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		<id>https://www.scipedia.com/wd/index.php?action=history&amp;feed=atom&amp;title=Pia_et_al_2021a</id>
		<title>Pia et al 2021a - Revision history</title>
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		<updated>2026-04-22T21:17:16Z</updated>
		<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://www.scipedia.com/wd/index.php?title=Pia_et_al_2021a&amp;diff=220235&amp;oldid=prev</id>
		<title>Scipediacontent at 07:37, 12 March 2021</title>
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				<updated>2021-03-12T07:37:04Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 07:37, 12 March 2021&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-l1&quot; &gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Abstract ==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Abstract ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; 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;Numerical simulations of gravitational planar liquid sheet flows, interacting with unconfined gaseous environments located on both sides of the liquid phase, are performed through Volume-of-Fluid (VOF) technique. The global unsteady dynamics of the non-parallel flow is analyzed by perturbing the initial steady configuration by means of a Gaussian bump in the transverse velocity component of relatively very small amplitude, thereby exciting sinuous modes. Thanks to the development of a theoretical linear one-dimensional model, more physical insights are gained on the flow system. It is found that surface tension plays a stabilizing role for the gravitational sheet, and for relatively high values of density ratio r&amp;lt;sub&amp;gt;ρ&amp;lt;/sub&amp;gt; of gaseous-to-liquid phases it becomes unstable. An analogy is shown between the global unstable behavior exhibited by the liquid sheet as &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;rρ &lt;/del&gt;increases, and the shear-induced global instability found by Tammisola et al. [“Surface tension-induced global instability of planar jets and wakes”, J. Fluid Mech. 713, 632–658 (2012)] for planar jet and wake flows of two immiscible fluids in the presence of surface tension.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; 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;Numerical simulations of gravitational planar liquid sheet flows, interacting with unconfined gaseous environments located on both sides of the liquid phase, are performed through Volume-of-Fluid (VOF) technique. The global unsteady dynamics of the non-parallel flow is analyzed by perturbing the initial steady configuration by means of a Gaussian bump in the transverse velocity component of relatively very small amplitude, thereby exciting sinuous modes. Thanks to the development of a theoretical linear one-dimensional model, more physical insights are gained on the flow system. It is found that surface tension plays a stabilizing role for the gravitational sheet, and for relatively high values of density ratio r&amp;lt;sub&amp;gt;ρ&amp;lt;/sub&amp;gt; of gaseous-to-liquid phases it becomes unstable. An analogy is shown between the global unstable behavior exhibited by the liquid sheet as &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;r&amp;lt;sub&amp;gt;ρ&amp;lt;/sub&amp;gt; &lt;/ins&gt;increases, and the shear-induced global instability found by Tammisola et al. [“Surface tension-induced global instability of planar jets and wakes”, J. Fluid Mech. 713, 632–658 (2012)] for planar jet and wake flows of two immiscible fluids in the presence of surface tension.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Full document ==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Full document ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;pdf&amp;gt;Media:Draft_Content_421129461p5952.pdf&amp;lt;/pdf&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;pdf&amp;gt;Media:Draft_Content_421129461p5952.pdf&amp;lt;/pdf&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;

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		<author><name>Scipediacontent</name></author>	</entry>

	<entry>
		<id>https://www.scipedia.com/wd/index.php?title=Pia_et_al_2021a&amp;diff=220234&amp;oldid=prev</id>
		<title>Scipediacontent at 07:36, 12 March 2021</title>
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				<updated>2021-03-12T07:36:51Z</updated>
		
