Tag Archives: coriolis

The Turbulence of Van Gogh and the Labrador Shelf Current

Posted on May 8, 2013 by | 2 Comments

Vincent Van Gogh painted his most turbulent images when insane. The Labrador Current resembles Van Gogh’s paintings when it becomes unstable. There is no reason that mental and geophysical instability relate to each other. And yet they do. Russian physicist Andrey Kolmogorov developed theories of turbulence 70 years ago that Mexican physicist applied to some of Van Gogh’s paintings such as “Starry Sky:”

Vincent Van Gogh's "Starry Sky" painted in June 1889.

Vincent Van Gogh’s “Starry Sky” painted in June 1889.

The whirls and curls evoke motion. The colors vibrate and oscillate like waves that come and go. There are rounded curves and borders in the tiny trees, the big mountains, and the blinking stars. Oceanographers call these rounded curves eddies when they close on themselves much as is done by a smooth wave that is breaking when it hits the beach in violent turmoil.

Waves come in many sizes at many periods. The wave on the beach has a period of 5 seconds maybe and measures 50 meters from crest to crest. Tides are waves, too, but their period is half a day with a distance of more than 1000 km from crest to crest. These are scales of time and space. There exist powerful mathematical statements to tell us that we can describe all motions as the sum of many waves at different scales. Our cell phone and computer communications depend on it, as do whales, dolphins, and submarines navigating under water, but I digress.

The Labrador Shelf Current off Canada moves ice, icebergs, and ice islands from the Arctic down the coast into the Atlantic Ocean. To the naked eye the ice is white while the ocean is blue. Our eyes in the sky on NASA satellites sense the amount of light and color that ice and ocean when hit by sun or moon light reflects back to space. An image from last friday gives a sense of the violence and motion when this icy south-eastward flowing current off Labrador is opposed by a short wind-burst in the opposite direction:

Ice in the Labrador Current as seen by MODIS-Terra on May 3, 2013.

Ice in the Labrador Current as seen by MODIS-Terra on May 3, 2013. Blue colors represent open water while white and yellow colors represent ice of varying concentrations.

Flying from London to Chicago on April 6, 2008, Daniel Schwen photographed the icy surface of the Labrador Current a little farther south:

Ice fields seen in Labrador Current April 6, 2008 from a plane. [Photo Credit: Daniel Schwen]

Ice fields seen in Labrador Current April 6, 2008 from a plane. [Photo Credit: Daniel Schwen]

Ice in the Labrador Current as seen by MODIS-Terra on April 6, 2008. Blue colors represent open water while white and yellow colors represent ice of varying concentrations.

Ice in the Labrador Current as seen by MODIS-Terra on April 6, 2008. Blue colors represent open water while white and yellow colors represent ice of varying concentrations.

The swirls and eddies trap small pieces of ice and arrange them into wavy bands, filaments, and trap them. The ice visualizes turbulent motions at the ocean surface. Also notice the wide range in scales as some circular vortices are quiet small and some rather large. If the fluid is turbulent in the mathematical sense, then the color contrast or the intensity of the colors and their change in space varies according to an equation valid for almost all motions at almost all scales. It is this scaling law of turbulent motions that three Mexican physicists tested with regard to Van Gogh’s paintings. They “pretended” that the painting represents the image of a flow that follows the physics of turbulent motions. And their work finds that Van Gogh indeed painted intuitively in ways that mimics nature’s turbulent motions when the physical laws were not yet known.

There are two take-home messages for me: First, fine art and physics often converge in unexpected ways. Second, I now want to know, if nature’s painting of the Labrador Shelf Current follows the same rules. There is a crucial wrinkle in motions impacted by the earth rotations: While the turbulence of Van Gogh or Kolmogorov cascades energy from large to smaller scales, that is, the larger eddies break up into several smaller eddies, for planetary-scale motions influenced by the Coriolis force due to earth’s rotation, the energy moves in the opposite direction, that is, the large eddies get larger as the feed on the smaller eddies. There is always more to discover, alas, but that’s the fun of physics, art, and oceanography.

