THE DYNAMIC EARTH: A BLOG ABOUT GEOLOGY AND THE EARTH SCIENCES

Friday, October 31, 2008

At The Orogen of Madness

It seems that he pondered a great deal, and with alarmingly radical daring,
over that triangular striated marking in the slate; reading into it certain
contradictions in Nature and geological period which whetted his curiosity to
the utmost, and made him avid to sink more borings and blasting's in the
west-stretching formations to which the exhumed fragments belonged. He was
strangely convinced that the marking was the print of some bulky, unknown, and
radically unclassifiable organism of considerable advanced evolution,
notwithstanding that the rock which bore it was of so vastly ancient a date -
Cambrian if note actually pre-Cambrian-as to preclude the probable existence not
only of highly evolved life, but of any life at all above the unicellular or at
most trilobite stage. These fragments, with their odd marking, must have been
500 million to a thousand million years old.

H.P. Lovecraft, At The Mountains of Madness (1936)

Halloween is as good a time as any to reflect on the intersection between science (and, specifically, GEOLOGY) and Weird Fiction. One of my favorite Weird Authors has to be H.P. Lovecraft who, along with others like Robert E. Howard, Fritz Leiber, and Frank Belknap Long, transcended (sometimes) the simple medium of pulp horror and ushered in the modern age of science fiction. The quote above is from one of Lovecraft's most famous works, At The Mountains of Madness, and is one of my favorites for the very selfish reason that plot really hinges around geology. An online copy of the story is available here. It makes some good geo-Halloween reading!

First and foremost, the story is narrated by one Prof. Dyer, a professor of geology at the fictional Miskatonic University, in the fictional town of Arkham, Massachusetts, who is heading a scientific expedition to the Antarctic (set in the early 1910's); once there, they plan to take drill cores and sample the geology of the region. He's accompanied by other academics from the university, as well as graduate students. Already, it's a story near and dear to my heart.

Once in the frozen wastes of the Antarctica, the scientists' hopes of amazing discoveries are quickly realized; using the drill, they find many samples of fossils, including strange, ancient TRACE FOSSILS that no one can quite figure out. The quote at the head of this post is taken from the work, and is talking about these unusual triangular features. Interestingly, the geologist, Dyer, must be a sedimentologist, since he initially attributes the features to slightly metamorphosed "ripple effects". That's a good lesson, I think; always make the ichnologist convince YOU of the critter-origins for any weird marks.

Anyway, the biologist on the team apparently gets excited about these trace fossils, and as the quote above shows, draws some daring conclusions (spooooky conclusions, mind you) about what could have caused them. The search for the specific stratigraphic horizon on which these traces are found becomes the main focus of the expedition, who strike deeper and deeper into the unknown heart of Antarctica, and the increasingly more ancient mountains and strata that they discover.

Eventually, the biologist and some of the grads, who are pursuing the traces while Dyer and his students are doing other work (probably mapping...or drinking. They are geologists, after all), come across some "Comanchian" aged strata that host some cave deposits. Now, you and I probably have never heard of the Comanchian period, which was supposed to be between the Jurassic and Cretaceous periods, and was subsequently abandoned by the 1930's. However, since Lovecraft set the story in the Early 1900's, the geologists would still be using the term. Lovecraft, who was a very devoted lover of science, took special pains to make this story as scientifically valid (for its day) as he could, so it is actually an interesting historical document in that regard.

Anyway, within these caves, the biologists come across many fossils, of seemingly jumbled chronology, as well as huge, barrel-like "fossils" of an unknown, crinoid-like creatures, bigger than a human. They take these crinoid-creatures back to camp, where it turns out the Things may have some relation to the strange trace fossils found earlier. Oh, and they may not be quite so dead yet, either...

Lovecraft had a flair for the horrible and the weird, and took particular delight in how odd sea life was. A scholar of Lovecraft's life and work, S.T. Joshi, has made particular study of some of the influences on ol' Lovecraft (mostly using his 10,000+ letters that he wrote in his life), and has found that he had in mind for his crinoid-like Elder Things a particular Plate from the work of Ernst Haeckel. Below is the figure: Plate 90 from Haeckel's Kunstformen der Natur:




These crinoid Elder Things, with their alien physiognomy, also have another of Lovecraft's characteristic "horrible" attributes: incredible ancientness. Lovecraft commonly used the concept of Deep Time in his work, citing incredibly ancient things from the dawn of the universe, and describing how our minds could scarcely wrap our brains around such cosmically significant gulfs of time and space. Too, Lovecraft accurately describes the graduate student experience: as you dive deeper into your branch of Forbidden Knowledge, the Creeping Insanity starts to take hold...

