Volcán Reventador s Unusual Umbrella

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1 Volcán Reventador s Unusual Umbrella Pinaki Chakraborty, 1 Gustavo Gioia, 1 and Susan Kieffer 2 1 Department of Theoretical and Applied Mechanics, University of Illinois, Urbana, IL 61801, USA 2 Department of Geology, University of Illinois, Urbana, IL 61801, USA Photographs of a volcanic column in a recent eruption of Reventador show a prominently scalloped umbrella that is unlike any umbrella previously documented on a volcanic column. We propose that the scallops in this umbrella are the result of a turbulent Rayleigh Taylor instability with no precedents in volcanology. We ascribe the rare negative buoyancy that drives this instability to the fact that the Reventador column fed on a cool co-ignimbrite cloud. From the wavelength of the scallops, we estimate a value for the eddy viscosity of the umbrella, the first such value to be inferred directly from an observation in the field, and show that this value is consistent with a lower bound obtained previously by a disparate method. Last, we discuss the implications of our results for volcanic eruption dynamics and hazards. We hope this work will prompt and guide the documentation of other scalloped umbrellas. Volcán Reventador (Spanish for One that explodes ), 100 km from Quito, Ecuador, erupted cataclysmically on November 3, After seven hours of seismic activity and a steam phase, at 9:12 a.m. local time the eruption sent a towering Plinian column 17 km into the stratosphere (figure 1) and a pyroclastic flow 9 km down valleys (1). The pyroclastic flow caused severe To whom correspondence should be addressed; skieffer@uiuc.edu 1

2 damage to principal petroleum pipelines; the attendant co-ignimbrite (2) clouds and the columns that fed on them provided sufficient ash to close the Quito airport for 10 days (1). One of these columns displayed a peculiar, scalloped umbrella (figure 2). Scalloped umbrellas have not previously been reported in the volcanology literature to our knowledge. The usual volcanic column (figures 1 and 3a) as well as the usual nuclear-test column (figure 3b) consists of a stalk capped with an umbrella. The umbrella forms when the fluid in the stalk reaches neutral buoyancy, possibly with some overshooting in the center of the rising column (Figure 3c). The outer shape of the umbrella reflects a toroidal circulation (figure 3d) that draws ambient air in from the atmosphere at the bottom of the stalk and forces mixing of the ambient air with hotter, less dense fluid inside the ascending stalk (3). In most cases, the surface of the umbrella develops a knuckled or cauliflowered texture (figure 3). In contrast, on the Reventador column of figure 2 the umbrella was scalloped orthogonal to the plane of the toroidal circulation. Dimensions are difficult to ascertain from the eyewitness photos available to us, but the photograph of figure 2c allows for rough measurements (4). On the basis of these measurements, we estimate the diameter of the umbrella as 3.5 km (perhaps 3.5 ± 2.5 km in a very pessimistic scenario (4)), its half circumference as 5.5 km, and 8 scallops per half circumference, giving a scallop wavelength of about 0.7 km (perhaps 0.7 ± 0.5 km in a very pessimistic scenario). Further, we estimate the thickness of the umbrella as 0.9 km, the diameter of the stalk as 1 km, and the amplitude of the scallops as several hundred meters. The explanation proposed here is not affected by the likely uncertainties in these quantities. We ascribe the scalloped structure of the Reventador umbrella to the occurrence of a turbulent Rayleigh Taylor (RT) instability (5, 6) on the bottom surface of the umbrella. The instability occurs along the outer rim of the umbrella if the ashy suspension there is denser that the ambient air under the umbrella. By turbulent RT instability we mean an RT instability that is 2

3 governed by the eddy viscosity of the umbrella. (Note that the umbrella is already turbulent at the onset of the instability.) The turbulent RT instability appears to have no precedents in volcanology, but it has long been known in the atmospheric sciences, for example (7). We present an analysis that shows that the conditions necessary for such an instability are consistent with those likely in the Reventador column, given the geologic conditions of the eruption. The RT instability of the interface between a layer of denser fluid that tops a layer of lighter fluid may occur at all wavelengths. Nevertheless, the rate of growth of the instability is maximum for a wavelength (8) λ = 4π ( ν 2 ) 1/3 α, (1) where ν (µ d + µ l )/(ρ d + ρ l ), α (ρ d ρ l )/(ρ d + ρ l ), µ d is the viscosity of the denser fluid, µ l is the viscosity of the lighter fluid, ρ d is the density of the denser fluid, ρ l is the density of the lighter fluid, and g is the gravitational acceleration. The characteristic time associated with the wavelength of (1) is τ = g ( ) 1/3 ν (2) g 2 α and represents the time required for the RT instability to become manifest. In the case of interest here we assume that µ d (i.e., the viscosity of the umbrella) is much larger than µ l (i.e., the viscosity of the ambient air). In addition, we assume that along its outer rim the umbrella is denser than the ambient air, and write ρ ρ d ρ l and ρ d + ρ l 2ρ d. With these assumptions we have ν µ d /(2ρ d ) = ν d /2, where ν d is the kinematic viscosity of the umbrella, and α ρ/(2ρ d ), and (1) and (2) become λ 2π ν2/3 d g 1/3 ( ρ ρ d ) 1/3 and τ ν1/3 d g 2/3 ( ) 1/3 ρ. (3) Now we consider the quantity ( ρ/ρ d ) 1/3 that appears in (3). A positive value of ρ/ρ d signifies that the outer rim of the umbrella is negatively buoyant. As a result of the cubic root, even a modest value of ρ/ρ d leads to a value of ( ρ/ρ d ) 1/3 of order 1. (For example, 3 ρ d