Aragón, J., Naumis, G., Bai, M., Torres, M., & Maini, P. (2008). Turbulent Luminance in Impassioned van Gogh Paintings Journal of Mathematical Imaging and Vision, 30 (3), 275-283 DOI: 10.1007/s10851-007-0055-0

Ball, P. (2006). Van Gogh painted perfect turbulence news@nature DOI: 10.1038/news060703-17

Wu, Y., Tang, C., & Hannah, C. (2012). The circulation of eastern Canadian seas Progress in Oceanography, 106, 28-48 DOI: 10.1016/j.pocean.2012.06.005

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Arctic Sea Ice Cover and Extreme Weather Explained

Posted on September 19, 2012 by | Leave a comment

Addendum Sept.-24, 2012: A New Climate State, Arctic Sea Ice 2012 (video by Peter Sinclair).

I just discovered an outstanding interview that Dr. Jennifer Francis of Rutgers University gave to a non-profit community radio station out of Vancouver, British Columbia.

Jennifer Francis Interview 20120910

She connects and explains global warming, its much amplified signal in the Arctic, the extreme record minimal Arctic sea ice cover this summer, and how the warming Arctic and its disappearing sea ice impacts our weather in the northern hemisphere by slowing down the atmospheric jet stream separating polar from mid-latitude air masses. She explains all of this in non-technical language without loss of accuracy.

Dr. Jennifer Francis, Rutgers University [Photo Credit: ARCUS]

If this program piques your interest and you want to read more, Andrew Revkin of the New York time has led an informed discussion at his New York Times blog Dot Earth. And finally, Climate Central presented and illustrated Dr. Francis’ observations and ideas rather well with graphics and videos.

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New Ocean Observations in Petermann Fjord

Posted on August 22, 2012 by | 10 Comments

A new ice island separated from Petermann Glacier on July 16, 2012 as reported here first. Less than 4 weeks later, the Canadian Coast Guard Ship Henry Larsen reconnoitered the ice island on Aug.-9 when it blocked the northern half of the entrance of the fjord.

Petermann Ice Island 2012 (PII-2012) as seen Aug.-11, 2012 at the entrance of Petermann Fjord. The view is to the north-west. [Photo Credit: Canadian Coast Guard Ship Henry Larsen.]

I was aboard this ship when Captain Wayne Duffett decide to break into the largely ice-free fjord behind the ice-island after consultations with Ice Services Specialist Erin Clarke. The ice observer had just returned from her second helicopter survey in 2 days with pilot Don Dobbin to assess both ice cover and its time rate of change. From the time the ship entered the fjord behind the ice island, hourly flights to a fixed point at the south-western corner of the ice island ensured that its movement would not cut off the ship’s exit. This approach worked and it gave the science crew of 8 aboard about 18 hours to conduct the very first survey of a previously ice-covered ocean:

Petermann Glacier, Fjord, and Ice Island as seen by MODIS at 865 nm on Aug. 07, 2012 overlaid with survey lines of CCGS Henry Larsen on Aug.-9/10/11, 2012 in red.

We were not funded to do enter the fjord, but our main mission to recover an array of ocean moorings with 3-year long data records covering the 2009-12 period about 100 km to the south in Nares Strait has already been accomplished. So, what does a physical oceanographer do when in uncharted and unknown territory? He drops a number of CTDs, that is, measuring conductivity (C), temperature (T), and depth (D, pressure, really) as the instrument (the CTD) is lowered at a constant rate from the surface to the bottom of the ocean at a number of stations. The results from such work next to the present front of Petermann Glacier was a surprise for which we do not yet have a satisfactory explanation: The waters inside the fjord are much warmer at salinities 32.5-34.25 than they are outside the fjord:

Temperature as a function of salinity from 9 stations across Petermann Fjord next to the current seaward edge of Petermann Glacier on Aug.-10, 2012 in red. For comparison I show in blue a station done outside the fjord on Aug.-9, 2012. Note that temperatures increase with increasing salinity which is expected for waters that are a mixture of cold and fresh polar and saltier and warmer Atlantic waters. Density deviations from 1000 kg/m^3 are shown as solid contours along with the freezing temperature that decreases with increasing salinity.

