Global stability of two-dimensional and axisymmetric Euler flows

1994 ◽  
Vol 276 ◽  
pp. 273-305 ◽  
Author(s):  
P. A. Davidson
Keyword(s):  
Magnetic Relaxation ◽  
Two Dimensional ◽  
Inviscid Flows ◽  
Wide Range ◽  
Recirculating Flows ◽  
Close Relationship ◽  
Euler Flows ◽  
Relaxation Procedure ◽  
The Stability ◽  
Planar Flows

This paper is concerned with the stability of steady inviscid flows with closed streamlines. In increasing order of complexity we look at two-dimensional planar flows, poloidal (r, z) flows, and swirling recirculating flows. In each case we examine the relationship between Arnol’d's variational approach to stability, Moffatt's magnetic relaxation technique, and a more recent relaxation procedure developed by Valliset al.We start with two-dimensional (x, y) flows. Here we show that Moffatt's relaxation procedure will, under a wide range of circumstances, produce Euler flows which are stable. The physical reasons for this are discussed in the context of the well-known membrane analogy. We also show that there is a close relationship between Hamilton's principle and magnetic relaxation. Next, we examine poloidal flows. Here we find that, by and large, our planar results also hold true for axisymmetric flows. In particular, magnetic relaxation once again provides stable Euler flows. Finally, we consider swirling recirculating flows. It transpires that the introduction of swirl has a profound effect on stability. In particular, the flows produced by magnetic relaxation are no longer stable. Indeed, we show that all swirling recirculating Euler flows are potentially unstable to the extent that they fail to satisfy Arnol’d's stability criterion. This is, perhaps, not surprising, as all swirling recirculating flows include regions where the angular momentum decreases with radius and we would intuitively expect such flows to be prone to a centrifugal instability. The paper concludes with a discussion of marginally unstable modes in swirling flows. In particular, we examine the extent to which Rayleigh's original ideas on stability may be generalized, through the use of the Routhian, to include flows with a non-zero recirculation.

On the application of the Kelvin–Arnol'd energy principle to the stability of forced two-dimensional inviscid flows

1998 ◽  
Vol 356 ◽  
pp. 221-257 ◽  
Author(s):  
P. A. DAVIDSON
Keyword(s):  
Magnetic Field ◽  
Nonlinear Stability ◽  
Broad Class ◽  
Mhd Flow ◽  
Two Dimensional ◽  
Energy Principle ◽  
Inviscid Flows ◽  
Virtual Displacement ◽  
Euler Flows ◽  
Universal Procedure

Arnol'd developed two distinct yet closely related approaches to the linear stability of Euler flows. One is widely used for two-dimensional flows and involves constructing a conserved functional whose first variation vanishes and whose second variation determines the linear (and nonlinear) stability of the motion. The second method is a refinement of Kelvin's energy principle which states that stable steady Euler flows represent extremums in energy under a virtual displacement of the vorticity field. The conserved-functional (or energy-Casimir) method has been extended by several authors to more complex flows, such as planar MHD flow. In this paper we generalize the Kelvin–Arnol'd energy method to two-dimensional inviscid flows subject to a body force of the form −ϕ∇f. Here ϕ is a materially conserved quantity and f an arbitrary function of position and of ϕ. This encompasses a broad class of conservative flows, such as natural-convection planar and poloidal MHD flow with the magnetic field trapped in the plane of the motion, flows driven by electrostatic forces, swirling recirculating flow, self-gravitating flows and poloidal MHD flow subject to an azimuthal magnetic field. We show that stable steady motions represent extremums in energy under a virtual displacement of ϕ and of the vorticity field. That is, d1E=0 at equilibrium and whenever d2E is positive or negative definite the flow is (linearly) stable. We also show that unstable normal modes must have a spatial structure which satisfies d2E=0. This provides a single stability test for a broad class of flows, and we describe a simple universal procedure for implementing this test. In passing, a new test for linear stability is developed. That is, we demonstrate that stability is ensured (for flows of the type considered here) whenever the Lagrangian of the flow is a maximum under a virtual displacement of the particle trajectories, the displacement being of the type normally associated with Hamilton's principle. A simple universal procedure for applying this test is also given. We apply our general stability criteria to a range of flows and recover some familiar results. We also extend these ideas to flows which are subject to more than one type of body force. For example, a new stability criterion is obtained (without the use of Casimirs) for natural convection in the presence of a magnetic field. Nonlinear stability is also considered. Specifically, we develop a nonlinear stability criterion for planar MHD flows which are subject to isomagnetic perturbations. This differs from previous criteria in that we are able to extend the linear criterion into the nonlinear regime. We also show how to extend the Kelvin–Arnol'd method to finite-amplitude perturbations.

