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|Title:||Nonlinear dynamics of mushy layers induced by external stochastic fluctuations|
|Authors:||Alexandrov, D. V.|
Bashkirtseva, I. A.
Ryashko, L. B.
|Publisher:||Royal Society Publishing|
|Citation:||Alexandrov, D. V. Nonlinear dynamics of mushy layers induced by external stochastic fluctuations / D. V. Alexandrov, I. A. Bashkirtseva, L. B. Ryashko. — DOI 10.1098/rsta.2017.0216 // Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. — 2018. — Vol. 2113. — Iss. 376. — 20170216.|
|Abstract:||The time-dependent process of directional crystallization in the presence of a mushy layer is considered with allowance for arbitrary fluctuations in the atmospheric temperature and friction velocity. A nonlinear set of mushy layer equations and boundary conditions is solved analytically when the heat and mass fluxes at the boundary between the mushy layer and liquid phase are induced by turbulent motion in the liquid and, as a result, have the corresponding convective form. Namely, the ‘solid phase–mushy layer’ and ‘mushy layer–liquid phase’ phase transition boundaries as well as the solid fraction, temperature and concentration (salinity) distributions are found. If the atmospheric temperature and friction velocity are constant, the analytical solution takes a parametric form. In the more common case when they represent arbitrary functions of time, the analytical solution is given by means of the standard Cauchy problem. The deterministic and stochastic behaviour of the phase transition process is analysed on the basis of the obtained analytical solutions. In the case of stochastic fluctuations in the atmospheric temperature and friction velocity, the phase transition interfaces (mushy layer boundaries) move faster than in the deterministic case. A cumulative effect of these noise contributions is revealed as well. In other words, when the atmospheric temperature and friction velocity fluctuate simultaneously due to the influence of different external processes and phenomena, the phase transition boundaries move even faster. This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’. 10.1098/rsta.2017.0216|
PHASE TRANSITION INTERFACE
ATMOSPHERIC BOUNDARY LAYER
|metadata.dc.description.sponsorship:||Ministry of Education and Science of the Russian Federation, Minobrnauka: 1.9527.2017/8.9|
Data accessibility. This article has no additional data. Authors’ contributions. All authors contributed equally to the present research article. Competing interests. We declare we have no competing interests. Funding. This work was supported by the Ministry of Education and Science of the Russian Federation (project no. 1.9527.2017/8.9).
|Appears in Collections:||Научные публикации, проиндексированные в SCOPUS и WoS CC|
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