Another way to show the same data is to actually plot the section, that is, the distribution of temperature and salinity in physical space across the fjord as a function of depth:

Section across the seaward edge Petermann Glacier on Aug.-10, 2012 for salinity (left panel) and temperature (right panel). Symbols indicate station locations from which color contours are drawn. Note that the display is cropped to the top 300 meters while real recordings extend to the bottom which exceeds 1000 meters. The view is eastward towards the glacier with north to the left.

Note the doming salinity contours which to classically trained oceanographers suggest a flow out of the page on the right and into the page on left with maximum at about 90 meter depth relative to no flow at, say, 500 meter depth. Another way to view this distinct property distribution is that the flow above 90 meters is clockwise (outflow on left, inflow on right) relative to the more counter-clockwise flow below this depth. This feature, too, comes as a surprise and requires more thought and analyses to explain.

There is much more work to be done to figure out what all this means. I feel like scratching the surface of a large iceberg half-blind. The data from below 300 meter depth, too, contain clues on how some this glacier interacts with the ocean. As for the purpose of this post, I merely wanted to report that the ice island is presently having a hitting or scratching tiny Hans Island. The latter is unlikely to move, but Petermann’s Ice Island will slow on impact, swivel counter-clockwise, bump into Ellesmere, and pretend nothing has happened on its merry way south. This is the latest image I have:

Petermann Ice Island 2012 on Aug.-22, 2012 as seen by MODIS Terra at 21:45 UTC. The tiny red dot marks Hans Island, the location of a weather station in the Kennedy Channel section of Nares Strait. Petermann Fjord is towards the top right out of view.

ADDENDUM Sept.-1, 2012: PII-2010B had a maximum thickness of at least 144 meters as it passed over a mooring that measures ocean currents from the Doppler shift of acoustic backscatter that is shown here for one of four beams:

Time-depth series of acoustic scatter from a bottom-mounted acoustic Doppler current profiler for 24 hours starting Sept-22, 2010 9:30 UTC. Red colors indicate high backscatter from a “hard” surface like ice. The vertical axis depth in meters above the transducers while the horizontal is ensemble number into the record (0.5 hours between ensembles). The 2010 ice island from Petermann Glacier (PII-2010B) passed over the mooring. When PII-2010B was attached to the glacier it was adjacent to the segment that became PII-2012 this year.

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Ice Island Flotilla From Petermann Glacier Continue Southward Flow

Posted on May 3, 2012 by | Leave a comment

More icebergs and ice island from Greenland are heading south along northern North-America this year. Petermann Glacier’s first piece arrived last year off Newfoundland causing a local tourist sensation for a stunning display of ice along its shores. There are many more pieces from Petermann to come for a few more years.

Track of Petermann Ice Island from Aug.-2010 through Aug.-2011 traveling in shallow water from northern Greenland along Baffin Island and Labrador to Newfoundland.

April 29/30, 2012 locations of Petermann Ice Island 2010 on their way south along northern North America. [Credit: Luc Desjardins, Canadian Ice Service]

Yet, how come that these arrivals are both so predictable in their pattern, but are almost impossible to pin down for an exact location and time? The answer involves mystical and fake forces, stunningly beautiful experiments, elegant mathematical equations, and, most important of all: spin.

