scholarly journals Thermohaline layering in dynamically and diffusively stable shear flows

2016 ◽  
Vol 805 ◽  
pp. 147-170 ◽  
Author(s):  
Timour Radko
Keyword(s):  
Shear Flows ◽  
World Ocean ◽  
Critical Value ◽  
Dissipative Systems ◽  
Widespread Occurrence ◽  
Salty Water ◽  
Two Component ◽  
Stratified Ocean ◽  
Double Diffusive ◽  
Horizontal Layers

In this study we examine two-component shear flows that are stable with respect to Kelvin–Helmholtz and to double-diffusive instabilities individually. Our focus is on diffusively stratified ocean regions, where relatively warm and salty water masses are located below cool fresh ones. It is shown that such systems may be destabilized by the interplay between shear and thermohaline effects, caused by unequal molecular diffusivities of density components. Linear stability analysis suggests that parallel two-component flows can be unstable for Richardson numbers exceeding the critical value for non-dissipative systems $(Ri=1/4)$ by up to four orders of magnitude. Direct numerical simulations indicate that these instabilities transform the initially linear density stratification into a series of well-defined horizontal layers. It is hypothesized that the combined thermohaline–shear instabilities could be ultimately responsible for the widespread occurrence of thermohaline staircases in diffusively stable regions of the World Ocean.

Settling-driven instability in two-component stably stratified Hele-Shaw flows

2018 ◽  
Vol 843 ◽  
Author(s):  
Rafael M. Oliveira ◽  
Eckart Meiburg
Keyword(s):  
Stability Problem ◽  
Settling Velocity ◽  
Critical Value ◽  
Neutral Stability ◽  
Instability Mode ◽  
Two Component ◽  
Linear Stability Problem ◽  
Constant Gradient ◽  
Double Diffusive ◽  
Hele Shaw Cell

We investigate the onset of instability in a stably stratified two-component fluid in a vertical Hele-Shaw cell when the unstably stratified scalar has a settling velocity. This linear stability problem is analysed on the basis of Darcy’s law, for constant-gradient base states. The settling velocity is found to trigger a novel instability mode characterized by pairs of inclined waves. For unequal diffusivities, this new settling-driven mode competes with the traditional double-diffusive mode. Below a critical value of the settling velocity, the double-diffusive elevator mode dominates, while, above this threshold, the inclined waves associated with the settling-driven instability exhibit faster growth. The analysis yields neutral stability curves and allows for the discussion of various asymptotic limits.

The ‘colour polarigraph’ -a simple method for determining the two-dimensional distribution of sugar concentration

1981 ◽  
Vol 109 ◽  
pp. 277-282 ◽  
Author(s):  
Barry R. Ruddick
Keyword(s):  
Weight Fraction ◽  
Sugar Concentration ◽  
Laboratory Model ◽  
Two Dimensional ◽  
Simple Method ◽  
Dimensional Distribution ◽  
Diffusive Effects ◽  
Visual Record ◽  
Double Diffusive ◽  
Horizontal Layers

A method is described for photographically recording the two-dimensional distribution of sugar concentration in a tank, which typically yields a resolution of 0·01 in weight fraction sugar. The tank image is coloured according to the sugar concentration, giving a quantitative visual record of sugar contours. The technique is demonstrated in photographs of a laboratory model of an oceanic front, in which interleaving quasi-horizontal layers are formed by double-diffusive effects.