If you have the time, At The Mountains of Madness is a fun read. It has a geologist as the main character, uses all sorts of archaic geological and stratigraphic terms, centers around horrible space crinoids (and their trace fossils), and even has a little bit about Continental Drift, which Lovecraft supported at a time when most American workers thought it was nonsense. Plus, there are some genuinely creepy parts (blind albino penguins...and, oh God! Shoggoths!) which might make for a fun Halloween.

Thursday, October 30, 2008

Spooooooooky Geology

While trying to avoid the shambling, slavering attacks of killer Internet memes, might I suggest some appropriately festive, geology themed podcasting? Steve Mirsky hosts the Scientific American Podcast, Science Talk, and can run a pretty good interview. Anyway, today's show has Sidney Horenstein (a geologist from the AMNH) and Susan Olsen discussing theWoodlawn Cemetery, focusing on the geology of the monuments.

You can get the show here.



And remember, memes are repelled by silver and garlic. GOOD LUCK, AND GOD SPEED.

Rainbows!

First trees, now rainbows (originality is so banal). But, so long as the pictures are lovely, I guess it's all right.

Silver Fox has posted some rainbow pictures, from the Great State of Nevada, so I thought I'd show some Wyoming pride. Below are some pictures from the summer, showing rainbows leading to a sedimentological pot-o'-gold (the Green River Fm):





And finally, a double rainbow!


Wednesday, October 29, 2008

Small World Photography

Microscopy plays a big part in geology, whether it's picking out forams for biostrat, describing microfacies in carbonates, point-counting grains in a sandstone, or identifying metamorphic mineral assemblages. But along with the academic value of microscope work, I think we can all appreciate the aesthetic beauty of these micro-worlds.

I recently ran across the Nikon Small World contest, which allows people to submit photomicrographs of really small stuff, which are then judged on their beauty and composition. There 2008 winners (and honorable mentions) are up, and show lots of really cool images of a variety of subjects. Unfortunately, I didn't see any strictly geological examples out there, which is a shame; you'd think someone would have a picture of a schist with crossed polars out there! I think the 2009 competition needs some geo-representation.

Anyway, I nabbed a few of the really slick ones from this year for your viewing enjoyment.

This is a cute little diatom, just kicking back and relaxing on a branch of red algae (100x):


I think diatoms must be a favorite, since there are several of them; here are some, along side some Closterium and Spirogyra (40x):


Showing some silacecous love, here are some radiolarians (160x):


More diatoms (100x):


And, finally, something near and dear to grad students everywhere, caffeine crystals (400x):

Sunday, October 26, 2008

Just in Time for Halloween: A New Paleozoic Sea Level Curve

Sequence stratigraphy, regardless of what one thinks of the specific methods, has played a major role in fundamentally changing the way we look at the stratigraphic record. It's a major conceptual framework that helps us interrogate the "time-as-rock" and "time-as-surfaces" relationships represented by the stratigraphic record, and has served as the dominant correlation strategy for much of the community of working sed/strat types.

So it's kind of a big deal.

Historiographically, the central concepts of the practice began with the work of Suess (1906), Blackwelder (1909), Barrell (1917), Wheeler (1958; 1964) and Sloss (1963). Despite these early works, however, "sequence stratigraphy" is represented (for good or bad) by the iconic 1977 AAPG Memoir 26, which brought the Exxon-ian Depositional Sequence to the conceptual and terminological landscape. And of all the contentious terms and ideas put forward by subsequent seq. strat. workers, perhaps none is more (in)famous than the dread Eustatic Sea Level Curve.

Eustatic sea-level curves have been used and abused in a variety of ingenious ways, and the literature is full of delightful arguments as to their merit and meaning. Sea-level curves are a complicated theoretical construct that really requires some serious and thoughtful interrogation. Or, alternatively, Sea-level curves are things you put up on the wall, and then match your particular rocks to your favorite wiggle. The community is divided as to which approach is correct.

