<p>Theoretically, I agree that there should be one instable equilibrium point between the two stable equilibrium points when we have a 2D current field. However, there are some additional components of the problem:</p>

<ul>
<li>Ocean currents are not 2D but 3D currents. Considering only the sea surface might lets field lines disappear. </li>
<li>The wind has an additional forcing. This is not true for all items and the wind already affects the ocean currents. However, litter items which are partly above the sea surface experience an additional wind forcing (see e.g. Yoon et al., 2010)</li>
<li>Ocean currents are not time independent and equilibrium points may undergo a seasonal multi-annual cycling</li>
<li>Accumulation zones are not necessarily stable equilibrium points but the residence time of the marine litter items in the named regions just needs to be sufficient long.</li>
<li>The gyres are macroscopic accumulation regions. Thus, if we have regions with a higher density of particle trajectories and lower particles velocities we could identify these regions as accumulation regions from a macroscopic perspective. </li>
</ul>

<p>About item three (<em>Ocean currents are not time independent</em>) I am not completely sure, but I think to remember an animation or plots in a publication which showed seasonal variations between the both garbage patches you showed.</p>

<p>As far as I remember the publications on that topic of global transport modeling of marine litter correctly, the eastern North Pacific Garbage patch is the actual accumulation region. It has a long tail towards west. Howell et al. (2012) writes about the North Pacific Gyre and plastic debris accumulation within it. I did not have time to read it in detail.</p>

<p>For further reading it might be interesting to look into these publications:</p>

<ul>
<li>Eriksen et al., 2014. doi: <a href="http://dx.doi.org/10.1371/journal.pone.0111913">10.1371/journal.pone.0111913</a></li>
<li>Howell et al., 2012. doi: <a href="http://dx.doi.org/10.1016/j.marpolbul.2011.04.034">10.1016/j.marpolbul.2011.04.034</a></li>
<li>Lebreton et al., 2012. doi: <a href="http://dx.doi.org/10.1016/j.marpolbul.2011.10.027">10.1016/j.marpolbul.2011.10.027</a></li>
<li>Martinez et al., 2009. doi: <a href="http://dx.doi.org/10.1016/j.marpolbul.2009.04.022">10.1016/j.marpolbul.2009.04.022</a></li>
<li>Maximenko et al., 2012. doi: <a href="http://dx.doi.org/10.1016/j.marpolbul.2011.04.016">10.1016/j.marpolbul.2011.04.016</a></li>
<li>Yoon et al., 2010. doi: <a href="http://dx.doi.org/10.1016/j.marpolbul.2009.09.033">10.1016/j.marpolbul.2009.09.033</a></li>
</ul>

CC BY-SA 3.0
2016-03-28T14:32:04.720Z
Donovan Hohn's "Moby Duck" is a very good book about the garbage patch.  It has two diagrams showing the gyres and current's etc. but the explanation in the book is better.
ssimm
CC BY-SA 3.0
2016-03-28T17:59:28.513Z
Your first point about the three-dimensional nature of the ocean is key.
Isopycnal Oscillation
CC BY-SA 3.0
2016-03-29T08:20:50.627Z
Thanks @IsopycnalOscillation for the remark. Actually, I wasn't sure how relevant (and strong) upwelling and downwelling processes are in this specific region.
daniel.heydebreck
CC BY-SA 3.0
2016-03-27T12:18:49.507Z
2016-03-27T12:18:49.507Z
daniel.heydebreck
<p>Yes, you're right, there should be (at least one) saddle point in the middle of the loop.  And indeed, if you search for illustrations of <a href="https://www.google.fi/search?q=pacific+ocean+circulation&amp;tbm=isch" rel="nofollow noreferrer">Pacific ocean circulation</a>, you can see the saddle point in some of them, like this one:</p>

<p><a href="http://www.goes-r.gov/users/comet/tropical/textbook_2nd_edition/navmenu.php_tab_4_page_3.1.0.htm" rel="nofollow noreferrer"><img src="https://i.sstatic.net/mJWLX.jpg" alt=""><br>
<sup>Source: <em>Introduction to Tropical Meteorology</em>, 2nd ed., chapter 3.3.1, fig. 3.20.</sup></a></p>

<p>Now, in a lot of other maps, the saddle region is just left more or less blank.  Apparently, that's because there just aren't any strong currents there; <em>most</em> of the circulation is going in a loop around both sinks (and the saddle), with only a relatively small fraction diverted into the middle.  <a href="https://commons.wikimedia.org/wiki/File:Ocean_currents_1943_%28borderless%293.png" rel="nofollow noreferrer">This illustration from Wikipedia</a> is a good example:</p>

