scholarly journals The effects of Prandtl number on the nonlinear dynamics of Kelvin–Helmholtz instability in two dimensions

2021 ◽  
Vol 915 ◽  
Author(s):  
J.P. Parker ◽  
C.P. Caulfield ◽  
R.R. Kerswell
Keyword(s):  
Nonlinear Dynamics ◽  
Prandtl Number ◽  
Two Dimensions ◽  
Helmholtz Instability

Abstract

Convection in a compressible fluid with infinite Prandtl number

1980 ◽  
Vol 96 (3) ◽  
pp. 515-583 ◽  
Author(s):  
Gary T. Jarvis ◽  
Dan P. Mckenzie
Keyword(s):  
Prandtl Number ◽  
Viscous Dissipation ◽  
Coefficient Of Thermal Expansion ◽  
Frictional Heating ◽  
Finite Amplitude ◽  
Two Dimensions ◽  
Adiabatic Temperature ◽  
Time Dependent ◽  
Dependent Manner ◽  
Rayleigh Numbers

An approximate set of equations is derived for a compressible liquid of infinite Prandtl number. These are referred to as the anelastic-liquid equations. The approximation requires the product of absolute temperature and volume coefficient of thermal expansion to be small compared to one. A single parameter defined as the ratio of the depth of the convecting layer,d, to the temperature scale height of the liquid,HT, governs the importance of the non-Boussinesq effects of compressibility, viscous dissipation, variable adiabatic temperature gradients and non-hydrostatic pressure gradients. Whend/HT[Lt ] 1 the Boussinesq equations result, but whend/HTisO(1) the non-Boussinesq terms become important. Using a time-dependent numerical model, the anelastic-liquid equations are solved in two dimensions and a systematic investigation of compressible convection is presented in whichd/HTis varied from 0·1 to 1·5. Both marginal stability and finite-amplitude convection are studied. Ford/HT[les ] 1·0 the effect of density variations is primarily geometric; descending parcels of liquid contract and ascending parcels expand, resulting in an increase in vorticity with depth. Whend/HT> 1·0 the density stratification significantly stabilizes the lower regions of the marginal state solutions. At all values ofd/HT[ges ] 0·25, an adiabatic temperature gradient proportional to temperature has a noticeable stabilizing effect on the lower regions. Ford/HT[ges ] 0·5, marginal solutions are completely stabilized at the bottom of the layer and penetrative convection occurs for a finite range of supercritical Rayleigh numbers. In the finite-amplitude solutions adiabatic heating and cooling produces an isentropic central region. Viscous dissipation acts to redistribute buoyancy sources and intense frictional heating influences flow solutions locally in a time-dependent manner. The ratio of the total viscous heating in the convecting system, ϕ, to the heat flux across the upper surface,Fu, has an upper limit equal tod/HT. This limit is achieved at high Rayleigh numbers, when heating is entirely from below, and, for sufficiently large values ofd/HT, Φ/Fuis greater than 1·00.

Nonlinear dynamics of vertical vorticity in low-Prandtl-number thermal convection

1990 ◽  
Vol 214 (-1) ◽  
pp. 579 ◽  
Author(s):  
Josep M. Massaguer ◽  
Isabel Mercader ◽  
Marta Net
Keyword(s):  
Nonlinear Dynamics ◽  
Prandtl Number ◽  
Thermal Convection ◽  
Vertical Vorticity

scholarly journals Nonlinear dynamics and rheology of active fluids: Simulations in two dimensions

2011 ◽  
Vol 83 (4) ◽  
Author(s):  
S. M. Fielding ◽  
D. Marenduzzo ◽  
M. E. Cates
Keyword(s):  
Nonlinear Dynamics ◽  
Two Dimensions

scholarly journals Dynamics of Nanoparticle Self-Assembly by Liquid Crystal Sorting in Two Dimensions

2021 ◽  
Vol 9 ◽  
Author(s):  
F. Gael Segura-Fernández ◽  
Erick F. Serrato-García ◽  
J. Emmanuel Flores-Calderón ◽  
Orlando Guzmán
Keyword(s):  
Nonlinear Dynamics ◽  
Liquid Crystal ◽  
Order Parameter ◽  
Domain Walls ◽  
Langmuir Monolayers ◽  
Two Dimensions ◽  
Excitable Media ◽  
Orientation Field ◽  
Dynamical Equations ◽  
Lag Period

