A Linear Stability Analysis of Saltwater as Applied to Land Sea Ice

• Main Author: Katherine Roddy
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Published: 2008
• Subjects: Batchelor; 1954; e.g.) and scientific (oceanography; metallurgy; atmospheric science; vulcanology; etc; Ice Shelf; Sea ice
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.511.4932

We seek to investigate the next generation of mathematical models used to understand climate variability. We hope to further what little is understood about small scale flows within global climate models. Specifically, the flow of saltwater near ice is examined with a simple box model. Possible physical applications include flows within a crack found in land sea ice and flows found near an ice shelf and saltwater interface. The box model could also provide subgrid scale for larger land and ocean climate models. A linear stability analysis of the governing equations for saltwater is performed to quantify various flow regimes. Using a set of functions in MATLAB, a Chebyshev collocation method is used to reduce the resulting differential eigenvalue problem to a matrix eigenvalue problem. The solution of the matrix eigenvalue problem follows in MATLAB. Neutral stability curves and associated critical Grashof numbers and wavenumbers are supplied for parameters representing pure and saltwater near the freezing point. A graphical comparison of the growth rates for secondary flows found in pure water and saltwater is conducted. 1