## Exact Solution of Viscous-Plastic Flow Equations for Glacier Dynamics in 2-Dimensional Case

**Authors:** Sergey V. Ershkov

A new exact solution of Glacier dynamics is presented here in terms of viscous-plastic theory of movements for 2-dimensional profile (x, y), where x(t) = y(t). Such a 2-D solution of Glacier dynamics could be associated with Riccati’s type in general case. Due to a very special character of Riccati’s type ordinary differential equation, it’s general solution is proved to have a proper gap for the components of a solution.
It means a possibility of sudden gradient catastrophe at definite meaning of time-parameter (for 2-D flat profile of Glacier, (x, y)-components of ice velocity moving).
So, Glacier might be moving suddenly with acceleration periodically: (x, y)-components of ice velocity achieve hundred meters /per day from few meters (per day).

**Comments:** 7 Pages. Keywords: Glacier dynamics, basal slip, glacial ice, Riccati ODE

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### Submission history

[v1] 11 Jun 2011

[v2] 20 Jun 2011

[v3] 23 Jun 2011

[v4] 2015-01-09 09:46:50

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