scholarly journals Two-Dimensional Convection Induced by Gravity and Centrifugal Forces in a Rotating Porous Layer Far Away from the Axis of Rotation

1998 ◽  
Vol 4 (2) ◽  
pp. 73-90 ◽  
Author(s):  
Peter Vadasz ◽  
Saneshan Govender
Keyword(s):  
Rayleigh Number ◽  
Porous Layer ◽  
Temperature Fields ◽  
Wave Number ◽  
Marginal Stability ◽  
Two Dimensional ◽  
Wide Range ◽  
Gravity Driven ◽  
Gravity Driven Flow ◽  
The Stability

The stability and onset of two-dimensional convection in a rotating fluid saturated porous layer subject to gravity and centrifugal body forces is investigated analytically. The problem corresponding to a layer placed far away from the centre of rotation was identified as a distinct case and therefore justifying special attention. The stability of a basic gravity driven convection is analysed. The marginal stability criterion is established in terms of a critical centrifugal Rayleigh number and a critical wave number for different values of the gravity related Rayleigh number. For any given value of the gravity related Rayleigh number there is a transitional value of the wave number, beyond which the basic gravity driven flow is stable. The results provide the stability map for a wide range of values of the gravity related Rayleigh number, as well as the corresponding flow and temperature fields.

On the stability of high-Reynolds-number flows with closed streamlines

1989 ◽  
Vol 200 ◽  
pp. 19-38 ◽  
Author(s):  
A. J. Mestel
Keyword(s):  
Rotating Magnetic Field ◽  
Two Dimensional ◽  
Inviscid Flows ◽  
Stability Theorems ◽  
High Reynolds ◽  
The Stability ◽  
Two Parameters ◽  
Reynolds Number Flows ◽  
Flow Reversals ◽  
Entire Theory

In steady, two-dimensional, inertia-dominated flows it is well known that the vorticity is constant along the streamlines, which, in a bounded domain, are necessarily closed. For inviscid flows, the variation of vorticity across the streamlines is arbitrary, while for forced, weakly dissipitative flows, it is determined by the balance between viscous diffusion and the forcing. This paper discusses the linear stability of flows of this type to two-dimensional disturbances. Arnol'd's stability theorems are discussed. An alternative functional to Arnol'd's is found, which gives the same stability criteria and which permits a representation of the problem in terms of a Schrödinger equation. Conditions for stability are derived from this functional. In particular it is shown that total flow reversals are potentially unstable. The results are illustrated with respect to the geometrically simple case when the streamlines are circular and the forcing is due to a rotating magnetic field, for which case the stability regions are calculated as a function of two parameters. It is shown that the entire theory, including Arnol'd's theorems, applies also to poloidal axisymmetric flows.

Structure and stability of solutions of the Euler equations: a lagrangian approach

1990 ◽  
Vol 333 (1631) ◽  
pp. 321-342 ◽  
Keyword(s):  
Euler Equations ◽  
Vector Fields ◽  
Saddle Points ◽  
Relaxation Processes ◽  
Two Dimensional ◽  
Scalar And Vector Fields ◽  
Euler Flows ◽  
Relaxation Procedure ◽  
Unbounded Fluid

