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--- docs:tutorials:findsoln [2014/12/04 12:46]
gibson [periodic orbit of plane Couette flow]
+++ docs:tutorials:findsoln [2015/08/28 06:52] (current)
gibson
@@ Line 33: / Line 33: @@
 \begin{eqnarray*}
   \sigma_{xyz} : [u,v,w] (x,y,z) &\rightarrow [-u,-v,-w] (-x,-y,-z) \\
-  \sigma_{xy*} \tau_{xz} : [u,v,w] (x,y,z) &\rightarrow [-u,v,-w] (-x+L_x/2,y,-z+L_z/2)
+  \sigma_{xy} \tau_{xz} : [u,v,w] (x,y,z) &\rightarrow [-u,-v,w] (-x+L_x/2,-y,z+L_z/2)
 \end{eqnarray*}
@@ Line 55: / Line 55: @@
 {{:docs:tutorials:2014-12-04-a.png?direct&600|}}
-You can see a nice horizontal blue streak at $T \approx 60$ over the range $825 \leq t \leq 1000$ that indicates a long period over which $\|u(t) - u(t+60)\|$ is small. This suggests the turbulent trajectory is shadowing a periodic orbit with period $T \approx 60$ over this interval. The minimum of $\| u(t) - u(t+T) \|$ in this region occurs at $t=917$ and $T=63$. That's a good candidate for a search.
+You can see strikingly periodic behavior over the range $825 \leq t \leq 1000$ with nice horizontal blue streak at $T \approx 65$. This suggests the turbulent trajectory is shadowing a periodic orbit with period $T \approx 65$. The minimum of $\| u(t) - u(t+T) \|$ in this region occurs at $t=917$ and $T=63$. That's an unusually promising initial guess for a periodic orbit.
 === 4. Find the periodic orbit with ''findsoln'' ===

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