On the two-phase free boundary problem for two-dimensional water waves

1997 ◽  
Vol 309 (2) ◽  
pp. 199-223 ◽  
Author(s):  
Tatsuo Iguchi ◽  
Naoto Tanaka ◽  
Atusi Tani
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Water Waves ◽  
Two Dimensional ◽  
Two Phase

Instability modelling of drumlin formation incorporating lee-side cavity growth

2009 ◽  
Vol 465 (2109) ◽  
pp. 2681-2702 ◽  
Author(s):  
A. C. Fowler
Keyword(s):  
Mathematical Model ◽  
Free Boundary ◽  
Numerical Method ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Cavity Growth ◽  
Finite Amplitude ◽  
Two Dimensional

It is proposed that the formation of the subglacial bedforms known as drumlins occurs through an instability associated with the flow of ice over a wet deformable till. We pose a mathematical model that describes this instability, and we solve a simplified version of the model numerically in order to establish the form of finite-amplitude two-dimensional waveforms. A feature of the solutions is that cavities frequently form downstream of the bedforms; we allow the model to cater for this possibility and we provide an efficient numerical method to solve the resulting free boundary problem.

scholarly journals Revisiting the Meandering Instability During Step-Flow Epitaxy

2019 ◽  
Vol 9 (22) ◽  
pp. 4840
Author(s):  
Yue Chen
Keyword(s):  
Stability Analysis ◽  
Free Boundary ◽  
Boundary Problem ◽  
Linear Stability ◽  
Free Boundary Problem ◽  
Linear Stability Analysis ◽  
Chemical Potential ◽  
Two Dimensional ◽  
Step Flow ◽  
Morphological Instabilities

This paper starts with a generalized Burton, Cabrera and Frank (BCF) model by considering the energetic contribution of the adjacent terraces to the step chemical potential. We use the linear stability analysis of the quasistatic free-boundary problem for a two-dimensional step separated by broad terraces to study the step-meandering instabilities. The results show that the equilibrium adatom coverage has influence on the morphological instabilities.

Some Free Boundary Problem for Two-Phase Inhomogeneous Incompressible Flows

2020 ◽  
Vol 52 (4) ◽  
pp. 3397-3443
Author(s):  
Hirokazu Saito ◽  
Yoshihiro Shibata ◽  
Xin Zhang
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Incompressible Flows ◽  
Two Phase
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