<p>There are two physical processes at play here:</p>

<ul>
<li>Wind speed relative to the ocean surface</li>
<li>Wave focusing and blocking in opposing current</li>
</ul>

<h3>Wind speed relative to the ocean surface</h3>

<p>As you describe in your question, wind speed relative to the ocean surface varies depending on the current orientation and magnitude. The rate of wave growth is proportional to the wind speed $U$ in direction of the wave relative to the phase speed of the wave $c_p$, squared:</p>

<p>$$
S_{in} \sim \left( U - c_p \right)^2
$$</p>

<p>However, the wave phase speed is modulated by the current:</p>

<p>$$
c_p = c_{p0} + u 
$$
where $c_{p0}$ is the intrinsic phase speed (phase speed in absence of currents) and $u$ is in the direction of the wave. Negative value of $u$ is then an opposing current. Wave growth is then:</p>

<p>$$
S_{in} \sim \left( U - c_{p0} - u \right)^2
$$</p>

<p>Let's plug in some numbers here. Let's say $U = 10\ m/s$, $c_{p0} = 3\ m/s$, and $u = \pm 1\ m/s$:</p>

<ul>
<li>In the case of following current, $u = 1\ m/s$, $S_{in} \sim 36\ m^2/s^2$ ;</li>
<li>In the case of opposing current, $u = -1\ m/s$, $S_{in} \sim 64\ m^2/s^2$ ;</li>
</ul>

<p>Thus, by changing the orientation of a moderate current in characteristic wind and wave conditions, we increased the rate of wave growth by a factor of 1.78! This effect will be more powerful the smaller the relative wind speed $U - c_{p0}$ is.</p>

<h2>Wave focusing and blocking in opposing currents</h2>

<p>Wave energy is advected (transported) by the waves' own group speed $c_{g0}$ and also by currents. If for simplocity we drop all the other terms in the wave energy balance equation, we get:</p>

<p>$$
\dfrac{\partial E}{\partial t} = -\dfrac{\partial \left[\left(c_{g0} + u \right)E\right]}{\partial x}
$$</p>

<p>The crux here is in the modulated group speed $c_{g0} + u$. If the waves propagate into an area of increasingly stronger opposing current, there will be a convergence of wave energy in that space, which will manifest itself in increase of high and steep waves. At the point where $c_{g0} = -u$, that is, the current is exactly countering the group speed of the waves, they can no longer propagate in that direction! Wave energy accumulates locally and vigorous wave breaking ensues.</p>

<h3>Summary</h3>

<p>Wave blocking is a different process from the wave growth dependence on relative wind speed described above, but, they often correlate because young windsea (short waves locally generated by wind) are almost always aligned with wind direction, so all you need is the currents to oppose wind for both of these effects to come into play at the same time. </p>

<p>Both are likely to occur in strong and steady western boundary currents such as the Gulf Stream, Kuroshio, Aghulas, and Brazil current, and also in any region with strong tidal currents.</p>

<p>More on this topic in the answer to <a href="https://earthscience.stackexchange.com/questions/2860/what-visual-wave-behaviour-help-to-tell-if-a-tide-is-going-in-or-out">this question</a>.</p>

CC BY-SA 3.0
2018-04-07T17:00:44.767Z
2018-04-07T17:00:44.767Z
milancurcic
<p>It's a well known fact that wind will cause very big waves if blowing against a strong current, for example in the gulf stream off the US coast, or in the bay of San Francisco with a very strong (5 knots+) tidal current.</p>

<p>Notably, a 30 knots wind against a 3 knots current will create way bigger waves than a 33 knots wind against no current at all, even-though the relative speeds are obviously the same.</p>

<p>What is the explanation of this phenomenon?</p>

CC BY-SA 3.0
2018-03-11T22:32:53.450Z
If it was a narrow current, faster in the middle and slower at the edges, there could be a focusing effect, since the wavefronts at the edges are moving faster in the upstream direction.
Keith McClary
CC BY-SA 3.0
2018-03-11T22:34:43.500Z
I think the effect is well documented for very wide currents (eg the gulf stream), so I don't think this is the explanation!
Brann
CC BY-SA 3.0
2018-03-11T23:39:14.897Z
"Wave trapping" is mentioned [here](https://eos.org/research-spotlights/sun-glitter-provides-a-detailed-map-of-ocean-waves).
Keith McClary
CC BY-SA 3.0
2018-03-12T03:47:59.000Z
Interesting question. It would be great if you could provide some references documenting the phenomena.
Camilo Rada
CC BY-SA 3.0
2018-03-12T05:14:51.680Z
Wide currents like the Gulf Stream seem to be [made up of many narrower swirls](https://ourworld.unu.edu/en/concern-as-climate-impacts-on-gulf-stream-flow).
Keith McClary
CC BY-SA 3.0
2018-03-12T09:14:47.490Z
@KeithMcClary Fair enough; actually, most currents are made of a lot of narrower sub-currents, and the same goes for tidal currents. Still, I'm not sure this is the correct physical explanation of this phenomenon, and if it is I'd love to see a detail explanation!
Brann
CC BY-SA 3.0
2018-03-12T12:37:16.700Z
You can also check the info in: https://earthscience.stackexchange.com/questions/2860/what-visual-wave-behaviour-help-to-tell-if-a-tide-is-going-in-or-out/2868#2868
arkaia
CC BY-SA 3.0
2018-03-12T14:48:37.903Z
[This paper](https://www.lume.ufrgs.br/bitstream/handle/10183/103762/000922322.pdf?sequence=1) has some mathematical theory and references. On p.4 they mention a channel width of 500 m. Their Fig. 1 is what I was imagining.
Keith McClary
CC BY-SA 3.0
2018-03-12T21:12:19.807Z
This question needs the `[wind]` tag.
Eevee
CC BY-SA 3.0
2018-03-13T07:08:58.687Z
@Eevee I think the question is probably not that interesting for someone interested in the "wind" tag, as it is really wave centric, so I didn't add the tag.
Brann
<wind><ocean-currents><waves><wave-modeling>
Why does wind blowing against a strong current create way bigger waves?
Brann
# Why does wind blowing against a strong current create way bigger waves?

