Linear and nonlinear instability of stratified flows with strong stratification

2003 ◽  
pp. 31-47
Keyword(s):  
Stratified Flows ◽  
Nonlinear Instability ◽  
Linear And Nonlinear

scholarly journals LINEAR AND NONLINEAR INSTABILITY OF FLOW IN CHANNEL OCCUPIED POROUS MEDIA

2017 ◽  
Vol 39 (3) ◽  
pp. 40-46
Author(s):  
A.A. Avramenko ◽  
N.P. Dmitrenko ◽  
Y.Y. Kovetskaya
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Kinematic Viscosity ◽  
Hydrodynamic Instability ◽  
Linear Instability ◽  
Nonlinear Instability ◽  
Linear Perturbations ◽  
Linear And Nonlinear

The paper investigates linear and nonlinear hydrodynamic instability of flow in channel ocuped porous medium. The effects of linear instability are considered using the method of linear perturbations. The nonlinear instability of the flow is considered using the renormalized expression for the coefficient of the kinematic viscosity.

scholarly journals The linear and nonlinear instability of the Akhmediev breather

Nonlinearity ◽  
2021 ◽  
Vol 34 (12) ◽  
pp. 8331-8358
Author(s):  
P G Grinevich ◽  
P M Santini
Keyword(s):  
Nonlinear Instability ◽  
Linear And Nonlinear

scholarly journals Baroclinic and barotropic instabilities in planetary atmospheres - energetics, equilibration and adjustment

2019 ◽  
Author(s):  
Peter Read ◽  
Neil Lewis ◽  
Daniel Kennedy ◽  
Hélène Scolan ◽  
Fachreddin Tabataba-Vakili ◽  
...  
Keyword(s):  
Thermal Structure ◽  
Planetary Atmospheres ◽  
Stability Theorem ◽  
Unstable State ◽  
Nonlinear Instability ◽  
Background Flow ◽  
Flow Configuration ◽  
The Earth ◽  
Open Questions ◽  
Linear And Nonlinear

Abstract. Baroclinic and barotropic instabilities, are well known as the mechanisms responsible for the production of the dominant energy-containing eddies in the atmospheres of the Earth and several other planets, as well as the Earth's oceans. Here we consider insights provided by both linear and nonlinear instability theories into the conditions under which such instabilities may occur, with reference to forced and dissipative flows obtainable in the laboratory, in simplified numerical atmospheric circulation models and in the planets of our Solar System. The equilibration of such instabilities is also of great importance in understanding the structure and energetics of the observable circulation of atmospheres and oceans. Various ideas have been proposed concerning the ways in which baroclinic and barotropic instabilities grow to large amplitude and saturate, whilst also modifying their background flow and environment. This remains an area that continues to challenge theoreticians and observers, though some progress has been made. The notion that such instabilities may act under some conditions to adjust the background flow towards a critical state is explored here in the context of both laboratory systems and planetary atmospheres. Evidence for such adjustment processes is found relating to baroclinic instabilities under a range of conditions where the efficiency of eddy and zonal mean heat transport may mutually compensate to maintain a nearly invariant thermal structure in the zonal mean. In other systems, barotropic instabilities may efficiently mix potential vorticity to result in a flow configuration that is found to approach a marginally unstable state with respect to Arnol'd's second stability theorem. We discuss the implications of these findings and identify some outstanding open questions.

Noise Reduction and Pattern Formation in Rapid Granular Flows

1998 ◽  
Vol 09 (08) ◽  
pp. 1339-1351 ◽  
Author(s):  
R. Brito ◽  
M. H. Ernst
Keyword(s):  
Flow Field ◽  
Noise Reduction ◽  
Granular Flows ◽  
Density Field ◽  
Dissipative Systems ◽  
Nonlinear Instability ◽  
Simulation Methods ◽  
Spatial Fluctuations ◽  
Linear And Nonlinear ◽  
Elastic Fluids

Spatial fluctuations in dissipative systems, such as rapid granular flows, behave very differently from those in elastic fluids. Fluctuations in the flow field drive the linear and nonlinear instability in the density field (clustering), while vortex structures appear and grow through the mechanism of noise reduction. The dynamics of the flow field on the largest space and time scales is described by diffusion equations with different diffusivities for the transverse and longitudinal flow fields. The results are obtained from analytic and simulation methods.