Anyway, Haq et al. (1987) published the seminal Sea Level Curve for the Triassic and Younger; now, Haq and Schutter (2008) have put out a Paleozoic Sea Level Curve for our consumption. The paper, published in Science, is available here. The real meat, including a pretty graph, is located in the Supplemental Online Text (SOM), available here.

Haq and Schutter (2008) produce a series of designated "Reference Districts", which in reality represent composite stratigraphic sections for the time intervals in questions; this is a necessity, as Paleozoic rocks are commonly seriously eroded and possibly deformed, required multiple stratigraphic sections to transect a larger chuck of time. These reference districts span the world, and are taken from the literature; the SOM details these and their references. Additionally, the authors identify Ancillary Sections, which are not in Reference Districts, but show the same interpreted sequences and surfaces.

Anyway, without further ado, below is their pretty Paleozoic Sea-Level Curve; both the figure and text are from the SOM to Haq and Schutter (2008):


To summarize the curve, Haq and Schutter identify a long-term sea-level trend that shows a gradual rise through the Cambrian, a zenith in the Late Ordovican, a rapid, short-lived sea-level low related to Hirnantian (~445 Mya) glaciation, with subsequent (though smaller) highs in the mid-Silurian, the Middle/Late Devonian, and in the Latest Carboniferous, and lows interpreted in the early Devonian, the Mississippian/Pennsylvanian boundary, and in the Late Permian. Overall magnitude of the 170+ eustatic events is interpreted by the authors to range from a few meters to ~125 m.

The authors do acknowledge a couple of potential issues with their work: first and foremost, they are very up-front about the difficulty of interpreting magnitudes of change from the rocks, particularly from aerally disparate outcrops with often complex unconformity relationships. The authors also recognize the difficulty of chronostratigraphic and geochronological calibrations, particularly given that the biostratigraphy of these sections is often complex and dominated by endemic, restricted faunas.

Haq and Schutter also cut-off one of the loudest (and, in some ways, most damning) criticisms made for the Haq et al. (1987) curve: the availability for reexamination of the data used in the analysis. The Triassic and younger curve was commonly criticised for the proprietary seismic data used to calibrate coastal onlap; in other words, you kind of had to take the authors' word on their interpretations, because Exxon sure wasn't going to hand over the data. In this 2008 paper, however, Haq and Schutter make a special point of noting that these sections are "public-domain", in that they are freely accessible to other workers who want to go look at them.

Admirable though that recognition may be, the fact of the matter is that this opens up other problems. Namely, this work is a meta-analysis, and therefore, subject to all the prejudices and problems that sort of broad-brush examination are subject to. In the SOM, Haq and Schutter cite 82 primary sources for their Reference Districts (which form the core of their interpretations), and a subsequent 192 for their Ancillary Sections. While that's a lot of papers, a perusal of the work shows a dominance of North American sections, with Australian sections coming in a close second. The statistical significance of the dataset is therefore complicated by the geographic and temporal distribution of the sections, which are already on the low end for a global synthesis anyway. At some point, we as a discipline are going to have to ask ourselves about the suitability of meta-analyses for geological or stratigraphic studies.

Furthermore, the old "tectonically quiescent" thing is a problem, particularly given the publication of a couple of papers that specifically refute the existence of such settings at the applicable time-scales (specifically, Cogne and Humler, 2008 and Moucha et al., 2008, both in EPSL). The argument for these settings always comes off as a little circular: we get a eusatic sea-level curve, so these settings must be tectonically quiet, right? Given the problems with actually backstripping some of these settings (which, to their credit, Haq and Schutter do acknowledge), the attribution of accommodation creation to eustasy seems suspect.

The biggest potential hurdle, to me at least, seems to be deconvolving the accommodation curve from the sediment supply curve; simple changes in sediment delivery to the coast can produce a coastal onlap curve. Without at least mentioning it, let alone actually interrogating the potential impact on your curve, I really can't suss out how important a factor it is in your sections. This was the point of Christie-Blick (1991), which seems to be a constantly unanswered challenge to these onlap curves.

There is obviously a very interesting story to be found in the record of Phanerozoic sea-level changes; the fact that many of these studies have found inexplicable high-frequency, high-magnitude changes during decidedly non-glacial phases suggests that there are still poorly understood depositional and stratigraphic principles out there (though these MAY be of the sed supply:accommodation ratio nature, rather than any crazy unknown water cycle issue). Also, the utility of accurately and unequivocally pinning down the history of eustatic sea level changes has important implications across a variety of earth science disciplines. Here's hoping that this work re-energizes the community!

