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	<id>https://www.wikiwaves.org/index.php?action=history&amp;feed=atom&amp;title=Template%3ACoordinate_definition_in_two_dimension</id>
	<title>Template:Coordinate definition in two dimension - Revision history</title>
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	<updated>2026-04-17T23:22:09Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
	<generator>MediaWiki 1.43.1</generator>
	<entry>
		<id>https://www.wikiwaves.org/index.php?title=Template:Coordinate_definition_in_two_dimension&amp;diff=9677&amp;oldid=prev</id>
		<title>Meylan at 10:36, 21 August 2009</title>
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		<updated>2009-08-21T10:36:40Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 10:36, 21 August 2009&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l7&quot;&gt;Line 7:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 7:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;vertical upwards direction (we denote &amp;lt;math&amp;gt;\mathbf{x}=\left( x,z\right) ).&amp;lt;/math&amp;gt; The&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;vertical upwards direction (we denote &amp;lt;math&amp;gt;\mathbf{x}=\left( x,z\right) ).&amp;lt;/math&amp;gt; The&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;free surface is at &amp;lt;math&amp;gt;z=0&amp;lt;/math&amp;gt; and the sea floor is at &amp;lt;math&amp;gt;z=-h&amp;lt;/math&amp;gt;. The&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;free surface is at &amp;lt;math&amp;gt;z=0&amp;lt;/math&amp;gt; and the sea floor is at &amp;lt;math&amp;gt;z=-h&amp;lt;/math&amp;gt;. The&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;fluid motion is described by a velocity potential &amp;lt;math&amp;gt;\Phi&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;fluid motion is described by a velocity potential &amp;lt;math&amp;gt;\Phi&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;/math&amp;gt; and free surface by&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;math&amp;gt;\zeta&lt;/ins&gt;&amp;lt;/math&amp;gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Meylan</name></author>
	</entry>
	<entry>
		<id>https://www.wikiwaves.org/index.php?title=Template:Coordinate_definition_in_two_dimension&amp;diff=9675&amp;oldid=prev</id>
		<title>Meylan at 10:33, 21 August 2009</title>
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		<updated>2009-08-21T10:33:10Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;We consider a two-dimensional fluid domain of constant depth, which&lt;br /&gt;
contains a finite number of fixed bodies of arbitrary geometry. We&lt;br /&gt;
denote the fluid domain by &amp;lt;math&amp;gt;\Omega&amp;lt;/math&amp;gt;, the boundary of the fluid domain&lt;br /&gt;
which touches the fixed bodies by &amp;lt;math&amp;gt;\partial\Omega&amp;lt;/math&amp;gt;, and the free&lt;br /&gt;
surface by &amp;lt;math&amp;gt;F.&amp;lt;/math&amp;gt; The &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;z&amp;lt;/math&amp;gt; coordinates are such that &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is&lt;br /&gt;
pointing in the horizontal direction and &amp;lt;math&amp;gt;z&amp;lt;/math&amp;gt; is pointing in the&lt;br /&gt;
vertical upwards direction (we denote &amp;lt;math&amp;gt;\mathbf{x}=\left( x,z\right) ).&amp;lt;/math&amp;gt; The&lt;br /&gt;
free surface is at &amp;lt;math&amp;gt;z=0&amp;lt;/math&amp;gt; and the sea floor is at &amp;lt;math&amp;gt;z=-h&amp;lt;/math&amp;gt;. The&lt;br /&gt;
fluid motion is described by a velocity potential &amp;lt;math&amp;gt;\Phi&amp;lt;/math&amp;gt;.&lt;/div&gt;</summary>
		<author><name>Meylan</name></author>
	</entry>
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