		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 07:36, 12 March 2021&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-l1&quot; &gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Abstract ==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Abstract ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; 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;Numerical simulations of gravitational planar liquid sheet flows, interacting with unconfined gaseous environments located on both sides of the liquid phase, are performed through Volume-of-Fluid (VOF) technique. The global unsteady dynamics of the non-parallel flow is analyzed by perturbing the initial steady configuration by means of a Gaussian bump in the transverse velocity component of relatively very small amplitude, thereby exciting sinuous modes. Thanks to the development of a theoretical linear one-dimensional model, more physical insights are gained on the flow system. It is found that surface tension plays a stabilizing role for the gravitational sheet, and for relatively high values of density ratio r&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; 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;Numerical simulations of gravitational planar liquid sheet flows, interacting with unconfined gaseous environments located on both sides of the liquid phase, are performed through Volume-of-Fluid (VOF) technique. The global unsteady dynamics of the non-parallel flow is analyzed by perturbing the initial steady configuration by means of a Gaussian bump in the transverse velocity component of relatively very small amplitude, thereby exciting sinuous modes. Thanks to the development of a theoretical linear one-dimensional model, more physical insights are gained on the flow system. It is found that surface tension plays a stabilizing role for the gravitational sheet, and for relatively high values of density ratio r&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;&amp;lt;sub&amp;gt;ρ&amp;lt;/sub&amp;gt; of gaseous-to-liquid phases it becomes unstable. An analogy is shown between the global unstable behavior exhibited by the liquid sheet as rρ increases, and the shear-induced global instability found by Tammisola et al. [“Surface tension-induced global instability of planar jets and wakes”, J. Fluid Mech. 713, 632–658 (2012)] for planar jet and wake flows of two immiscible fluids in the presence of surface tension.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Full document ==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Full document ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;pdf&amp;gt;Media:Draft_Content_421129461p5952.pdf&amp;lt;/pdf&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;lt;pdf&amp;gt;Media:Draft_Content_421129461p5952.pdf&amp;lt;/pdf&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;

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		<author><name>Scipediacontent</name></author>	</entry>

	<entry>
		<id>https://www.scipedia.com/wd/index.php?title=Pia_et_al_2021a&amp;diff=220008&amp;oldid=prev</id>
		<title>Scipediacontent: Scipediacontent moved page Draft Content 421129461 to Pia et al 2021a</title>
		<link rel="alternate" type="text/html" href="https://www.scipedia.com/wd/index.php?title=Pia_et_al_2021a&amp;diff=220008&amp;oldid=prev"/>
				<updated>2021-03-11T16:42:38Z</updated>
		
		<summary type="html">&lt;p&gt;Scipediacontent moved page &lt;a href=&quot;/public/Draft_Content_421129461&quot; class=&quot;mw-redirect&quot; title=&quot;Draft Content 421129461&quot;&gt;Draft Content 421129461&lt;/a&gt; to &lt;a href=&quot;/public/Pia_et_al_2021a&quot; title=&quot;Pia et al 2021a&quot;&gt;Pia et al 2021a&lt;/a&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan='1' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='1' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 16:42, 11 March 2021&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan='2' style='text-align: center;' lang='en'&gt;&lt;div class=&quot;mw-diff-empty&quot;&gt;(No difference)&lt;/div&gt;
&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;</summary>
		<author><name>Scipediacontent</name></author>	</entry>

	<entry>
		<id>https://www.scipedia.com/wd/index.php?title=Pia_et_al_2021a&amp;diff=220007&amp;oldid=prev</id>
		<title>Scipediacontent: Created page with &quot;== Abstract ==  Numerical simulations of gravitational planar liquid sheet flows, interacting with unconfined gaseous environments located on both sides of the liquid phase, a...&quot;</title>
		<link rel="alternate" type="text/html" href="https://www.scipedia.com/wd/index.php?title=Pia_et_al_2021a&amp;diff=220007&amp;oldid=prev"/>
				<updated>2021-03-11T16:42:35Z</updated>
		
		<summary type="html">&lt;p&gt;Created page with &amp;quot;== Abstract ==  Numerical simulations of gravitational planar liquid sheet flows, interacting with unconfined gaseous environments located on both sides of the liquid phase, a...&amp;quot;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;== Abstract ==&lt;br /&gt;
&lt;br /&gt;
Numerical simulations of gravitational planar liquid sheet flows, interacting with unconfined gaseous environments located on both sides of the liquid phase, are performed through Volume-of-Fluid (VOF) technique. The global unsteady dynamics of the non-parallel flow is analyzed by perturbing the initial steady configuration by means of a Gaussian bump in the transverse velocity component of relatively very small amplitude, thereby exciting sinuous modes. Thanks to the development of a theoretical linear one-dimensional model, more physical insights are gained on the flow system. It is found that surface tension plays a stabilizing role for the gravitational sheet, and for relatively high values of density ratio r&lt;br /&gt;
&lt;br /&gt;
== Full document ==&lt;br /&gt;
&amp;lt;pdf&amp;gt;Media:Draft_Content_421129461p5952.pdf&amp;lt;/pdf&amp;gt;&lt;/div&gt;</summary>
		<author><name>Scipediacontent</name></author>	</entry>

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