Saturday, October 25, 2008

Tree vs Rock

The eternal struggle between rocks and their mortal enemies, plants, continues in the battleground of Providence Canyon, GA.

Trees!

Geotripper shared a picture of a lovely, Middle-Earthish tree in the midst of Yosemite Park, while Clastic Detritus showed a picture of some Brushy Canyon vintage Madrone, so I reckon I'll just share a picture of my favorite tree: The Juniper.



I like junipers for two reasons. One, if you see them, then you are Probably somewhere close to some good rocks, which is always good news.



Second, I like Junipers because you can make gin from their berries.

Junipers: are they the best trees? They just might be.

EDIT: Holy Smokes! So Many Pictures of Trees!

Monday, October 20, 2008

Neoichnology II: Revenge of the Scorpion

While organizing my geo-picture collection, I ran across a Death Valley picture I hadn’t shared that ALSO tied in with the whole neoichnology trend from yesterday. The picture below is from the dune field in Death Valley, and shows a scorpion track left in a fine-grained sand substrate:


You can see the somewhat confusing scratch marks along either side of the trail; I guess having several pairs of legs skittering away all at once makes for some convoluted footprints. The central furrow in the trackway is from the tail. I’ve been told, though I’d have to look up a cite to be sure, that scorpions commonly only produce tail-dragging marks at night (or when it’s cool and shady), and will hold their tails up off the ground during the day. Thus, in SOME cases, you might be able to tell whether it’s night/day in the rock record depending on the scorpion trace fossil.

Seeing this picture again reminded me of a paper I had read a while back. Davis et al. (2007) wrote up a pretty nice summary paper of some experimental work on the neoichnology of some modern terrestrial arthropods. The point of their work was to investigate the effect of substrate conditions on both the morphology and taphonomy of the resultant traces. They used a variety of trace-making bugs (including Giant African Millipedes, Cockroaches, Tarantulas, Woodlice, and some Emperor Scorpions) to investigate the generalized range of bug bauplans, and they used a range of grain-sizes and moisture content to simulate varying substrate conditions, producing two taphoseries: A dry- to dampground series, meant to mimic fully subaerial conditions, and a soft- to firmground, meant to mimic a transitional state similar to a recently flooded overbank setting.

The approach used to produce the substrates was one I had never encountered in the literature before, and seemed fairly rigorous. For the subaerial setting, they simply sprayed an amount of water onto the substrate, and then the critter walked across it. For the transitional setting, though, they put 2 cm of sediment into the tray, removed it, filled the tray with 2.5 cm of water, and then sprinkled the sediment back into the tray. After allowing it to stand overnight, the siphoned off the water, and then proceeded to dump the animals into the experimental setup at regular intervals after the siphoning (0 mins, 60-75 min, 120-150 min).

The picture below is taken from Davis et al (2007; p. 292), and shows the dry to damp series for the Scorpion:


This picture is from Davis et al (2007; p. 293) and shows the soft- to firmground series:


The authors conclude that the increasing firmness of the substrate, related mostly to moisture content, exerted the largest control on the resultant morphologies. Overall, the authors saw a decrease in track width (or track row width) with increasing moisture. They also found, unsurprisingly, that big heavy animals make the best, most preservable trackways in these conditions.

The potential utility of the work is pretty interesting: maybe we could make interpretations of substrate moisture content, qualitatively at least, in some very special trackway settings, letting us get into some nitty gritty paleoenvironmental interpretations. Of course, all the old caveats would apply, least of which not being the fact that we don’t really KNOW how big the animal was or its specific physiology. Still, Davis et al. (2007) suggest a good starting point for this sort of work, and I think make a good case for the importance of careful neoichnological research and its potential impact to sedimentary geology.

WORKS CITED:

Davis, R.B., Minter, N.J., Braddy, S.J., 2007, The neoichnology of terrestrial arthropods: Palaeogeography, Palaeoclimatology, Palaeoecology, v. 255, p. 284-307.

Sunday, October 19, 2008

Neoichnology

Wandering around the autumnal woods here, I ran across a muddy little puddle that had been visited by at least a couple of different kinds of critters. You can clearly see the weird, hand-like footprints of a raccoon, as well as a the huge footprint of an extant therapod known for it's deliciousness (a turkey). Beercap I had in my pocket for scale.