The earth spins rapidly around its axis and neither ocean nor glaciers leave the planet for outer space. The obvious answer that gravity holds all the pieces in place is neither the correct nor the full answer. A subtle balance of several other forces makes Planet Earth the perfect place to keep us supplied with water to drink and air to breath. Additional forces besides gravity relate to the difference in pressure between the top and the bottom of the ocean as well as the rotational force that forces our car off the road if we speed too fast around a curve. The net effect of these is that earth fatter at the equator than at the North Pole. There appears to be more of gravity pulling us in at the North Pole than there is at the equator. Put another way, a scale measuring our own weight dips almost a pound more in Arctic Greenland than it does in the tropical forests of Borneo even if we do it naked in both places. Lose a pound of your weight instantly, travel to the far north. (GRACE)

This makes no sense intuitively, but common sense and intuition help little when it comes to how the ocean’s water and the atmosphere’s air move on a rotating planet. For example, we all know intuitively that a down-pour of rain flows down a slope into the ditch. It requires work to bring water up to the top of a hill or into the water towers to make sure that water flows when we open the faucet. Not true for the ocean at scales that relate to climate, weather, and changes of both. Here all water flows along, not down the hill. Better yet, it requires no work at all to keep it moving that way for all times. This is why Greenland’s ice keeps coming our way as soon as pieces break off. The earth’s spin makes it go around the hill, to speak loosely of pressure differences. Winds and friction have little effect. The ocean’s natural and usually stable state is in geostrophic balance. Geostrophy is a fancy word for saying that the ocean’s water flows along, not down a hill, because it is balanced by a fake and mystical Coriolis force that I will not explain. I teach a graduate class on Geophysical Fluid Dynamics for that.

In technical language, most of the oceans tend to flow along not down a pressure gradient. A kettle of boiling water discharges water from high pressure inside the kettle to the lower pressure in the kitchen. Yet the steam dissolved in the atmosphere moves around high or low-pressure systems. That’s how we read weather maps: Clockwise winds around high-pressure over Europe, North-America, and Asia to the north of the equator, counter-clockwise winds around low-pressure systems. If I apply this spin-law to Baffin Bay containing all the icebergs and ice islands, the spin rule states that these large and deep pieces flow along lines where the earth’s local rate of rotation, lets call it planetary spin f, divided by the local water depth, lets call it H, is a constant. So, to a first approximation, the icebergs and ice islands flow along a path where f/H is constant. If the planetary spin is constant, then the ice island follow lines of constant water depth H. There is more to the story, much more, such as the effects of waters of different densities residing next to each other, but I better continue this later, as I got a dinner date with a sweetheart and “Thermal Wind” can wait ;-)

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Melting Greenland’s Icebergs and Ice Islands by the Ocean

Posted on January 11, 2012 by | 1 Comment

The BBC keeps asking good and penetrating questions about the fate of Greenland’s many icebergs in general and Petermann Glacier’s Ice Island in particular. A poor telephone connection across the Atlantic this morning prevented an interview, but made me answer a number of questions in writing. When answering these questions, I was thinking of those icebergs and ice islands one finds in abundance in the frigid waters of Baffin Bay, the Labrador Sea, and next to Greenland. I am not talking about what happens once icebergs enter the subtropical Atlantic Ocean and meet the Gulf Stream to the south of the Grand Banks, that is a different story.

USCG Healy besides massive iceberg in northern Baffin Bay, July 2003

1. What can icebergs tell us about oceans?

Icebergs are particles that track averaged ocean currents over the top 200-m or so. These currents are often refered to as “geostrophic” currents which is really a different word for an ocean force balance between pressure gradients (estimated from measurements of temperature and salinity changes with depth at many locations) and the Coriolis force due to the earth’s rotation. This is why RADM Edward H. “Iceberg” Smith of the US Coast Guard spent so much time sailing and taking measurements off northern Canada in the 1920ies and 1930ies as part of the International Ice Patrol. His outstanding publications 80 years old are a first example on how to apply theory (the Scandinavian or Bergen School of the 1920ies regarding dynamical physical oceanography) to a very specific application.