This paper reviews methods that are essentially lagrangian in character for determination of solutions of the Euler equations having prescribed topological characteristics. These methods depend in the first instance on the existence of lagrangian invariants for convected scalar and vector fields. Among these, the helicity invariant for a convected or ‘frozen-in’ vector field has particular significance. These invariants, and the associated topological interpretation are discussed in §§1 and 2. In §3 the method of magnetic relaxation to magnetostatic equilibria of prescribed topology is briefly described. This provides a powerful method for determining steady Euler flows through the well-known exact analogy between Euler flows and magnetostatic equilibria. Stability considerations relating to magnetostatic equilibria obtained in this way and to the analogous Euler flows are reviewed in §4. In §5 the related relaxation procedure is discussed; for two-dimensional and axisymmetric situations this technique provides stable solutions of the Euler equations for which the vorticity field has prescribed topology. The concept of flow signature is described in §6: this is the relevant topological characteristic for two-dimensional or axisymmetric situations, which is conserved during frozen-field relaxation processes. In §§7 and 8, the formation of tangential discontinuities as a normal part of the relaxation process when saddle points of the frozen-field are present is discussed. Section 9 considers briefly the application of these ideas to the theory of vortons, i.e. rotational disturbances that propagate without change of structure in an unbounded fluid. The paper concludes with a brief discussion, with comment on the possible development of the results in the context of turbulence.

Vibrations of an Elastically Mounted Spinning Rotor Partially Filled With Liquid

1982 ◽  
Vol 104 (2) ◽  
pp. 389-396 ◽  
Author(s):  
G. Lichtenberg
Keyword(s):  
Equations Of Motion ◽  
Constant Angular Velocity ◽  
Two Dimensional ◽  
Field Equations ◽  
Stability Boundaries ◽  
Inviscid Incompressible Fluid ◽  
Wide Range ◽  
The Stability ◽  
Elastically Supported ◽  
Dimensional Surface

The stability of a rotor with a cylindrical cavity, spinning with constant angular velocity and partially filled with an inviscid, incompressible fluid is studied. The rotor is elastically supported on a vertically mounted massless shaft in overhung position. A set of coupled linearized spatial equations of motion of the rotor and field equations, as well as boundary conditions of the liquid, is established and solved, leading to a characteristic equation. First numerical results predict a wide range of rotor speeds, where the system performs unstable motions caused by a two-dimensional surface wave of the liquid. The stability boundaries are calculated for a flat rotor in dependence on the mass of the contained liquid and agree extremely well with experimental data.

High-throughput computational material screening of the cycloalkane-based two-dimensional Dion–Jacobson halide perovskites for optoelectronics

2021 ◽  
Author(s):  
Guoqi Zhao ◽  
Jiahao Xie ◽  
Kun Zhou ◽  
Bangyu Xing ◽  
Xinjiang Wang ◽  
...  
Keyword(s):  
High Throughput ◽  
Density Functional ◽  
Perovskite Solar Cells ◽  
Two Dimensional ◽  
Photovoltaic Properties ◽  
Wide Range ◽  
Stability Issue ◽  
Halide Perovskites ◽  
The Stability ◽  
Inorganic Framework

Abstract Two-dimensional (2D) layered perovskites have emerged as potential alternates to traditional 3D analogs to solve the stability issue of perovskite solar cells. In recent years, many efforts have been spent on manipulating the interlayer organic spacing cation to improve the photovoltaic properties of Dion–Jacobson (DJ) perovskites. In this work, a serious of cycloalkane (CA) molecules were selected as the organic spacing cation in 2D DJ perovskites, which can widely manipulate the optoelectronic properties of DJ perovskites. The underlying relationship between the CA interlayer molecules and the crystal structures, thermodynamic stabilities, and electronic properties of 58 DJ perovskites has been investigated by using automatic high-throughput workflow cooperated with density-functional (DFT) calculations. We have found that these CA-based DJ perovskites are all thermodynamic stable. The sizes of the cycloalkane molecules can influence the degree of inorganic framework distortion and further tune the bandgaps with a wide range of 0.9~2.1 eV. These findings indicate the cycloalkane molecules are suitable for spacing cation in 2D DJ perovskites and provide a useful guidance in designing novel 2D DJ perovskites for optoelectronic applications.

