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Date: Tue, 10 Dec 1996 23:20:01 GMTServer: NCSA/1.4.2Content-type: text/htmlLast-modified: Fri, 22 Mar 1996 03:32:37 GMTContent-length: 3765<html><head> <title>Rayleigh-Benard Convection</title></head><body><h2> <img align=bottom src=lr5.gif> <a name="top">A stable state</a><br> </h2><hr><img align=bottom src=palette.gif> <a name="palette"></a><br><hr><a href=abstract.html> Abstract.</a> This experiment models the spatial patterns formed by fluid convectionclose to onset. You are looking down at a large thin square box,filled with (an infinitely viscous) slow-moving fluid. The dimensionsof the box are twenty by twenty by one unit deep.<p>The areas shaded blue represent fluid moving downwards, and those shaded redrepresent fluid moving up. Green is motionless fluid; at theboundary the fluid is constrained to be motionless, so we willeventually see all of the patterns fading out at the boundary.<p> The convection rolls that ultimately form have diameter comparableto the depth of the box.<p><hr><img align=middle src=lr0.gif> <a name="lr0"></a><b>Frame 0</b>. We start with some initial conditions, velocities small anddistributed randomly. <hr><p> <img align=middle src=lr1.gif> <a name="lr1"></a><b>Frame 1</b>. As time progresses the fluid begins to develop local coherence. <hr><img align=middle src=lr2.gif> <a name="lr2"></a><b>Frame 2</b>. Distinct local convection rolls form, of measurable diameter.<hr><img align=middle src=lr3.gif> <a name="lr3"></a><b>Frame 3</b>. The rolls become locally parallel, but defectsform in the center of the box.<hr><img align=middle src=lr4.gif> <a name="lr4"></a><b>Frame 4</b>. The center defects are resolved, leaving defects only at the boundary.<hr><img align=middle src=lr5.gif> <a name="lr5"></a><b>Frame 5</b>. The fluid eventually reaches a steady state.<hr>These evolutions also make spiffy movies. Unfortunately, to make them small enough to be reasonable over thenetwork, the geometries are so small that the fluid motion is a littlecontrived. But the pictures are pretty cute anyway. Here's onewith rigid boundary conditions (as above, only smaller).<p><a href="evolve.qt">Rigid/rigid boundaries<img src=re.gif alt="(picture)" align=middle> </a>(Quicktime format, 2.1Mb.) <!-- (Or <a href="evolve.qtmov">download</a> the file.) --><p>The final frames from some other movies still under construction:<p><a href="periodic_evol.qt">Rigid/periodic boundaries<img src=pe.gif alt="(picture)" align=middle> </a>(Picture only.)<!-- (Quicktime format, 1.3Mb.) --><!-- (Or <a href="file://periodic_evol.qt">download</a> the file.) --><hr>The second picture plainly shows the specific effect we're trying topin down, the bending of the convection rolls as they leave theboundary. This effect was first described by S. Zaleski et als.,"Optimal merging of rolls near a plane boundary", 29 Phys. Rev. A.366 (1984).<hr>The numerical problems are challenging principally because thesteady state takes an enormously long time to achieve. There is hopefor improved techniques, because the successive differences from onestate to another have considerable coherence. Here are final frames(the movies are still under construction) of the successive differences between frames of the above twosimulations. <p><a href="rigid_diff.qt">Rigid/rigid boundaries <img src=rd.gif alt="(picture)" align=middle> </a>(Picture only.)<!-- (Quicktime format, 2.1Mb.) --><!-- (Or <a href="file://rigid_diff.qt">download</a> the file.) --><p><a href="periodic_diff.qt">Rigid/periodic boundaries <img src=pd.gif alt="(picture)" align=middle> </a>(Picture only.)<!-- (Quicktime format, 1.3Mb.) --><!-- (Or <a href="file://periodic_diff.qt">download</a> the file.) --><hr></body><address>eric@cs.washington.edu <DD> 26 Mar 1996</address></html>⌨️ 快捷键说明
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