2. How does the trajectory of the ice-islands/ and other icebergs show information about the ocean currents?

Ice islands and icebergs are thick (50-200 m) and mostly submerged below the surface. Hence they are largely moved by the ocean currents about 30-200 m below the surface. I think of them as ocean drifters with a very large and deep drogue element that changes with time as the iceberg melts or tips over. This is different from sea ice that may reach only 5-m into the water column and thus only “sees” the very surface layer of the ocean that is largely influenced by winds. This is not entirely true for icebergs, because they are driven by ocean currents below the thin (10-20 m) ocean “mixed layer” that sea ice is embedded in.

3. What are the current unknowns or poorly understood parameters with regards to iceberg science and iceberg interactions with oceans in the High Arctic?

I think the problem with any prediction scheme of individual particles is that the ocean always has a strong turbulent and unpredictable part to it. This problem is fundamentally no different from trying to predict where oil from a spill will come ashore. We can do it “on average” rather well, but we are very poor trying to do in one specific case for a specific iceberg (or spill). Oh, this certainly also applies to climate predictions, easy to do “on average,” very hard to do in a specific case for a specific time and place that may be affected.

4. What sort of temperatures would the water be?

Meltwater plumes at zero salinity with pieces of ice floating in it have a temperature of 0 C, meltwater plumes with pieces of ice in it at ocean salinities have temperatures of about -1.8C, depending on the amount of sunlight and how much mixing takes place, these fresh and very thin surface layers (1-10 meters) can heat up substantially fast, and cool just as fast. In June/July you have 24 hours of sunlight, so temperatures of 4-10 C are not out of the ordinary, but these waters will do very little melting, because most of the mass is well below a 10 m depth of such fresh surface plumes.

Temperature (left) and salinity (right) distribution off Labrador in the summer of 2009 with depth and distance from the coast (from Colbourne et al., 2010). Note the very cold waters near the freezing point (blue and purple) on the continental shelf below 50-m depth.

5. How would changes in ocean stratification and temperature alter the melting of icebergs?

First, ocean temperature (or heat) and stratification are two very different things. In the Arctic almost all stratification is done by salinity, temperature is a tracer that has very little effect on density stratification. This is also the reason, that most of the ocean’s heat in the Arctic is at depths 200-400 m below the surface. This warm water does NOT rise towards the surface, because it is also salty water, it is often refered to the Atlantic Layer. This deep reservoir of heat is what many oceanographers (myself included) have in mind when they talk about the melting of Greenland’s glaciers by the ocean from below.

Petermann Glacier, for example, has a grounding line at 600-m below the surface. This grounding line is in contact with the heat from the Atlantic Layer that is melting it, but the melted water is fresh and cold, immediately stratifying the water column under the ice, so a source of energy is needed also to move or mix this cold fresh melt water away. An inclined slope may do so, tides may do so, internal waves traveling and breaking on the interface between cold-fresh and warm-salty waters may do so. At Petermann Glacier this Atlantic layer does not reach most of the floating element of this glacier, because it is only 100-200 m thick and thus does not extend into the heat of the Atlantic Layer. So, vertical stratification and location of heat are two different things.

Breaking waves on an interface due to a shear instability, i.e., flow in the (fresh and cold) upper layer is less than the flow in the denser (warm and salty) lower layer.

Second, think of ocean stratification as a blanket that insulates one region from the other. Removing the blanket requires kinetic energy (something or someone has to do the work, doing work requires energy). As you melt freshwater ice via conduction of heat to the ice, the melt has zero salinity and a temperature at the freezing point. This zero salinity water acts as the insolation blanket that reduces the heat reaching the ice. So, again, you need (a) a source of kinetic energy to do work to break down the stratification (of salinity) to (b) enable the transfer of heat from the ocean to the ice.