Double-diffusive depletion of layers in hydrothermal systems

2021 ◽  
Author(s):  
Thomas Le Reun ◽  
Duncan Hewitt
Keyword(s):  
Thermal Convection ◽  
Temporal Evolution ◽  
Porous Matrix ◽  
Hydrothermal Systems ◽  
Sharp Interface ◽  
Layered System ◽  
Salty Water ◽  
Separation Layers ◽  
Diffusive Effects ◽  
Double Diffusive

<p>In hydrothermal systems, the circulation of water through the porous matrix is strongly influenced by the joint effects of heat and salinity. Because of phase separation, layers of different salinities and temperature are thought to form, but their stability or their typical lifetime remains unclear. Moreover, the dynamics of heat transport across such a layered system is considerably enriched by double diffusive effects due to the slower diffusion of salinity relative to heat. Here, we study numerically the time evolution of an ideal two-layer configuration where a heavy layer of warm and salty water is overlain by a light layer of cold and fresh water. Thermal convection quickly develops in each layer and maintains a thin diffusive interface between the layers. There is long-standing controversy on the temporal evolution of such a system. Although Griffiths (1981) found experimentally that the sharp interface seemed to persist indefinitely, Schoofs & Hansen (2000) reported via numerical simulations systematic depletion and vanishing of the layers. We resolve this apparently inconsistency. In our simulations, we find systematic depletion of the two-layer initial condition in all cases. However, the timescale over which it occurs depends strongly on the ratio between salinity and temperature contributions to density. When salinity is weakly stabilising, thermal convection and layers are maintained over (very long) diffusive timescales. When salt is strongly stabilising, however, convection becomes quiescent over much shorter times and the sharp interface between layers is quickly diffused away. We determine scalings on the lifetime of the layers in both regimes as a function of the governing parameters.</p>

BIFURCATIONS IN A HUMAN MIGRATION MODEL OF SCHEURLE–SEYDEL TYPE-I: TURING BIFURCATION

2003 ◽  
Vol 13 (05) ◽  
pp. 1303-1308 ◽  
Author(s):  
SÁNDOR KOVÁCS
Keyword(s):  
Graduate Programs ◽  
Critical Value ◽  
Human Migration ◽  
Fickian Diffusion ◽  
Type I ◽  
Two Component System ◽  
Component System ◽  
Turing Bifurcation ◽  
Cross Diffusion ◽  
Two Component

In this paper we consider a model for the behavior of students in graduate programs at neighboring universities which is a modified form of the model proposed by [Scheurle & Seydel, 2000], and observe that the stationary solution of this two-component system becomes unstable in the presence of diffusion. We assume that both types of individuals are continuously distributed throughout a bounded two-dimensional spatial domain of two types (regular hexagon and rhombus), across whose boundaries there is no migration, and which simultaneously undergo simple (Fickian) diffusion but the spatial flow is influenced not only by its own but also by the other's density (cross diffusion). We will show that at a critical value of a parameter a Turing bifurcation takes place: a spatially nonhomogenous solution (pattern) arises.

scholarly journals Interpretation of Some Properties of Extragalactic Jets in the Context of a Two Component Model

1994 ◽  
Vol 159 ◽  
pp. 433-433
Author(s):  
Lourdes Vicente
Keyword(s):  
Magnetic Field ◽  
Accretion Disk ◽  
Thermal Plasma ◽  
Slow Component ◽  
Critical Value ◽  
Component Model ◽  
Parallel Magnetic Field ◽  
Electron Positron ◽  
Extragalactic Jets ◽  
Two Component

We have studied a sample of extragalactic jets within the context of a two component model. This model supposes the existence of two flows in the extragalactic jets. An electron-positron fast beam coming from the internal regions of the accretion disk, responsible for the VLBI jet at the parsec scale and for the observed superluminal speeds. A second slow component, responsible for the jet observed at larger scales. The fast beam is destroyed when the parallel magnetic field is smaller than a critical value, BII < Bcrit = 3.2 × 10−3np1/2, where np is the density of the background thermal plasma of the slow component.