<p><a href="https://commons.wikimedia.org/wiki/File:Ocean_currents_1943_%28borderless%293.png" rel="nofollow noreferrer"><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/67/Ocean_currents_1943_(borderless)3.png/600px-Ocean_currents_1943_(borderless)3.png" alt=""></a></p>

<p>Also, unlike sinks, saddle points in general won't accumulate debris; any flotsam on the surface will just float in along the stable axis, and then away again along the unstable axis.  So even if there were strong surface currents in the region, you wouldn't expect any visible "garbage patch" there.</p>

<p>Besides, at least if you look closely enough, reality will almost certainly be more complicated, with multiple equilibrium points that shift over time.  The following two maps (found on <a href="https://www.lib.utexas.edu/maps/historical/pacific_islands_1943_1945.html" rel="nofollow noreferrer">this page</a>), although fairly old and probably of limited accuracy, may show a hint of the true complexity:</p>

<p><a href="https://i.sstatic.net/sZ6GU.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/sZ6GU.jpg" alt="Pacific ocean circulation in northern summer"></a></p>

<p><a href="https://i.sstatic.net/wRdfX.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/wRdfX.jpg" alt="Pacific ocean circulation in northern winter"></a></p>

CC BY-SA 3.0
2016-03-27T16:02:00.867Z
2016-03-27T21:20:25.747Z
2016-03-27T21:20:25.747Z
Ilmari Karonen
<p>I was watching the science channel yesterday and the program mentioned the Great Pacific Garbage rim. I was struck by the illustration (and pretty much every subsequent animation/picture I've seen now has the same basic illustration) below:<a href="https://i.sstatic.net/JuEln.jpg" rel="noreferrer"><img src="https://i.sstatic.net/JuEln.jpg" alt="enter image description here"></a></p>

<p>Unless I'm not understanding something, the garbage swirls around in a huge  closed trajectory and encloses two sinks ( the colorful swirly things; one on the left and one on the right). This isn't physically possible though, with the perfectly reasonable assumption that the tidal force field is continuously differentiable. Any closed curve has to enclose equilibrium points who's indices add to $+1$, but a sink has an index of $+1$ so this curve encloses a total of $+2$. There would have to be at least one other equilibrium point inside the closed trajectory that had an index of $-1$, so something like a saddle node:</p>

<p><a href="https://i.sstatic.net/n0agM.gif" rel="noreferrer"><img src="https://i.sstatic.net/n0agM.gif" alt="![enter image description here"></a></p>

<p>But I can't find any illustrations showing any other equilibrium points other than these two. Does anyone know what they are, or perhaps if I'm not understanding something?</p>

<ocean><oceanography><models><ocean-currents>
Great Pacific Garbage Patch Equilibrium Points
user153582
# Great Pacific Garbage Patch Equilibrium Points

(Asked by: username_0 on 2016-03-27)

I was watching the science channel yesterday and the program mentioned the Great Pacific Garbage rim. I was struck by the illustration (and pretty much every subsequent animation/picture I've seen now has the same basic illustration) below:[![enter image description here](https://i.sstatic.net/JuEln.jpg)](https://i.sstatic.net/JuEln.jpg)

Unless I'm not understanding something, the garbage swirls around in a huge closed trajectory and encloses two sinks ( the colorful swirly things; one on the left and one on the right). This isn't physically possible though, with the perfectly reasonable assumption that the tidal force field is continuously differentiable. Any closed curve has to enclose equilibrium points who's indices add to $+1$, but a sink has an index of $+1$ so this curve encloses a total of $+2$. There would have to be at least one other equilibrium point inside the closed trajectory that had an index of $-1$, so something like a saddle node:

[![![enter image description here](https://i.sstatic.net/n0agM.gif)](https://i.sstatic.net/n0agM.gif)

But I can't find any illustrations showing any other equilibrium points other than these two. Does anyone know what they are, or perhaps if I'm not understanding something?

