# What is (negative) wind stress curl?

I'm currently doing research for a paper in school where we need to research on a university-like level. When I read the paper Causes and impacts of the 2014 warm anomaly in the NE Pacific, I found the sentence:

The wind stress curl was negative, which has precedence but is still quite unusual.

The wind stress curl was given as $-0.5*10^6 \ \text{N}*m^{-3}$. I neither know what wind stress curl is, nor what the negative sign is, nor what the unit of it exactly describes (of course, pressure per meter, but what does that mean?).

Can anyone explain what it is?

Skimming the paper, I believe the relevance of the wind stress curl is its relation to "Ekman pumping". I haven't found a simple, concise reference for this, but this page might be a good start, and this page has a couple of formulas about wind stress curl. I'll try to summarize here.

When wind blows over water, the top of the water starts moving. It shears against the water below it, so that water starts moving too. The momentum from the wind is transferred down into lower layers of the water. This water also feels the Coriolis force. The direction it ends up moving in depends on the balance of friction/drag and Coriolis force. On average, the water moves to the right of the wind in the northern hemisphere; if the wind is blowing northward, the water moves eastward.

Now imagine you have strong wind blowing northward at one location and weaker wind to the right of it. The water at the first location moves to the right, and it does so faster than the water at the second location (because the wind forcing the water is stronger at the first location). The water converges at the second location, pushing the water downward. This is how the curl of the wind stress (the northward wind changing in the east-west direction) is related to the water convergence (the eastward current changing in the east-west direction) and hence to water being pushed down or pulled up. Positive wind stress curl pulls water up; negative wind stress curl pushes it down.

The last relevant part here is that this kind of motion suppresses ocean mixing. The relevant sentence from that paper is

The wind stress curl and hence Ekman pumping anomalies were negative, which also is consistent with relatively weak entrainment.

"Entrainment" is how much of the deep, cold ocean water mixes with the relatively warm upper ocean water, cooling it. The negative wind stress curl leads to water being pushed down and less deep water mixing with the upper ocean. The upper ocean stayed warmer, so the whole heat blob lasted longer.

In physical oceanography and fluid dynamics, the wind stress is the shear stress exerted by the wind on the surface of large bodies of water – such as oceans, seas, estuaries and lakes. It is the force component parallel to the surface, per unit area, as applied by the wind on the water surface.