On estimates for short wave stability and long wave instability in three-layer Hele-Shaw flows

2011 ◽  
Vol 390 (18-19) ◽  
pp. 3069-3076 ◽  
Author(s):  
Prabir Daripa
Keyword(s):  
Short Wave ◽  
Wave Instability ◽  
Wave Stability ◽  
Long Wave

scholarly journals On the porosity influence on stability of flow over porous medium

2020 ◽  
Vol 30 (1) ◽  
pp. 134-144
Author(s):  
K.B. Tsiberkin
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Short Wave ◽  
Wave Instability ◽  
Plane Parallel ◽  
Long Wave ◽  
The Stability ◽  
Critical Wavenumber

The stability of incompressible fluid plane-parallel flow over a layer of a saturated porous medium is studied. The results of a linear stability analysis are described at different porosity values. The considered system is bounded by solid wall from the porous layer bottom. Top fluid surface is free and rigid. A linear stability analysis of plane-parallel stationary flow is presented. It is realized for parameter area where the neutral stability curves are bimodal. The porosity variation effect on flow stability is considered. It is shown that there is a transition between two main instability modes: long-wave and short-wave. The long-wave instability mechanism is determined by inflection points within the velocity profile. The short-wave instability is due to the large transverse gradient of flow velocity near the interface between liquid and porous medium. Porosity decrease stabilizes the long wave perturbations without significant shift of the critical wavenumber. Simultaneously, the short-wave perturbations destabilize, and their critical wavenumber changes in wide range. When the porosity is less than 0.7, the inertial terms in filtration equation and magnitude of the viscous stress near the interface increase to such an extent that the Kelvin-Helmholtz analogue of instability becomes the dominant mechanism for instability development. The stability band realizes in narrow porosity area. It separates the two branches of the neutral curve.

On the stability of crystal lattices VII. Long-wave and short-wave stability for the face-centred cubic lattice

1942 ◽  
Vol 38 (1) ◽  
pp. 61-66 ◽  
Author(s):  
S. C. Power
Keyword(s):  
Short Wave ◽  
Long Waves ◽  
Three Dimensions ◽  
Linear Lattice ◽  
Crystal Lattices ◽  
Cubic Lattice ◽  
Wave Stability ◽  
Long Wave ◽  
The Face ◽  
The Stability

It is shown that the theorem stated in Born's paper, and proved for the case of a linear lattice of N equal particles under certain restrictions concerning the forces between the particles, that macroscopic stability (stability for long waves) implies microscopic stability, may be extended to three dimensions for the particular case of a face-centred cubic lattice, where the effects of all neighbours, other than the first twelve neighbours, are neglected.I take this opportunity of expressing my sincere thanks to Prof. Born for much valuable advice.

The stability of a helical vortex filament

1972 ◽  
Vol 54 (4) ◽  
pp. 641-663 ◽  
Author(s):  
Sheila E. Widnall
Keyword(s):  
Short Wave ◽  
Mutual Inductance ◽  
The Self ◽  
Vortex Filament ◽  
Wave Instability ◽  
Long Wave ◽  
Amplification Rate ◽  
Helical Vortex ◽  
Induced Motion ◽  
The Stability

The stability of a helical vortex filament of finite core and infinite extent to small sinusoidal displacements of its centre-line is considered. The influence of the entire perturbed filament on the self-induced motion of each element is taken into account. The effect of the details of the vorticity distribution within the finite vortex core on the self-induced motion due to the bending of its axis is calculated using the results obtained previously by Widnall, Bliss & Zalay (1970). In this previous work, an application of the method of matched asymptotic expansions resulted in a general solution for the self-induced motion resulting from the bending of a slender vortex filament with an arbitrary distribution of vorticity and axial velocity within the core.The results of the stability calculations presented in this paper show that the helical vortex filament has three modes of instability: a very short-wave instability which probably exists on all curved filaments, a long-wave mode which is also found to be unstable by the local-induction model and a mutual-inductance mode which appears as the pitch of the helix decreases and the neighbouring turns of the filament begin to interact strongly. Increasing the vortex core size is found to reduce the amplification rate of the long-wave instability, to increase the amplification rate of the mutual-inductance instability and to decrease the wavenumber of the short-wave instability.

scholarly journals Linear temporal and spatio-temporal stability analysis of a binary liquid film flowing down an inclined uniformly heated plate

