The Great Arctic Cyclone of 2012 from satellite.

It works like a spoon stirring hot coffee, attracting cold air from Siberia. In this respect they serve as confined research regions, like a unique field laboratory experiment.

This post presents an article by John S. Wettlaufer who sees not only the oceans but cosmic patterns in coffee cup vorticies. His essay is The universe in a cup of coffee.  (Bolded text is my emphasis.)

John Wettlaufer is the A. M. Bateman Professor of Geophysics, Physics, and Applied Mathematics at Yale University in New Haven, Connecticut.

As people throughout the world awake, millions of them every minute perform the apparently banal act of pouring cold milk into hot coffee or tea. Those too groggy to reach for a spoon might notice upwelling billows of milk separated by small, sinking, linear dark features such as shown in panel a of the figure. The phenomenon is such a common part of our lives that even scientists—trained to be observant—may overlook its importance and generality. The pattern bears resemblance to satellite images of ocean color, and the physics behind it is responsible for the granulated structure of the Sun and other cosmic objects less amenable to scrutiny.

(a) Everyone knows that if you wait for a while coffee will get cold. The primary agent doing the cooling is evaporatively driven convection. Pour cold milk into hot coffee and wait. The cold milk mixes very little as it sinks to the bottom of the cup, but eventually cold plumes created by evaporation at the surface sink down and displace the milk. In time, a pattern forms of upwelling (lighter) and downwelling (darker) fluid.

Archimedes pondered the powerful agent of motion known as buoyancy more than two millennia ago. Children do, too, when they imagine the origins of cloud animals on a summer’s day. The scientific study of thermal and compositional buoyancy originated in 1798 with a report by Count Rumford intended to disabuse believers of the caloric theory. Nowadays, buoyancy is at the heart of some of the most challenging problems in nonlinear physics—problems that are increasingly compelling. Answers to fundamental questions being investigated today will have implications for understanding Earth’s heat budget, the transport of atmospheric and oceanographic energy, and, as a corollary, the climate and fate of stars and the origins of planets. Few avenues of study combine such basic challenges with such a broad swath of implications. Nonetheless, the richness of fluid flow is rarely found in undergraduate physics courses. 

Wake up and smell the physics

The modern theory of hydrodynamic stability arose from experiments by Henri Bénard, who heated, from below, a thin horizontal layer of spermaceti, a viscous, fluid wax. For small vertical temperature gradients, Bénard observed nothing remarkable; the fluid conducted heat up through its surface but exhibited no wholesale motion as it did so. However, when the gradient reached a critical value, a hexagonal pattern abruptly appeared as organized convective motions emerged from what had been an homogenous fluid. The threshold temperature gradient was described by Lord Rayleigh as reflecting the balance between thermal buoyancy and viscous stresses, embodied in a dimensionless parameter now called the Rayleigh number. 

When the momentary thermal buoyancy of a blob of fluid—provided by the hot lower boundary—overcomes the viscous stresses of the surrounding fluid, wholesale organized motion ensues. The strikingly structured fluid, with its up-and-down flow assuming specific geometries, is an iconic manifestation of how a dissipative system can demonstrate symmetry breaking (the up-and-down flow distinguishes horizontal positions even though the lower boundary is at a uniform temperature), self-organization, and beauty. (See the article by Leo Kadanoff in PHYSICS TODAY, August 2001, page 34.)

Astrophysicists and geophysicists can hardly make traction on many of the problems they face unless they come to grips with convection—and their quests are substantially complicated by their systems’ rotations. Despite the 1835 publication of Gaspard-Gustave Coriolis’s Mémoire sur les équations du mouvement relatif des systèmes de corps (On the Equations of Relative Motion of a System of Bodies), debate on the underlying mechanism behind the deflection of the Foucault pendulum raged in the 1905 volume of Annalen der Physik, the same volume in which Albert Einstein introduced the world to special relativity. Maybe the lack of comprehension is not so surprising: Undergraduates still more easily grasp Einstein’s theory than the Coriolis effect, which is essential for understanding why, viewed from above, atmospheric circulation around a low pressure system over a US city is counterclockwise but circulation over an Australian city is clockwise. 