This little puddle must have been a busy place; lots of animals had stopped by for a visit. Of course, if I was feeling snarky, I might make a joke at the expense of some dinosaur track people (about the Raccoon actively stalking the turkey, who had fled in terror from its masked foe). But, I'm not felling snarky, so I won't.

On an unrelated note, is it just me, or does everyone else out there ALWAYS want to somehow ensure animal tracks get preserved? Like dump a bunch of sand on em or something, so they enter the record. Whence comes this weird compulsion, I wonder?

Tuesday, October 14, 2008

OzCoasts

For a bunch of debtors and criminals, those Australians can put together some slick online Sciencey type resources, man. I just found this online: OzCoasts, which is a huge database of coastal environments, including much of the geomorphic, meteorological, biological, and geological data from something like 780 coastal waterways in Australia. These data are all searchable, so it seems to be a pretty powerful set of tools for looking at a variety of environments.

They also have a pretty impressive library of general block diagrams and coastal system models, tailored for specific settings, and detailing any number of attributes, including hydrodynamics, depositional environments, and critters living in the setting. Furthermore, you can make your own block diagram, which is actually a pretty handy little tool for quickly whipping up a diagram for class. There are also whole lot of "Coastal Indicator Factsheets", including sections on sea-level rise, sediment quality, and habitat issues (among other things).

Also, they have some very nice interactive 3-D models of several localities, including Cockburn Sound and Sydney Harbor, which are both areas where a lot of work has been done. These maps include CHIRP derived bathymetry and sub-surface data, as well as details on grab-cores and samples from these localities.

All in all, there is a lot of stuff to look at on this site, and it would serve as a nice model for other databases for other geographic (or geomorphic) settings. Someone should really get on that.

Anyway, just so this isn't only text, here's a picture (from NASA WorldWind) of the Gascoyne River Delta:


And here's an unknown river a little south of the Gascoyne, winding its way through some dunes.

Apparent Dip: Blog of Note

Congratulations to Apparent Dip, who is the "Blog of Note" as awarded by Blogger for October 14, 2008. Now that you're famous, I hope you can still find the time to blog...

I wonder what you win?

Saturday, October 11, 2008

Fish Five Miles Down

The "deepest ever fish on film" was mentioned on the NPR website recently, and I thought I'd pass it along so that everyone could start celebrating early. The fish, a Liparid (or Snailfish) lives at around 7,700+ meters (that's nearly 5 miles) down in the Japan Trench.



The footage was taken by a "free-form lander", which is described in the news story as being some sort of a lunar lander type of device that they just hork off the side of the ship and come back for later. It's a weird looking fish, and some of the footage is available for viewing.

Thursday, October 9, 2008

Wyoming Vista

Just a little picture to cleanse the Thursday-afternoon palate, straight from Wyoming to the interblogospherenet.

Tuesday, October 7, 2008

Earth Science Literacy

So the first Draft of the Earth Science Literacy Document is up and available for comments (right...HERE). This is an NSF-supported effort meant to explicitly spell-out the state of our knowledge of the Earth in a way that everyday, non-specialist citizens can understand. Effectively, it's a list of the Things Folks Should Know About the Earth, and is meant to go along with all the Ocean, Climate, and Atmosphere Literacy work that was recently undertaken.

Anyway, the document identifies 8 Big Ideas in the Earth Sciences, which I've summarized below. These ideas are supplemented by a series of Supporting Concepts that flesh out the overarching concept. The 8 Big Ideas (paraphrased) are:

1) Earth is 4.6 Ga, and the rock record contains its history.

2) Earth is a complexly interacting system

3) Earth is a continuously changing planet

4) Earth is the Water Planet

5) Life evolves in concert with the evolving Earth, and similarly modifies and effects the Earth in turn.

6) Humans depend on Earth for Resources

7) Earth Science helps us understand and mitigate natural disasters

8) Humans are a significant agent of change on the Earth

It's a pretty nice list, in my opinion, and would make a great hand-out in an undergrad intro class. I also like how the foundational concepts of Plate Tectonics and Evolution are distributed throughout the supporting points, driving home the unifying power of both of these fundamental concepts.