6. Can you recommend any key journal papers you think we should read?

The classical paper on this subject is [Gade, H.G., 1979: Melting of ice in sea water: A primitive model with application to the Antarctic Ice Shelf and Icebergs. J. Phys. Oceanogr., 9, 189-198], but this paper is a thorough theoretical development. I have professors of glaciology asking me what it means, so the material is not easy to penetrate. In a 2011 publication on the oceanography of Petermann Fjord impacting this Glacier, we made extensive use of the arguments and concepts presented in Gade (1979). That publication is more readable and accessible.

Its first author is Dr. Helen Johnson at Oxford University with whom I have collaborated since 2003 aboard US and Canadian icebreakers. She also published an illustrated diary of our 2007 expedition to Nares Strait.

ADDED Jan-12: My mind yesterday was unclear on the in situ temperature at which glacier ice of zero salinity is melting in seawater such as found on the Labrador shelf. The comment below points this out concisely, while this link to TheNakedScientist perhaps provides the longer and more visual explanation. Another fun explanation of the melting and freezing of ice in a salt solution relates to the making of ice cream. A subsurface temperature at -1.5 C at a salinity of 33.5 psu such as found on the Labrador shelf does melt the zero salinity ice of the iceberg somewhat. A boundary layer consisting of fresh meltwater will lower the salinity adjacent to the iceberg which will increase the freezing point which will reduce the melting until a new stable equilibria is reached.

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Swirling Ice in Coastal Waters off Eastern Greenland

Posted on September 12, 2011 by | Leave a comment

Nature provides us with art that is always changing in time and space. Delicate swirls and vortices give a rare glimpse of how the ocean’s surface looked today off eastern Greenland. The data originate from the MODIS/Terra satellite which from 440 miles above the earth captures light that is reflected from anything below. Here it shows the ice-free ocean (bottom right) and Greenland’s ice-free Scoresby Sound (bottom left) in very dark blues, lightly vegetated lands (left) in light blue, and a highly organized pattern of sea ice (top right) in white. The resolution of this image of light just beyond the visible, just beyond the red is about 300 yards and the swirls and elongated filaments are about 3-5 miles. To me, they vividly show the ocean’s surface circulation.

Swirling surface motion on the continental shelf off eastern Greenland Sept.-12, 2011 as indicated by sea ice. Black lines show contours of bottom depth from 300 to 1200 meters in 300 meter increments.

The physics of these motions are similar to those I was reading into another beautiful work of art to the north of Norway. The postulated physics involve the earth’s rotation as well as differences in density. The density of the ocean relates to its temperature a little and to its salinity a lot. Near the coast and at the surface, ocean waters are much fresher and thus lighter than they are offshore and at depth, because Greenland’s melting glaciers and sea ice are fresher than the waters of the Atlantic Ocean. The thin black lines show bottom depths to distinguish the deep Atlantic Ocean to the right in the image from the shallow continental shelf off eastern Greenland to the left in the image. Note that all the swirls, eddies, and filaments are within 30 kilometers (20 miles) off the coast in water less than 300-m deep. The same physics apply to the algal blooms off Norway which is the reason that the swirls and eddies are of similar size here and there as well.

Incidentally, the same physics also apply the discharges from rivers and estuaries such as the Delaware or Cheasapeake Bay. There, the pattern are not quiet as visible to the naked (satellite) eye as off Norway or Greenland, but if one takes measurements of the ocean, similar patterns of ocean salinity and velocity as, I speculate, they do here for the ice (Greenland) and algae blooms (Norway). While my academic journey of fresh water discharges started with the discharge of the Delaware River into the Atlantic almost 25 years ago, I am still fascinated by the many ways these patterns always come back to me. Physics and oceanography are beautiful in both their many natural manifestations and its unique balance of forces. There is so much more in how the oceans interact with the ice and glaciers off Greenland and elsewhere. To be continued …

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