Practitioners of rotating-fluid mechanics generally credit mathematical physicist Vagn Walfrid Ekman for putting things in the modern framework, in another key paper from 1905. Several years earlier, during his famous Fram expedition, explorer Fridtjof Nansen had observed that ice floes moved to the right of the wind that imparted momentum to them. Nansen then suggested to Ekman that he investigate the matter theoretically. That the deflection was due to the ocean’s rotating with Earth was obvious, but Ekman described the corrections that must be implemented in a noninertial reference frame. Since so much in the extraterrestrial realm is spinning, scientists taken by cosmological objects eventually embraced Ekman’s formulation and sought evidence for large-scale vortex structures in the accretion disks around stars. Vortices don’t require convection and when convection is part of a vortex-producing system, additional and unexpected patterns ensue. 

Cream, sugar, and spinning

The Arctic Ocean freezes, cooling and driving salt into the surface layers. Earth’s inner core solidifies, leaving a buoyant, iron-depleted metal. Rapidly rising air from heated land surfaces creates thunderstorms. Planetary accretion disks receive radiation from their central stars. In all these systems, rotation has a hand in the fate of rising or sinking fluid. What about your steaming cup of coffee: What happens when you spin that?

(b) Several views of a volume of water 11.4 cm deep with a cross section of 22.9 × 22.9 cm. Panel b shows the liquid about 7.5 minutes after the fluid is set in motion at a few tenths of a radian per second. The principal image indicates particle density (light is denser) at a depth of 0.6 cm below the surface. The inset is a thermal image of the surface

Place the cup in the center of a spinning record player— some readers may even remember listening to music on one of those. The friction from the wall of the cup transmits stresses into the fluid interior. If the coffee is maintained at a fixed temperature for about a minute, every parcel of fluid will move at the same angular velocity; the coffee is said to be spun up.

On the time scales of contemporary atmospheric and oceanographic phenomena, Earth’s rotation is indeed a constant, whereas the time variation of the rotation could be important for phenomena in planetary interiors, the evolution of an accretion disk, or tidal perturbations of a distant moon. Thus convective vortices are contemplated relative to a rotating background flow. Perturbations in the rotation rate revive the role of boundary friction and substantially influence the interior circulation. Moreover, evaporation and freezing represent additional perturbations, which alter how the fluid behaves as stresses attempt to enforce uniform rotation. Returning to the coffee mug as laboratory, the model system shown in panel b of the figure reveals how the added complexity of rotation momentarily organizes the pattern seen in panel a into concentric rings of cold and warm fluid.

(c) Panel c shows the breakup of the rings, 11 minutes after the initiation of rotation, due to a shearing instability.

Fundamental competitions play out when you rotate your evaporating coffee. As we have seen, evaporative cooling drives narrow regions of downward convection; significant viscous and Coriolis effects balance each other in those downwelling regions. Rotation then dramatically organizes the sinking cold sheets and rising warm billows into concentric rings that first form at the center of the cup. By about 7.5 minutes after rotation has been initiated, the rings shown in panel b have grown to cover most of the horizontal plane. Their uniform azimuthal motion exists for about 3.5 minutes, at which time so-called Kelvin–Helmholtz billows associated with the shearing between the rings appear at their boundaries, grow, and roll up into vortices; see panel c. Three minutes later, as shown in panel d, those vortices lose their azimuthal symmetry and assemble into a regular vortex grid whose centers contain sinking fluid.

(d) As panel d shows, at 14 minutes the breakup leads to a grid of vortices. (Adapted from J.-Q. Zhong, M. D. Patterson, J. S. Wettlaufer, Phys. Rev. Lett. 105, 044504, 2010.)

Panel d shows one type of coherent structure that forms in rotating fluids and other mathematically analogous systems if the persistence time of the structure—vortices here— is much longer than the rotational period. Other well-known examples are Jupiter’s Great Red Spot, which is an enduring feature of the chaotic Jovian atmosphere, and the meandering jet streams on Earth.

Moreover, persistent vortices in superconductors and superfluids organize themselves. Indeed, it appears that vortices in superconductors are as mobile as their counterparts in inviscid fluids. And although scientists have long studied rotating convective superfluids, the classical systems considered in this Quick Study suggest that we may yet find surprising analogies in superconductors. Will we one day see superconducting jet streams?