Use of a Lyophilized Reference Plasma to Compare Coagulation Test Procedures

1975 ◽  
Vol 34 (02) ◽  
pp. 426-444 ◽  
Author(s):  
J Kahan ◽  
I Nohén
Keyword(s):  
Oral Anticoagulant Therapy ◽  
Repeated Measurements ◽  
Test Procedures ◽  
Coagulation Activity ◽  
Close Relationship ◽  
Measured Activity ◽  
Test Materials ◽  
The Difference ◽  
The Stability ◽  
The One

SummaryIn 4 collaborative trials, involving a varying number of hospital laboratories in the Stockholm area, the coagulation activity of different test materials was estimated with the one-stage prothrombin tests routinely used in the laboratories, viz. Normotest, Simplastin-A and Thrombotest. The test materials included different batches of a lyophilized reference plasma, deep-frozen specimens of diluted and undiluted normal plasmas, and fresh and deep-frozen specimens from patients on long-term oral anticoagulant therapy.Although a close relationship was found between different methods, Simplastin-A gave consistently lower values than Normotest, the difference being proportional to the estimated activity. The discrepancy was of about the same magnitude on all the test materials, and was probably due to a divergence between the manufacturers’ procedures used to set “normal percentage activity”, as well as to a varying ratio of measured activity to plasma concentration. The extent of discrepancy may vary with the batch-to-batch variation of thromboplastin reagents.The close agreement between results obtained on different test materials suggests that the investigated reference plasma could be used to calibrate the examined thromboplastin reagents, and to compare the degree of hypocoagulability estimated by the examined PIVKA-insensitive thromboplastin reagents.The assigned coagulation activity of different batches of the reference plasma agreed closely with experimentally obtained values. The stability of supplied batches was satisfactory as judged from the reproducibility of repeated measurements. The variability of test procedures was approximately the same on different test materials.

Performance of Electronic Structure Methods for the Description of Hückel-Möbius Interconversions in Extended π-Systems

2019 ◽  
Author(s):  
Tatiana Woller ◽  
Ambar Banerjee ◽  
Nitai Sylvetsky ◽  
Xavier Deraet ◽  
Frank De Proft ◽  
...  
Keyword(s):  
Electronic Structure ◽  
Basis Set ◽  
Dft Methods ◽  
Molecular Switching ◽  
Wide Range ◽  
Electronic Structure Methods ◽  
Explicitly Correlated ◽  
Relative Errors ◽  
The Stability ◽  
Basis Set Expansion

<p>Expanded porphyrins provide a versatile route to molecular switching devices due to their ability to shift between several π-conjugation topologies encoding distinct properties. Taking into account its size and huge conformational flexibility, DFT remains the workhorse for modeling such extended macrocycles. Nevertheless, the stability of Hückel and Möbius conformers depends on a complex interplay of different factors, such as hydrogen bonding, p···p stacking, steric effects, ring strain and electron delocalization. As a consequence, the selection of an exchange-correlation functional for describing the energy profile of topological switches is very difficult. For these reasons, we have examined the performance of a variety of wavefunction methods and density functionals for describing the thermochemistry and kinetics of topology interconversions across a wide range of macrocycles. Especially for hexa- and heptaphyrins, the Möbius structures have a pronouncedly stronger degree of static correlation than the Hückel and figure-eight structures, and as a result the relative energies of singly-twisted structures are a challenging test for electronic structure methods. Comparison of limited orbital space full CI calculations with CCSD(T) calculations within the same active spaces shows that post-CCSD(T) correlation contributions to relative energies are very minor. At the same time, relative energies are weakly sensitive to further basis set expansion, as proven by the minor energy differences between MP2/cc-pVDZ and explicitly correlated MP2-F12/cc-pVDZ-F12 calculations. Hence, our CCSD(T) reference values are reasonably well-converged in both 1-particle and n-particle spaces. While conventional MP2 and MP3 yield very poor results, SCS-MP2 and particularly SOS-MP2 and SCS-MP3 agree to better than 1 kcal mol<sup>-1</sup> with the CCSD(T) relative energies. Regarding DFT methods, only M06-2X provides relative errors close to chemical accuracy with a RMSD of 1.2 kcal mol<sup>-1</sup>. While the original DSD-PBEP86 double hybrid performs fairly poorly for these extended p-systems, the errors drop down to 2 kcal mol<sup>-1</sup> for the revised revDSD-PBEP86-NL, again showing that same-spin MP2-like correlation has a detrimental impact on performance like the SOS-MP2 results. </p>