4 ρ/ρ d = 0.1 leads to ( ρ/ρ d ) 1/3 0.5.) Nevertheless, the outer rim of the umbrella must be negatively buoyant, at least to a small degree, or there would be no driving force to propel the RT instability. With this assumption in place, we can set ( ρ/ρ d ) 1/3 1 in (3). Next we consider the kinematic viscosity ν d in the context of a turbulent RT instability. If the umbrella is turbulent, it is populated by turbulent eddies in a vast range of lengthscales. These turbulent eddies can effect momentum transfer and therefore endow the umbrella with an eddy viscosity (9). (To visualize the origin of the eddy viscosity, imagine a vertical plane bisecting the umbrella and one side of the plane being sheared downwards with respect to the opposite side; this is the sort of shearing required to form scallops. Then, the turbulent eddies provide currents orthogonal to the plane, thereby sewing the two sides of the plane together. Thus the eddies resist the shearing motion, much as a stitch prevents two pieces of cloth from sliding relative to one another (10).) The largest turbulent eddies have a size comparable with the thickness of the umbrella (which we denote by h) and can be identified with the toroidal circulation of figure 3d. These eddies dominate the momentum transfer and therefore the eddy viscosity (11). If we denote the characteristic velocity of the largest eddies by v, we can estimate the eddy viscosity as ν d vh (11), the dominant wavelength as λ 2π(vh) 2/3 /g 1/3, and the characteristic time as τ (vh) 1/3 /g 2/3. To obtain λ 0.7 km (the wavelength observed in the Reventador umbrella) we must have an eddy viscosity of about 4, 000 m 2 /s (12). This value of eddy viscosity is consistent with a lower bound, 200 m 2 /s, obtained by Wohletz by a disparate method (13, 14). The attendant velocity of the largest turbulent eddies is v 5 m/s (for h 0.9 km). The characteristic time is τ 5 s. From the previous paragraph, we conclude that scallops of a wavelength comparable with the wavelength of the Reventador umbrella can form in a suitably short time if the largest eddies in the umbrella are sufficiently fast, with a characteristic velocity of several meters per second. 4

5 Note that the characteristic velocity of the largest eddies scales with the turbulent power per unit mass, i.e., with the rate of production of turbulent energy per unit mass, denoted by ɛ, in the form v (hɛ) 1/3 (11). Volcanic columns are invariably very turbulent and can, in principle, develop scalloped umbrellas as prominent as Reventador s. Yet most volcanic columns do not develop scalloped umbrellas (e.g., figures 3a and c), because in most volcanic columns the outer rim of the umbrella remains neutrally buoyant. In fact, if the fluid rising in the stalk is superheated steam, if the particle loading is light, or if the entrained particles are hot and transmit heat to the vapor phase, for example, then the umbrella can undergo an extensive lateral expansion while its outer rim remains neutrally buoyant (15). On the other hand, the occurrence of a scalloped umbrella requires that the outer rim of the umbrella become negatively buoyant. As we have seen, the increase in relative density, ρ/ρ d, need only be moderate but there must be a loss of neutral buoyancy, or the umbrella will not form scallops. The rarity of scalloped umbrellas indicates that some unusual conditions must have prevailed in the Reventador column of figure 2, leading to a ready loss of neutral buoyancy. We propose that the Reventador column was unusually dense and cool. The eruption of 9:12 a.m. was a steam-driven eruption that entrained cool lithic material from the destruction of a summit cone. The material was sufficiently dense that it formed pyroclastic flows that ran down the slopes of the volcano. Some of the ash was partitioned into the co-ignimbrite column that displayed the scalloped umbrella. We conclude that scalloped umbrellas may be more common on co-ignimbrite columns or mixed co-ignimbrite-plinian columns than on Plinian columns without surrounding pyroclastic flows. Explosive phreatic or vulcanian eruptions might also meet the criteria required for a cool, dense umbrella and therefore for a scalloped umbrella. Nevertheless, these types of eruption often last for only a fraction of a second. Thus the absence of any reports of scalloped umbrellas on columns from phreatic or vulcanian eruptions may be due to the duration of such eruptions, which is too short compared with the characteristic time 5

