Bounds for Arbitrary Steady Gravity Waves on Water of Finite Depth |
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Authors: | Vladimir Kozlov Nikolay Kuznetsov |
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Institution: | (1) Wolfgang Pauli Institute, c/o Faculty of Mathematics of Vienna University, Nordbergstrasse 15, 1090 Vienna, Austria;(2) Faculty of Mathematics of Vienna University, Nordbergstrasse 15, 1090 Vienna, Austria;(3) Department of Mathematics and Statistics, UNC at Charlotte, Charlotte, NC 28223, USA |
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Abstract: | Necessary conditions for the existence of arbitrary bounded steady waves are proved (earlier, these conditions, that have
the form of bounds on the Bernoulli constant and other wave characteristics, were established only for Stokes waves). It is
also shown that there exists an exact upper bound such that if the free-surface profile is less than this bound at infinity
(positive, negative, or both), then the profile asymptotes the constant level corresponding to a unform stream (supercritical
or subcritical). Finally, an integral property of arbitrary steady waves is obtained. A new technique is proposed for proving
these results; it is based on modified Bernoulli’s equation that along with the free surface profile involves the difference
between the potential and its vertical average. |
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