If you are reading this article with a cup of coffee, put it down and take a closer look at what is going on in your cup.

Summary

Wettlaufer has been an advocate for getting the physics right in climate models.  His analogy of a cuppa coffee is actually a demonstration of mesoscale fluid and rotational dynamics and perturbations that still defy human attempts to simulate climate operations.

Dr. Arnd Bernaerts is again active with edifying articles on how humans impact upon the oceans and thereby the climate. His recent post is Global Cooling 1940 – 1975 explained for climate change experts

I and others first approach Dr. Bernaerts’ theory relating naval warfare to climate change with a properly skeptical observation. The ocean is so vast, covering 71% of our planet’s surface and up to 11,000 meters deep, with such a storage of solar energy that it counteracts all forcings including human ones.

As an oceanographer, Bernaerts is well aware of that generalization, having named his website Oceans Govern Climate. But his understanding is much more particular and more clear to me in these recent presentations. His information is encyclopedic and his grasp of the details can be intimidating, but I think I get his main point.

When there is intense naval warfare concentrated in a small, shallow basin like the North Sea, the disturbance of the water structure and circulation is profound. The atmosphere responds, resulting in significant regional climate effects. Nearby basins and continents are impacted and eventually it ripples out across the globe.

The North Atlantic example is explained by Bernaerts Cooling of North Sea – 1939 (2_16) Some excerpts below.

Follow the Water

Water, among all solids and liquids, has the highest heat capacity except for liquid ammonia. If water within a water body remained stationary and did not move (which is what it does abundantly and often forcefully for a number of reasons), the uppermost water surface layer would, to a very high percentage, almost stop the transfer of any heat from a water body to the atmosphere.

However, temperature and salt are the biggest internal dynamic factors and they make the water move permanently. How much the ocean can transfer heat to the surface depends on how warm the surface water is relative to atmospheric air. Of no lesser importance is the question, as to how quickly and by what quantities cooled-down surface water is replaced by warmer water from sub-surface level. Wind, cyclones and hurricanes are atmospheric factors that quickly expose new water masses at the sea surface. Another ‘effective’ way to replace surface water is to stir the water body itself. Naval activities are doing just this.

War in the North Sea

Since the day the Second World War had started naval activities moved and turned the water in the North Sea at surface and lower levels at 5, 10, 20 or 30 metres or deeper on a scale that was possibly dozens of times higher than any comparable other external activity over a similar time period before. Presumably only World War One could be named in comparison.

The combatants arrived on the scene when the volume of heat from the sun had reached its annual peak. Impacts on temperatures and icing are listed in the last section: ‘Events’ (see below). The following circumstantial evidences help conclude with a high degree of certainty that the North Sea contributed to the arctic war winter of1939/40.

Climate Change in Response

On the basis of sea surface temperature record at Helgoland Station and subsequent air temperature, developments provide strong indication that the evaporation rate was high. This is confirmed by the following impacts observed:

More wind: As the rate of evaporation over the North Sea has not been measured and recorded, it seems there is little chance to prove that more vapour moved upwards during autumn 1939 than usual. It can be proved that the direction of the inflow of wind had changed from the usually most prevailing SW winds, to winds from the N to E, predominantly from the East. At Kew Observatory (London) general wind direction recorded was north-easterly only three times during 155 winter years; i.e. in 1814, 1841 and 1940[6]. This continental wind could have significantly contributed to the following phenomena of 1939: ‘The Western Front rain’.

More rain: One of the most immediate indicators of evaporation is the excessive rain in an area stretching from Southern England to Saxony, Silesia and Switzerland. Southern Baltic Sea together with Poland and Northern Germany were clearly separated from the generally wet weather conditions only three to four hundred kilometres further south. A demonstration of the dominant weather situation occurred in late October, when a rain section (supplied from Libya) south of the line Middle Germany, Hungary and Romania was completely separated from the rain section at Hamburg – Southern Baltic[7].