scholarly journals Baroclinic and barotropic instabilities in planetary atmospheres: energetics, equilibration and adjustment

2020 ◽  
Vol 27 (2) ◽  
pp. 147-173 ◽  
Author(s):  
Peter Read ◽  
Daniel Kennedy ◽  
Neil Lewis ◽  
Hélène Scolan ◽  
Fachreddin Tabataba-Vakili ◽  
...  
Keyword(s):  
Solar System ◽  
Thermal Structure ◽  
Planetary Atmospheres ◽  
Stability Theorem ◽  
Unstable State ◽  
Nonlinear Instability ◽  
Background Flow ◽  
Flow Configuration ◽  
Open Questions ◽  
Linear And Nonlinear

Abstract. Baroclinic and barotropic instabilities are well known as the mechanisms responsible for the production of the dominant energy-containing eddies in the atmospheres of Earth and several other planets, as well as Earth's oceans. Here we consider insights provided by both linear and nonlinear instability theories into the conditions under which such instabilities may occur, with reference to forced and dissipative flows obtainable in the laboratory, in simplified numerical atmospheric circulation models and in the planets of our solar system. The equilibration of such instabilities is also of great importance in understanding the structure and energetics of the observable circulation of atmospheres and oceans. Various ideas have been proposed concerning the ways in which baroclinic and barotropic instabilities grow to a large amplitude and saturate whilst also modifying their background flow and environment. This remains an area that continues to challenge theoreticians and observers, though some progress has been made. The notion that such instabilities may act under some conditions to adjust the background flow towards a critical state is explored here in the context of both laboratory systems and planetary atmospheres. Evidence for such adjustment processes is found relating to baroclinic instabilities under a range of conditions where the efficiency of eddy and zonal-mean heat transport may mutually compensate in maintaining a nearly invariant thermal structure in the zonal mean. In other systems, barotropic instabilities may efficiently mix potential vorticity to result in a flow configuration that is found to approach a marginally unstable state with respect to Arnol'd's second stability theorem. We discuss the implications of these findings and identify some outstanding open questions.

scholarly journals On instability of Rayleigh–Taylor problem for incompressible liquid crystals under $L^{1}$-norm

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mengmeng Liu ◽  
Xueyun Lin
Keyword(s):  
Gravitational Field ◽  
Incompressible Liquid ◽  
Steady State Solution ◽  
Nonlinear Instability ◽  
Linearized Problem ◽  
Unstable Solutions ◽  
Taylor Problem ◽  
Linear And Nonlinear ◽  
Nonlinear Solutions ◽  
Rt Instability

AbstractWe investigate the nonlinear Rayleigh–Taylor (RT) instability of a nonhomogeneous incompressible nematic liquid crystal in the presence of a uniform gravitational field. We first analyze the linearized equations around the steady state solution. Thus we construct solutions of the linearized problem that grow in time in the Sobolev space $H^{4}$ H 4 , then we show that the RT equilibrium state is linearly unstable. With the help of the established unstable solutions of the linearized problem and error estimates between the linear and nonlinear solutions, we establish the nonlinear instability of the density, the horizontal and vertical velocities under $L^{1}$ L 1 -norm.

Fluid Mechanics

2013 ◽  
Vol 43 (2) ◽  
pp. 5-30 ◽  
Author(s):  
St. Radev ◽  
F. R. A. Onofri ◽  
A. Lenoble ◽  
L. Tadrist
Keyword(s):  
Fluid Mechanics ◽  
Glass Fibre ◽  
Experimental Results ◽  
Nonlinear Instability ◽  
Paper Review ◽  
Linear And Nonlinear

Abstract The paper review key results [1-14] of the joint researches conducted by IMech and IUSTI. In the First part, we review models and experimental results on the linear and nonlinear instability of a capillary jet including both axisymmetric and nonaxisymmetric disturbances. In the Second part, results on draw resonances, occurring during a glass fibre process are reviewed, as well as the unique optical models and methods developed to perform these studies.

Linear and nonlinear instability in a cylindrical enclosure caused by a rotating magnetic field

2007 ◽  
Vol 19 (8) ◽  
pp. 088107 ◽  
Author(s):  
Kristina Koal ◽  
Jörg Stiller ◽  
Roger Grundmann
Keyword(s):  
Magnetic Field ◽  
Rotating Magnetic Field ◽  
Nonlinear Instability ◽  
Linear And Nonlinear
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