(Asked by: username_0 on 2018-03-11)

It's a well known fact that wind will cause very big waves if blowing against a strong current, for example in the gulf stream off the US coast, or in the bay of San Francisco with a very strong (5 knots+) tidal current.

Notably, a 30 knots wind against a 3 knots current will create way bigger waves than a 33 knots wind against no current at all, even-though the relative speeds are obviously the same.

What is the explanation of this phenomenon?

**Tags:** wind, ocean-currents, waves, wave-modeling

> **Comments:**
> **username_1**: If it was a narrow current, faster in the middle and slower at the edges, there could be a focusing effect, since the wavefronts at the edges are moving faster in the upstream direction.  
> **username_0**: I think the effect is well documented for very wide currents (eg the gulf stream), so I don't think this is the explanation!  
> **username_1**: "Wave trapping" is mentioned [here](https://eos.org/research-spotlights/sun-glitter-provides-a-detailed-map-of-ocean-waves).  
> **username_2**: Interesting question. It would be great if you could provide some references documenting the phenomena.  
> **username_1**: Wide currents like the Gulf Stream seem to be [made up of many narrower swirls](https://ourworld.unu.edu/en/concern-as-climate-impacts-on-gulf-stream-flow).  
> **username_0**: @username_1 Fair enough; actually, most currents are made of a lot of narrower sub-currents, and the same goes for tidal currents. Still, I'm not sure this is the correct physical explanation of this phenomenon, and if it is I'd love to see a detail explanation!  
> **username_3**: You can also check the info in: https://earthscience.stackexchange.com/questions/2860/what-visual-wave-behaviour-help-to-tell-if-a-tide-is-going-in-or-out/2868#2868  
> **username_1**: [This paper](https://www.lume.ufrgs.br/bitstream/handle/10183/103762/000922322.pdf?sequence=1) has some mathematical theory and references. On p.4 they mention a channel width of 500 m. Their Fig. 1 is what I was imagining.  
> **username_4**: This question needs the `[wind]` tag.  
> **username_0**: @username_4 I think the question is probably not that interesting for someone interested in the "wind" tag, as it is really wave centric, so I didn't add the tag.  

---

## 1 answers

### Answer by username_5 on 2018-04-07. Score: 4

There are two physical processes at play here:

* Wind speed relative to the ocean surface
* Wave focusing and blocking in opposing current

### Wind speed relative to the ocean surface

As you describe in your question, wind speed relative to the ocean surface varies depending on the current orientation and magnitude. The rate of wave growth is proportional to the wind speed $U$ in direction of the wave relative to the phase speed of the wave $c\_p$, squared:

$$
S\_{in} \sim \left( U - c\_p \right)^2
$$

However, the wave phase speed is modulated by the current:

$$
c\_p = c\_{p0} + u
$$
where $c\_{p0}$ is the intrinsic phase speed (phase speed in absence of currents) and $u$ is in the direction of the wave. Negative value of $u$ is then an opposing current. Wave growth is then:

$$
S\_{in} \sim \left( U - c\_{p0} - u \right)^2
$$

Let's plug in some numbers here. Let's say $U = 10\ m/s$, $c\_{p0} = 3\ m/s$, and $u = \pm 1\ m/s$:

* In the case of following current, $u = 1\ m/s$, $S\_{in} \sim 36\ m^2/s^2$ ;
* In the case of opposing current, $u = -1\ m/s$, $S\_{in} \sim 64\ m^2/s^2$ ;

Thus, by changing the orientation of a moderate current in characteristic wind and wave conditions, we increased the rate of wave growth by a factor of 1.78! This effect will be more powerful the smaller the relative wind speed $U - c\_{p0}$ is.

## Wave focusing and blocking in opposing currents

Wave energy is advected (transported) by the waves' own group speed $c\_{g0}$ and also by currents. If for simplocity we drop all the other terms in the wave energy balance equation, we get:

$$
\dfrac{\partial E}{\partial t} = -\dfrac{\partial \left[\left(c\_{g0} + u \right)E\right]}{\partial x}
$$

The crux here is in the modulated group speed $c\_{g0} + u$. If the waves propagate into an area of increasingly stronger opposing current, there will be a convergence of wave energy in that space, which will manifest itself in increase of high and steep waves. At the point where $c\_{g0} = -u$, that is, the current is exactly countering the group speed of the waves, they can no longer propagate in that direction! Wave energy accumulates locally and vigorous wave breaking ensues.

### Summary

Wave blocking is a different process from the wave growth dependence on relative wind speed described above, but, they often correlate because young windsea (short waves locally generated by wind) are almost always aligned with wind direction, so all you need is the currents to oppose wind for both of these effects to come into play at the same time.

Both are likely to occur in strong and steady western boundary currents such as the Gulf Stream, Kuroshio, Aghulas, and Brazil current, and also in any region with strong tidal currents.

More on this topic in the answer to [this question](https://earthscience.stackexchange.com/questions/2860/what-visual-wave-behaviour-help-to-tell-if-a-tide-is-going-in-or-out).


---