We study nonlinear dynamical equations for coupled conserved and non-conserved fields describing nanoparticle concentration and liquid crystal order parameter, respectively, and solve them numerically over bidimensional domains. These equations model the rapid segregation of nanoparticles away from nematic domains, which has been observed experimentally in a suspension of gold nanoparticles in 5CB below the isotropic-nematic transition temperature. We contrast the different behaviors obtained when the LC order parameter is treated as a scalar or a tensor, as well as the different rates of evolution observed with each of these. We find, after an instantaneous quench lowering the temperature below the transition one, an initial linear regime where the ordering of the nematic phase proceeds exponentially with time. Only after a lag period the nanoparticle material couples effectively to the LC order parameter and segregates to regions that are less orientationally ordered (extended domain walls for a scalar order parameter, but point disclinations for a tensor one). The lag period is followed by the onset of nonlinear dynamics and saturation of the order parameter. The choice of a scalar or tensor LC order parameter does not change this sequence but results in a clear overshooting of the nonlinear saturation level for the tensor order parameter case. These results are found to be insensitive to weak anchoring due to coupling of gradients of the conserved and non-conserved variables, for the nanoparticle concentrations and anchoring parameters studied. Our modeling approach can be extended in a straightforward manner to cases where the cooling rate is finite and to other systems where a locally conserved concentration is coupled to a orientation field, such as active Langmuir monolayers, and possibly to other examples of nonlinear dynamics in ecological or excitable media problems.

The tangled web of agency

2018 ◽  
Vol 41 ◽  
Author(s):  
Alain Pe-Curto ◽  
Julien A. Deonna ◽  
David Sander
Keyword(s):  
Two Dimensions ◽  
Bad Company

AbstractWe characterize Doris's anti-reflectivist, collaborativist, valuational theory along two dimensions. The first dimension is socialentanglement, according to which cognition, agency, and selves are socially embedded. The second dimension isdisentanglement, the valuational element of the theory that licenses the anchoring of agency and responsibility in distinct actors. We then present an issue for the account: theproblem of bad company.

A transmission electron microscopic study of structural transitions in fast ionic conductors

1987 ◽  
Vol 45 ◽  
pp. 156-157
Author(s):  
R. B. Queenan ◽  
P. K. Davies
Keyword(s):  
Optical Properties ◽  
Ionic Conduction ◽  
Recent Observation ◽  
Ionic Conductivities ◽  
Sodium Aluminate ◽  
Two Dimensions ◽  
Ionic Conductors ◽  
Electron Microscopic ◽  
Transmission Electron ◽  
Trivalent Cations

Na ß“-alumina (Na1.67Mg67Al10.33O17) is a non-stoichiometric sodium aluminate which exhibits fast ionic conduction of the Na+ ions in two dimensions. The Na+ ions can be exchanged with a variety of mono-, di-, and trivalent cations. The resulting exchanged materials also show high ionic conductivities.Considerable interest in the Na+-Nd3+-ß“-aluminas has been generated as a result of the recent observation of lasing in the pulsed and cw modes. A recent TEM investigation on a 100% exchanged Nd ß“-alumina sample found evidence for the intergrowth of two different structure types. Microdiffraction revealed an ordered phase coexisting with an apparently disordered phase, in which the cations are completely randomized in two dimensions. If an order-disorder transition is present then the cooling rates would be expected to affect the microstructures of these materials which may in turn affect the optical properties. The purpose of this work was to investigate the affect of thermal treatments upon the micro-structural and optical properties of these materials.

Laser Scanning Confocal Microscopy and Three-Dimesnsional Reconstruction of the Mitotic Spindles of Unequally Dividing Embryonic Cells

1990 ◽  
Vol 48 (3) ◽  
pp. 166-167
Author(s):  
J. Holy ◽  
G. Schatten
Keyword(s):  
Confocal Microscopy ◽  
Mitotic Spindle ◽  
Laser Scanning ◽  
Three Dimensional ◽  
Laser Scanning Confocal Microscopy ◽  
Two Dimensions ◽  
Embryonic Cells ◽  
Mitotic Spindles ◽  
Cleavage Division ◽  
Scanning Confocal Microscopy

One of the classic limitations of light microscopy has been the fact that three dimensional biological events could only be visualized in two dimensions. Recently, this shortcoming has been overcome by combining the technologies of laser scanning confocal microscopy (LSCM) and computer processing of microscopical data by volume rendering methods. We have employed these techniques to examine morphogenetic events characterizing early development of sea urchin embryos. Specifically, the fourth cleavage division was examined because it is at this point that the first morphological signs of cell differentiation appear, manifested in the production of macromeres and micromeres by unequally dividing vegetal blastomeres.The mitotic spindle within vegetal blastomeres undergoing unequal cleavage are highly polarized and develop specialized, flattened asters toward the micromere pole. In order to reconstruct the three-dimensional features of these spindles, both isolated spindles and intact, extracted embryos were fluorescently labeled with antibodies directed against either centrosomes or tubulin.

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