| Abstract
| - The super-Alfvénic, undulating “sea-serpent” flow configurations along thin magnetic flux tubes, proposed by Schlichenmaier (2002, Astron. Nachr., 323, 303; 2003, ASP Conf. Ser., 286, 24) to explain both the Evershed flow and moving penumbral grains in a sunspot, are shown to be gravitationally unstable. Any undulations that occur for super-Alfvénic flow speeds will form preferentially in a horizontal plane and hence will not explain Evershed downflows or outward-moving penumbral grains. Sub-Alfvénic, arched flow configurations, on the other hand, are gravitationally stable.
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