Aromatic Volatile Composition of Celery and Celeriac Cultivars

HortScience ◽  
1990 ◽  
Vol 25 (5) ◽  
pp. 556-559 ◽  
Author(s):  
Fredy Van Wassenhove ◽  
Patrick Dirinck ◽  
Georges Vulsteke ◽  
Niceas Schamp
Keyword(s):  
Volatile Compounds ◽  
Chromatographic Method ◽  
Apium Graveolens ◽  
Volatile Components ◽  
Two Dimensional ◽  
Qualitative Composition ◽  
Volatile Composition ◽  
Wide Range ◽  
Gas Chromatographic Method ◽  
Identification And Quantification

A two-dimensional capillary gas chromatographic method was developed to separate and quantify aromatic volatiles of celery in one analysis. The isolation, identification, and quantification of the volatile compounds of four cultivars of blanching celery (Apium graveolens L. var. dulce) and six cultivars of celeriac (Apium graveolens L. var. rapaceum) are described. The qualitative composition of Likens-Nickerson extracts of both cultivars is similar. The concentration of terpenes and phthalides, the key volatile components, found in various cultivars of both celery and celeriac varied over a wide range.

Insights into Potent Therapeutical Antileukemic Agent L-glutaminase Enzyme Under Solid-state Fermentation: A Review

2020 ◽  
Vol 21 (3) ◽  
pp. 211-220 ◽  
Author(s):  
Chandrasai Potla Durthi ◽  
Madhuri Pola ◽  
Satish Babu Rajulapati ◽  
Anand Kishore Kola
Keyword(s):  
Solid State ◽  
Solid State Fermentation ◽  
Food Industry ◽  
Energy Requirement ◽  
Production Studies ◽  
Wide Range ◽  
Hybridoma Technology ◽  
Bacteria And Fungi ◽  
The Stability ◽  
Glutaminase Activity

Aim & objective: To review the applications and production studies of reported antileukemic drug L-glutaminase under Solid-state Fermentation (SSF). Overview: An amidohydrolase that gained economic importance because of its wide range of applications in the pharmaceutical industry, as well as the food industry, is L-glutaminase. The medical applications utilized it as an anti-tumor agent as well as an antiretroviral agent. L-glutaminase is employed in the food industry as an acrylamide degradation agent, as a flavor enhancer and for the synthesis of theanine. Another application includes its use in hybridoma technology as a biosensing agent. Because of its diverse applications, scientists are now focusing on enhancing the production and optimization of L-glutaminase from various sources by both Solid-state Fermentation (SSF) and submerged fermentation studies. Of both types of fermentation processes, SSF has gained importance because of its minimal cost and energy requirement. L-glutaminase can be produced by SSF from both bacteria and fungi. Single-factor studies, as well as multi-level optimization studies, were employed to enhance L-glutaminase production. It was concluded that L-glutaminase activity achieved by SSF was 1690 U/g using wheat bran and Bengal gram husk by applying feed-forward artificial neural network and genetic algorithm. The highest L-glutaminase activity achieved under SSF was 3300 U/gds from Bacillus sp., by mixture design. Purification and kinetics studies were also reported to find the molecular weight as well as the stability of L-glutaminase. Conclusion: The current review is focused on the production of L-glutaminase by SSF from both bacteria and fungi. It was concluded from reported literature that optimization studies enhanced L-glutaminase production. Researchers have also confirmed antileukemic and anti-tumor properties of the purified L-glutaminase on various cell lines.

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