**Tags:** ocean, oceanography, models, ocean-currents


---

## 2 answers

### Answer by username_4 on 2016-03-27. Score: 18 | Accepted answer

Yes, you're right, there should be (at least one) saddle point in the middle of the loop. And indeed, if you search for illustrations of [Pacific ocean circulation](https://www.google.fi/search?q=pacific+ocean+circulation&tbm=isch), you can see the saddle point in some of them, like this one:

[![](https://i.sstatic.net/mJWLX.jpg)  
Source: *Introduction to Tropical Meteorology*, 2nd ed., chapter 3.3.1, fig. 3.20.](http://www.goes-r.gov/users/comet/tropical/textbook_2nd_edition/navmenu.php_tab_4_page_3.1.0.htm)

Now, in a lot of other maps, the saddle region is just left more or less blank. Apparently, that's because there just aren't any strong currents there; *most* of the circulation is going in a loop around both sinks (and the saddle), with only a relatively small fraction diverted into the middle. [This illustration from Wikipedia](https://commons.wikimedia.org/wiki/File:Ocean_currents_1943_%28borderless%293.png) is a good example:

[![](https://upload.wikimedia.org/wikipedia/commons/thumb/6/67/Ocean_currents_1943_(borderless)3.png/600px-Ocean_currents_1943_(borderless)3.png)](https://commons.wikimedia.org/wiki/File:Ocean_currents_1943_%28borderless%293.png)

Also, unlike sinks, saddle points in general won't accumulate debris; any flotsam on the surface will just float in along the stable axis, and then away again along the unstable axis. So even if there were strong surface currents in the region, you wouldn't expect any visible "garbage patch" there.

Besides, at least if you look closely enough, reality will almost certainly be more complicated, with multiple equilibrium points that shift over time. The following two maps (found on [this page](https://www.lib.utexas.edu/maps/historical/pacific_islands_1943_1945.html)), although fairly old and probably of limited accuracy, may show a hint of the true complexity:

[![Pacific ocean circulation in northern summer](https://i.sstatic.net/sZ6GU.jpg)](https://i.sstatic.net/sZ6GU.jpg)

[![Pacific ocean circulation in northern winter](https://i.sstatic.net/wRdfX.jpg)](https://i.sstatic.net/wRdfX.jpg)


---

### Answer by username_1 on 2016-03-27. Score: 18

Theoretically, I agree that there should be one instable equilibrium point between the two stable equilibrium points when we have a 2D current field. However, there are some additional components of the problem:

* Ocean currents are not 2D but 3D currents. Considering only the sea surface might lets field lines disappear.
* The wind has an additional forcing. This is not true for all items and the wind already affects the ocean currents. However, litter items which are partly above the sea surface experience an additional wind forcing (see e.g. Yoon et al., 2010)
* Ocean currents are not time independent and equilibrium points may undergo a seasonal multi-annual cycling
* Accumulation zones are not necessarily stable equilibrium points but the residence time of the marine litter items in the named regions just needs to be sufficient long.
* The gyres are macroscopic accumulation regions. Thus, if we have regions with a higher density of particle trajectories and lower particles velocities we could identify these regions as accumulation regions from a macroscopic perspective.

About item three (*Ocean currents are not time independent*) I am not completely sure, but I think to remember an animation or plots in a publication which showed seasonal variations between the both garbage patches you showed.

As far as I remember the publications on that topic of global transport modeling of marine litter correctly, the eastern North Pacific Garbage patch is the actual accumulation region. It has a long tail towards west. Howell et al. (2012) writes about the North Pacific Gyre and plastic debris accumulation within it. I did not have time to read it in detail.

For further reading it might be interesting to look into these publications:

* Eriksen et al., 2014. doi: [10.1371/journal.pone.0111913](http://dx.doi.org/10.1371/journal.pone.0111913)
* Howell et al., 2012. doi: [10.1016/j.marpolbul.2011.04.034](http://dx.doi.org/10.1016/j.marpolbul.2011.04.034)
* Lebreton et al., 2012. doi: [10.1016/j.marpolbul.2011.10.027](http://dx.doi.org/10.1016/j.marpolbul.2011.10.027)
* Martinez et al., 2009. doi: [10.1016/j.marpolbul.2009.04.022](http://dx.doi.org/10.1016/j.marpolbul.2009.04.022)
* Maximenko et al., 2012. doi: [10.1016/j.marpolbul.2011.04.016](http://dx.doi.org/10.1016/j.marpolbul.2011.04.016)
* Yoon et al., 2010. doi: [10.1016/j.marpolbul.2009.09.033](http://dx.doi.org/10.1016/j.marpolbul.2009.09.033)

> **Comments:**
> **username_2**: Donovan Hohn's "Moby Duck" is a very good book about the garbage patch.  It has two diagrams showing the gyres and current's etc. but the explanation in the book is better.  
> **username_3**: Your first point about the three-dimensional nature of the ocean is key.  
> **username_1**: Thanks @username_3 for the remark. Actually, I wasn't sure how relevant (and strong) upwelling and downwelling processes are in this specific region.  

---