Effects of dissolved solute on unsteady double-diffusive mixed convective flow of a Buongiorno’s two-component nonhomogeneous nanofluid

2019 ◽  
Vol 29 (1) ◽  
pp. 448-466 ◽  
Author(s):  
Davood Aliakbarzadeh Kashani ◽  
Saeed Dinarvand ◽  
Ioan Pop ◽  
Tasawar Hayat
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Boundary Layers ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Nonlinear Partial Differential Equations ◽  
Content Type ◽  
Similarity Transformations ◽  
Two Component ◽  
Double Diffusive

Purpose The purpose of this paper is to numerically study the unsteady double-diffusive mixed convective stagnation-point flow of a water-based nanofluid accompanied with one salt past a vertical flat plate. The effects of Brownian motion and thermophoresis parameters are also introduced through Buongiorno’s two-component nonhomogeneous equilibrium model in the governing equations. Design/methodology/approach In the present explanation of double-diffusive mixed convective model, there are four boundary layers entitled: velocity, thermal, solutal concentration and nanoparticle concentration. The resulting basic equations are solved numerically via an efficient Runge–Kutta fourth-order method with shooting technique after the governing nonlinear partial differential equations are converted into a system of nonlinear ordinary differential equations by the use of similarity transformations. Findings To avail the physical insight of problem, the effects of the mixed convection parameter, unsteadiness parameter and salt/nanoparticle parameters on the boundary layers behavior are investigated. Moreover, four possible types of diffusion problems entitled: double-diffusive nanofluid (DDNF), double-diffusive regular fluid (DDRF), mono-diffusive nanofluid (MDNF) and mono-diffusive regular fluid (MDRF) are considered to analyze and compare them in concepts of heat and mass transfer. Originality/value The results demonstrate that, for a regular fluid, without nanoparticle and salt (MDRF), the dimensionless heat transfer rate is smaller than other diffusion cases. As we include nanoparticle and salt (DDNF), the rate of heat transfer increases due to an increase in thermal conductivity and rate of diffusion of salt. Moreover, it is observed that the highest heat transfer rate is obtained for the situation that the thermophoretic effect of nanoparticles is negligible. Besides, the heat transfer rate enhances with the increase in the regular double-diffusive buoyancy parameter of salt.

Horton-Rogers-Lapwood Convection in a Binary Nanofluid Saturated Rotating Porous Layer

2014 ◽  
Author(s):  
Shilpi Agarwal ◽  
Puneet Rana
Keyword(s):  
Porous Medium ◽  
Base Fluid ◽  
Oscillatory Convection ◽  
Binary Fluid ◽  
Salty Water ◽  
Diffusive Convection ◽  
Medium Layer ◽  
Dimensional Parameters ◽  
Rayleigh Numbers ◽  
Double Diffusive

Double-diffusive convection in a horizontal rotating porous medium layer saturated by a nanofluid, for the case when the base fluid of the nanofluid is itself a binary fluid such as salty water, is studied. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis, while the Brinkman model is used for the porous medium. The Rayleigh numbers’ for stationary and oscillatory convection have been obtained in terms of various non-dimensional parameters. Several results are obtained as limiting cases of the present study.

scholarly journals A note on shock profiles in dissipative hyperbolic and parabolic models

2008 ◽  
Vol 84 (98) ◽  
pp. 97-107 ◽  
Author(s):  
Srboljub Simic
Keyword(s):  
Comparative Study ◽  
Equilibrium State ◽  
Critical Value ◽  
Dissipative Systems ◽  
Parabolic Model ◽  
Equilibrium System ◽  
Shock Speed ◽  
Dissipative Effects ◽  
Parabolic Case ◽  
Shock Profiles

This note presents a comparative study of shock profiles in dissipative systems. Main assumption is that both hyperbolic and parabolic model are reducible to the same underlying equilibrium system when dissipative effects are neglected. It will be shown that the highest characteristic speed of equilibrium system determines the critical value of the shock speed for which downstream equilibrium state bifurcates. It will be also shown that it obeys the same transcritical bifurcation pattern in hyperbolic, as well as in parabolic case.

Sign in / Sign up

Export Citation Format

Share Document