Coriolis Effect on the Linear Stability of Convection in Solidifying Mushy Layers

2003 ◽  
Author(s):  
S. Govender
Keyword(s):  
Linear Stability ◽  
Momentum Equation ◽  
Mushy Layer ◽  
Coriolis Effect ◽  
Mushy Layers ◽  
New Formulation

We consider the solidification in a mushy layer subject to rotation and adopt a near-eutectic approximation. The linear stability is used to investigate analytically the Coriolis effect on convection for a new formulation of the momentum equation.

scholarly journals Stability of Solutal Convection in a Gravity Modulated Mushy Layer During the Solidification of Binary Alloys

2005 ◽  
Author(s):  
S. Govender
Keyword(s):  
Linear Stability ◽  
Transition Point ◽  
Binary Alloys ◽  
Linear Stability Theory ◽  
Mushy Layer ◽  
Gravity Modulation ◽  
Solutal Convection ◽  
Mushy Layers ◽  
Stefan Number ◽  
Stability Results

The linear stability theory is used to investigate the effects of gravity modulation on solutal convection in mushy layers found in solidifying binary alloys. The gravitational field is modeled to consist of constant part and a sinusoidally varying part. The linear stability results are presented for both the synchronous and subharmonic solutions, and it is demonstrated that up to the transition point between the synchronous and subharmonic regions, increasing the frequency of vibration rapidly stabilizes the solutal convection. However, beyond the transition point, further increases in the frequency tends to destabilize convection. It is also demonstrated that the effect of increasing the ratio of the Stefan number and the solid composition (ηo) is to destabilize the solutal convection.

Interactions between steady and oscillatory convection in mushy layers

2010 ◽  
Vol 645 ◽  
pp. 411-434 ◽  
Author(s):  
PETER GUBA ◽  
M. GRAE WORSTER
Keyword(s):  
Standing Waves ◽  
Mushy Layer ◽  
Two Dimensional ◽  
Oscillatory Convection ◽  
Mushy Layers ◽  
Theoretical Predictions ◽  
Convection Patterns ◽  
The Stability ◽  
Nonlinear Solutions ◽  
Steady Convection

We study nonlinear, two-dimensional convection in a mushy layer during solidification of a binary mixture. We consider a particular limit in which the onset of oscillatory convection just precedes the onset of steady overturning convection, at a prescribed aspect ratio of convection patterns. This asymptotic limit allows us to determine nonlinear solutions analytically. The results provide a complete description of the stability of and transitions between steady and oscillatory convection as functions of the Rayleigh number and the compositional ratio. Of particular focus are the effects of the basic-state asymmetries and non-uniformity in the permeability of the mushy layer, which give rise to abrupt (hysteretic) transitions in the system. We find that the transition between travelling and standing waves, as well as that between standing waves and steady convection, can be hysteretic. The relevance of our theoretical predictions to recent experiments on directionally solidifying mushy layers is also discussed.

On the finite-amplitude steady convection in rotating mushy layers

2001 ◽  
Vol 437 ◽  
pp. 337-365 ◽  
Author(s):  
PETER GUBA
Keyword(s):  
Three Dimensional ◽  
Finite Amplitude ◽  
Taylor Number ◽  
Mushy Layer ◽  
Hexagonal Symmetry ◽  
Uniform Rotation ◽  
Mushy Layers ◽  
Solid Phases ◽  
Steady Convection ◽  
Liquid And Solid Phases

This study concentrates on a relatively simple model of a mushy layer originally proposed by Amberg & Homsy (1993) and later studied in further detail by Anderson & Worster (1995). We extend this model to the case in which the system is in a state of uniform rotation about the vertical. Of particular interest is to determine how the rotation of the system controls the bifurcating convection with both the oblique-roll planform and the planform of hexagonal symmetry. We find that two-dimensional oblique rolls can be either subcritically or supercritically bifurcating, depending on a pair of parameters (K1/CS, [Tscr ]), where K1 measures how the permeability linearly varies with the local solid fraction, CS relates the compositional difference between the liquid and solid phases to the variation of composition throughout the mushy layer, and the Taylor number [Tscr ] gives a measure of the local Coriolis acceleration relative to the viscous dissipation in a porous medium. The three-dimensional convection with hexagonal symmetry is found to be transcritical. Furthermore, distorted hexagons with upflow at the centres can be either subcritical or supercritical, depending on the value of the Taylor number [Tscr ].

