ◽  
Guide Vanes ◽  
The Past ◽  
Flow Through ◽  
Annular Cascade

SummaryA theory of the incompressible flow through two- and three-dimensional cascade actuator discs has been developed by several workers over the past ten years, and its accuracy has been confirmed in several experiments. This theory is briefly reviewed, and a parallel theory for subsonic compressible flow through actuator discs is developed. Approximate solutions for several examples are considered, including a compressible shear flow through a two-dimensional cascade, and a compressible flow through an annular cascade of guide vanes.

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