The only (vague) comment that I have would be that I'd like to see maybe a little more about radioactive decay and radiometric dating. Maybe not as a BIG IDEA, but as another supporting point (somewhere, maybe under #1?).

Importantly, this is only a draft, and if you've got any concerns or issues or burning bits of illumination to add, we have until Oct 31 to make comments, so get to it!

I'd also be more than happy to hear what you guys think about it too, of course.

EDIT: Here are some links to chew on! The Ocean Literacy Network, and their Ocean Literacy Statement; The Atmospheric Science Literacy Framework and their Statement; and the Climate Program Network, and their statement! Whew! That's a lot of statements!

Community Sedimentary Model for Carbonate Systems

I'm sure everyone has already read up on the CSDMS from the most recent "Sedimentary Record", but I thought I'd post a link to their website right here. It has some fairly slick pdfs of the talks, posters, and Working Group Summaries, which make for some pretty nice bleeding-edge "State of the Strata" resources for Carbonate naifs (like myself). Though it's not up yet, the Group says they hope to have a PDF copy of the resultant white paper up soon, so stay tuned!

Thursday, October 2, 2008

Sarah Palin - Dinosaur Rider

Ron Numbers, a scholar who studies the History of Science and Religion, and author of The Creationists, has a pretty nifty little assessment of Palin's creationist bullshit.


Enjoy!

Wednesday, October 1, 2008

Kinematic Theory of Unsteady Seperation

One of the problems with so much of our understanding of hydrodynamics (and, more broadly, all Earth Processes) is that we have to make so many damn generalizations and simplifications. Of course these are important first steps in developing greater insight into the world, but sometimes, you just want to have a firm grasp on what the hell is going on, you know?

Two recent papers, Weldon et al. 2008 and Lekien and Haller 2008, have made some impressive advances in our ability to describe and predict flow separation under unsteady conditions; the ramifications of this are pretty big, and if you've got a secret love of hydrodynamics (like me), it's pretty exciting stuff!

Fundamentally, flow separation occurs where a fluid is moving away from a solid boundary of some sort. In sedimentology, this is commonly illustrated by the behavior of a fluid flowing over a bedform, such as a dune in a river. While we have always had a general, qualitative appreciation of the effects of flow separation on bedform dynamics (i.e., back-flow eddies in the lee-sides of dunes, Kelvin-Helmholz instabilities in turbidity currents, etc), a quantitative description of the behavior has been lacking; as such, modeling these systems is difficult, and requires some arm-waving.

In fact, the nearest thing we've had to a kinematic solution for flow separation was Prandtl 1904. Using some mind-bogglingly complex math, ol' Prandtl was able to come up with a solution for laminar boundary separation in steady 2-D flows. Sentences like the previous one make sedimentologists involuntarily twitch: "laminar" and "steady" are both exceedingly rare in the natural world, making Prandtl's work useful for gross generalizations, but frustratingly weak in unsteady and turbulent flows.

Now, however, Weldon et al. and Lekien and Haller have both shown numerical and -most importantly- EXPERIMENTAL data that advances a kinematic theory of unsteady separation, allowing us to accurately predict separation points in unsteady flows. Furthermore, part of Weldon et al. (2008)'s work has shown that their kinematic theory accurately predicts flow separation in flows that are kinematically equivalent to turbulent flows.

Lekien and Haller (2008) also apply this particular kinematic theory to boundary separation models of the North Atlantic geostrophic current AND to boundary current separation and reattachment in Monteray Bay, based on field data collected from real live currents.

The public take on this (see here for MIT's own press release on the research) is focused on larger, non-geologic issues, such as increasing fuel efficiency by decreasing shear drag on cars. However, for selfish reasons, it will be particularly exciting to see where this sort of research leads to in the sed realm. We might finally start to home in on some robust models of mixing layer dynamics in sediment laden flows, or even (bestill my heart!) start being able to really interrogate bedform morphodynamics and evolution under realistically complex flow conditions!

WORKS CITED:

Weldon, M., Peacock, T., Jacobs, G.B., Helu, M., and Haller, G., 2008, Experimental and numerical investigation of the kinematic theory of unsteady separation: Journal of Fluid Mechanics, v. 611, p. 1 - 11.

Lekien, F., and Haller, G., 2008, Unsteady flow separation on slip boundaries: Physics of Fluids, v. 20