[bearcat]

Hi, all

Does anyone know about the linear (the simplest) analytical solution to free sloshing water surface elevation? Many people have simulated free sloshing water problem as a validation for free surface modeling.

As far as I know, the inviscid flow free sloshing in a 2D still rectangle tank is the simplest case. The motion can be approximated by the linear wave theory. And the solution expression can be pretty simple. With free surface starting from a constant slope as initial BC, I found from some paper the following equation:



in which
and


L is the tank length, h is the still water depth and　 is the initial free surface slope.


I wonder ｉｆ　the above expression has kind of typo　ｏｒ　ｍｉｓｓｉｎｇ　ｓｏｍｅｔｈｉｎｇ, as it introduceｓ some　ｏｂｖｉｏｕｓ wiggles when　Ｉ　ｐｌｏｔｔｅｄ　ｉｔ，　ｗｈｉｃｈ　ｓｈｏｕｌｄ　ｎｏｔ　ａｐｐｅａｒ　ｉｎ　ａ　ｌｉ ｎｅａｒ　ｓｏｌｕｔｉｏｎ．　

Ｓｏ　ｃａｎ　ａｎｙｏｎｅ　ｐｏｉｎｔ　ｏｕｔ　ｉｆ　ｔｈｉｓ　ｉｓ　ａ　ｃｏｒｒｅｃｔ　ｅｘｐｒｅ ｓｓｉｏｎ？　　Ｉｆ　ｎｏｔ，　ｗｈｅｒｅ　ｉｓ　ｗｒｏｎｇ？　Ｗｈｅｒｅ　ｃａｎ　Ｉ　ｆｉｎｄ　ａ 　ｃｏｒｒｅｃｔ　ｏｎｅ？　

Ｔｈａｎｋ　ｙｏｕ．