More cooling: Further, cooling observed from December 1939 onward can be linked to war activities in two ways. The most immediate effect, as has been explained (above), is the direct result from any excessive evaporation process. The second (at least for the establishment of global conditions in the first war winter) is the deprivation of the Northern atmosphere of its usual amount of water masses, circulating the globe as humidity.

Rippling Effects in Northern Europe and Beyond

Next to the Atlantic Gulf Current, the North Sea (Baltic Sea is discussed in the next chapter) plays a key role in determining the winter weather conditions in Northern Europe. The reason is simple. As long as these seas are warm, they help sustain the supremacy of maritime weather conditions. If their heat capacity turns negative, their feature turns ‘continental’, giving high air pressure bodies an easy opportunity to reign, i.e. to come with cold and dry air. Once that happens, access of warm Atlantic air is severely hampered or even prevented from moving eastwards freely.

The less moist air is circulating the globe south of the Arctic, the more easily cold polar air can travel south. A good piece of evidence is the record lack of rain in the USA from October – December 1939 followed by a colder than average January 1940, a long period of low water temperatures in the North Sea from October-March (see above) and the ‘sudden’ fall of air temperatures to record low in Northern Europe.

The graph above suggests that naval warfare is linked to rapid cooling. The climate system responds with negative feed backs to restore equilibrium. Following WWI, limited to the North Atlantic, the system overshot and the momentum continued upward into the 1930s. Following WWII, with both Pacific and Atlantic theaters, the climate feed backs show several peaks trying to offset the cooling, but the downward trend persisted until about 1975.

Summary

The Oceans Govern Climate. Man influences the ocean governor by means of an expanding fleet of motorized propeller-driven ships. Naval warfare in the two World Wars provide the most dramatic examples of the climate effects.

Neither I nor Dr. Bernaerts claim that shipping and naval activity are the only factors driving climate fluctuations. But it is disturbing that so much attention and money is spent on a bit player CO2, when a much more plausible human influence on climate is ignored and not investigated.

I was inspired by David Dilley’s weather forecasting based upon Atlantic water pulsing into the Arctic Ocean (see post: Global Weather Oscillations). So I went looking for that signal in the AMO dataset, our best long-term measure of sea surface temperature variations in the North Atlantic.

ATLANTIC MULTI-DECADAL OSCILLATION (AMO)

For this purpose, I downloaded the AMO Index from Kaplan SST v.2, the unaltered and untrended dataset. By definition, the data are monthly average SSTs interpolated to a 5×5 grid over the North Atlantic basically 0 to 70N.

For an overview the graph below presents a comparison between Annual, March and September averages from 1856 to 2016 inclusive.

We see about 4°C difference between the cold month of March, and warm September. The overall trend is slightly positive at 0.27°C per century, about 10% higher in September and 10% lower in March. It is also clear that monthly patterns resemble closely the annual pattern, so it is reasonable to look more closely into Annual variability.

The details of the Annual fluctuations in AMO reveal the pulse pattern suggested by Dilley.

We note firstly the classic pattern of temperature cycles seen in all datasets featuring quality-controlled unadjusted data. The low in 1913, high in 1944, low in 1975, and high in 1998. Also evident are the matching El Nino years 1998, 2009 and 2016, indicating that what happens in the Pacific does not stay in the Pacific.

Most interesting are the periodic peaking of AMO in the 8 to 10 year time frame. The arrows indicate the peaks, which as Dilley describes produce a greater influx of warm Atlantic water under the Arctic ice. And as we know from historical records and naval ice charts, Arctic ice extents were indeed low in the 1930s, high in the 1970s, low in the 1990s and on a plateau presently.

Conclusion

I am intrigued but do not yet subscribe to the Lunarsolar explanation for these pulses, but the AMO index does provide impressive indication of the North Atlantic role as a climate pacemaker. Oceans make up 71% of the planet surface, so SSTs directly drive global mean temperatures (GMT). But beyond the math, Atlantic pulses set up oscillations in the Arctic that impact the world.

In the background is a large scale actor, the Atlantic Meridional Overturning Circulation (AMOC) which is the Atlantic part of the global “conveyor belt” moving warm water from the equatorial oceans to the poles and back again.  For more on this deep circulation pattern see Climate Pacemaker: The AMOC