2008 ◽  
Vol 599 ◽  
pp. 269-298 ◽  
Author(s):  
JUN HU ◽  
HAMDA BEN HADID ◽  
DANIEL HENRY ◽  
ABDELKADER MOJTABI
Keyword(s):  
Soret Effect ◽  
Short Wave ◽  
Heated Plate ◽  
Surface Mode ◽  
Wave Instability ◽  
Binary Liquid ◽  
Long Wave ◽  
Neutral Curves ◽  
Spatio Temporal ◽  
Boundary Curves

Temporal and spatio-temporal instabilities of binary liquid films flowing down an inclined uniformly heated plate with Soret effect are investigated by using the Chebyshev collocation method to solve the full system of linear stability equations. Seven dimensionless parameters, i.e. the Kapitza, Galileo, Prandtl, Lewis, Soret, Marangoni, and Biot numbers (Ka,G,Pr,L, χ,M,B), as well as the inclination angle (β) are used to control the flow system. In the case of pure spanwise perturbations, thermocapillary S- and P-modes are obtained. It is found that the most dangerous modes are stationary for positive Soret numbers (χ≥0), and oscillatory for χ<0. Moreover, the P-mode which is short-wave unstable for χ=0 remains so for χ<0, but becomes long-wave unstable for χ>0 and even merges with the long-wave S-mode. In the case of streamwise perturbations, a long-wave surface mode (H-mode) is also obtained. From the neutral curves, it is found that larger Soret numbers make the film flow more unstable as do larger Marangoni numbers. The increase of these parameters leads to the merging of the long-wave H- and S-modes, making the situation long-wave unstable for any Galileo number. It also strongly influences the short-wave P-mode which becomes the most critical for large enough Galileo numbers. Furthermore, from the boundary curves between absolute and convective instabilities (AI/CI) calculated for both the long-wave instability (S- and H-modes) and the short-wave instability (P-mode), it is shown that for small Galileo numbers the AI/CI boundary curves are determined by the long-wave instability, while for large Galileo numbers they are determined by the short-wave instability.

Modeling internal rogue waves in a long wave-short wave resonance framework

2018 ◽  
Vol 3 (12) ◽  
Author(s):  
H. N. Chan ◽  
R. H. J. Grimshaw ◽  
K. W. Chow
Keyword(s):  
Rogue Waves ◽  
Short Wave ◽  
Long Wave ◽  
Wave Resonance

scholarly journals Evaluating the Effects of Façade Greening on Human Bioclimate in a Complex Urban Environment

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Britta Jänicke ◽  
Fred Meier ◽  
Marie-Therese Hoelscher ◽  
Dieter Scherer
Keyword(s):  
Heat Stress ◽  
Short Wave ◽  
Wave Radiation ◽  
Short Wave Radiation ◽  
Long Wave ◽  
Building Facades ◽  
Urban Heat ◽  
The Mean ◽  
Human Bioclimate ◽  
Radiant Temperature

The evaluation of the effectiveness of countermeasures for a reduction of urban heat stress, such as façade greening, is challenging due to lacking transferability of results from one location to another. Furthermore, complex variables such as the mean radiant temperature(Tmrt)are necessary to assess outdoor human bioclimate. We observedTmrtin front of a building façade in Berlin, Germany, which is half-greened while the other part is bare.Tmrtwas reduced (mean 2 K) in front of the greened compared to the bare façade. To overcome observational shortcomings, we applied the microscale models ENVI-met, RayMan, and SOLWEIG. We evaluated these models based on observations. Our results show thatTmrt(MD = −1.93 K) and downward short-wave radiation (MD = 14.39 W/m2) were sufficiently simulated in contrast to upward short-wave and long-wave radiation. Finally, we compare the simulated reduction ofTmrtwith the observed one in front of the façade greening, showing that the models were not able to simulate the effects of façade greening with the applied settings. Our results reveal that façade greening contributes only slightly to a reduction of heat stress in front of building façades.

On the modulation of water waves on shear flows

1976 ◽  
Vol 347 (1651) ◽  
pp. 537-546 ◽  
Keyword(s):  
Water Waves ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Vries Equation ◽  
Harmonic Wave ◽  
Short Wave ◽  
Long Wave ◽  
Stokes Waves ◽  
The Stability ◽  
Wave Limit

The method of multiple scales is used to examine the slow modulation of a harmonic wave moving over the surface of a two dimensional channel. The flow is assumed inviscid and incompressible, but the basic flow takes the form of an arbitrary shear. The appropriate nonlinear Schrödinger equation is derived with coefficients that depend, in a complicated way, on the shear. It is shown that this equation agrees with previous work for the case of no shear; it also agrees in the long wave limit with the appropriate short wave limit of the Korteweg-de Vries equation, the shear being arbitrary. Finally, it is remarked that the stability of Stokes waves over any shear can be examined by using the results derived here.

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