scholarly journals Comments on “A Combined Derivation of the Integrated and Vertically Resolved, Coupled Wave–Current Equations”

2017 ◽  
Vol 47 (9) ◽  
pp. 2377-2385 ◽  
Author(s):  
Fabrice Ardhuin ◽  
Nobuhiro Suzuki ◽  
James C. McWilliams ◽  
Hidenori Aiki
Keyword(s):  
Vertical Integration ◽  
Order Term ◽  
Momentum Equation ◽  
Total Momentum ◽  
Leading Order ◽  
Mean Flow ◽  
Wave Forcing ◽  
The Mean ◽  
New Formulation ◽  
Wave Momentum

AbstractSeveral equivalent equations for the evolution of the wave-averaged current momentum have been proposed, implemented, and used. In contrast, the equation for the total momentum, which is the sum of the current and wave momenta, has not been widely used because it requires a less practical wave forcing. In an update on previous derivations, Mellor proposed a new formulation of the wave forcing for the total momentum equation. Here, the authors show that this derivation misses a leading-order term that has a zero depth-integrated value. Corrected for this omission, the wave forcing is equivalent to that in the first paper by Mellor. When this wave forcing effect on the currents is approximated it leads to an inconsistency. This study finally repeats and clarifies that the vertical integration of several various forms of the current-only momentum equations are consistent with the known depth-integrated equations for the mean flow momentum obtained by subtracting the wave momentum equation from the total momentum equation. Several other claims in prior Mellor manuscripts are discussed.

Localisation of convection in mushy layers by weak background flow

2011 ◽  
Vol 675 ◽  
pp. 518-528 ◽  
Author(s):  
S. M. ROPER ◽  
S. H. DAVIS ◽  
P. W. VOORHEES
Keyword(s):  
Three Dimensional ◽  
Mushy Layer ◽  
Thermal Gradients ◽  
Two Dimensional ◽  
Amplitude Equations ◽  
Directionally Solidified ◽  
Background Flow ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Analysis ◽  
Mushy Layers

It is known that freckles form at the sidewalls of directionally solidified materials. We present a weakly nonlinear analysis of the effects of a weak and slowly varying background flow formed by non-axial thermal gradients on convection near onset in a mushy layer. We find that in the two-dimensional case, the onset of mush convection occurs away from the walls. However if three-dimensional disturbances are allowed, the onset occurs near the walls of the container confining the mush. We derive amplitude equations governing this behaviour and simulate their evolution numerically.

scholarly journals Mushy-layer growth and convection, with application to sea ice

2019 ◽  
Vol 377 (2146) ◽  
pp. 20180165 ◽  
Author(s):  
Andrew J. Wells ◽  
Joseph R. Hitchen ◽  
James R. G. Parkinson
Keyword(s):  
Sea Ice ◽  
Layer Growth ◽  
Phase Behaviour ◽  
Salt Transport ◽  
Future Research ◽  
Mushy Layer ◽  
Convective Flows ◽  
Ice Growth ◽  
Mushy Layers ◽  
The Impact

Sea ice is a reactive porous medium of ice crystals and liquid brine, which is an example of a mushy layer. The phase behaviour of sea ice controls the evolving material properties and fluid transport through the porous ice, with consequences for ice growth, brine drainage from the ice to provide buoyancy fluxes for the polar oceans, and sea-ice biogeochemistry. We review work on the growth of mushy layers and convective flows driven by density gradients in the interstitial fluid. After introducing the fundamentals of mushy-layer theory, we discuss the effective thermal properties, including the impact of salt transport on mushy-layer growth. We present a simplified model for diffusively controlled growth of mushy layers with modest cooling versus the solutal freezing-point depression. For growth from a cold isothermal boundary, salt diffusion modifies mushy-layer growth by around 5–20% depending on the far-field temperature and salinity. We also review work on the onset, spatial localization and nonlinear development of convective flows in mushy layers, highlighting recent work on transient solidification and models of nonlinear convection with dissolved solid-free brine channels. Finally, future research opportunities are identified, motivated by geophysical observations of ice growth. This article is part of the theme issue ‘The physics and chemistry of ice: scaffolding across scales, from the viability of life to the formation of planets’.

Sign in / Sign up

Export Citation Format

Share Document