6 of a turbulent RT instability. The fate of the scalloped umbrella subsequent to the photographs of figure 2 was not documented (but may eventually be revealed by field studies of the ash deposits). Our analysis suggests, however, that the umbrella could have collapsed back to the ground, forming yet more pyroclastic flows. Such flows would originate at a fallback point quite far removed (kilometers?) from the center of the eruption and could have possessed considerable initial momentum. Furthermore, they could be obscured as the eruption progresses. These likely scenarios should be considered as mapping of deposits is conducted, and in hazards planning. References and Notes 1. M. Hall, P. Ramon, P. Mothes, J. LePennec, A. Garcia, P. Samaniego, H. Yepes, Revista Geológica de Chile 31, 349 (2004). 2. A pyroclastic flow is a dense ash-laden gas cloud that descends from an erupting volcanic vent. A co-ignimbrite cloud forms from ash and gas sheared from the top of the descending pyroclastic flow. The co-ignimbrite cloud is sheared back toward the center of the eruption and may co-mingle with directly ascending material. See, e.g., R. S. J. Spars, G. Walker, J. Volcanology Geothermal Res. 2, 329 (1977). In the case of Reventador, the co-ignimbrite cloud hovered at lower elevation than the rapidly ascending buoyant cloud rising from the center of the eruption. (See (1) for a description of the eruption.) 3. S. Glasstone, P. J. Dolan, The Effects of Nuclear Weapons, 3rd edition (Department of Defense, 1977). 4. We estimate H = 1.75 m and h = 1 m (figure 2c). The distance d from the soldier standing on the pipeline to the soldier leaning on the pipeline coincides with the radius of the pipeline, d = 0.5 m, and the distance from the pipeline to the Reventador cone is = 7 km. Since 6

7 on the photograph H and D (the diameter of the umbrella) look the same and equal to 1.5h, we can write (D H)/ = (H 1.5h)/d and therefore D = (H 1.5h) /d + H (H 1.5h) /d = 3.5 km. To estimate an upper bound of the error we differentiate D (H 1.5h) /d to obtain δd/d ( /Dd) [(δh 1.5δh) + (H 1.5h)(δ / δd/d)]; then we assign the same value, ε, to the relative errors δh/h, δh/h, δ /, and δd/d, and assume a very pessimistic scenario, δh/h = δh/h = δ / = δd/d = ε, with the result δd/d ε( /Dd)(3H 1.5h). By setting ε = 0.05, we estimate δd/d 0.75 or D = 3.5 ±2.5 km (in a very pessimistic scenario). By applying the same error to our estimate of the wavelength, we obtain λ = 0.7 ± 0.5 km (in a very pessimistic secenario). 5. G. I. Taylor, Proc. Roy. Soc. A201, 192, (1950). 6. D. H. Sharp, Physica D 12, 3 (1984). 7. E. M. Agee, Journal of the Atmospheric Sciences 32, 642 (1975). 8. See, e.g., S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Dover, 1981). To grasp the physics of the RT instability, imagine that the initially horizontal interface between the fluids (y = 0 for all x) becomes sinusoidal, so that y = a sin(2πx/λ) and ẏ = ȧ sin(2πx/λ), where a is the amplitude of the instability and ȧ its rate of growth. A sinusoidal interface implies that lighter fluid moves up and denser fluid moves down, and therefore that the gravitational field yields energy. Now this energy is partly dissipated viscously and partly transformed into kinetic energy; by studying the associated equation of conservation of energy, it is possible to show that ȧ is maximum for a specific wavelength λ the wavelength given by (1). 9. H. Tennekes, J. L. Lumley, A First Course in Turbulence (MIT Press, Boston, Mass, 1972). 7

8 10. The molecular viscosity works in a similar way (9), only that the currents normal to the plane are diffusive currents, and therefore much weaker than the currents provided by the turbulent eddies unless there is no turbulence, in which case the molecular viscosity is the only available viscosity. 11. L. D. Landau, E. M. Lifshitz, Fluid Mechanics 2nd edition, ch. III (Butterworth, Oxford, UK, 2000). 12. Note that this value of the eddy viscosity is quite large. For comparison, the molecular viscosity of water is 10 9 times smaller. It is apparent that any feasible molecular viscosity could only give a wavelength orders of magnitude smaller than the observed wavelength. We conclude that the relevant viscosity cannot be the molecular viscosity: to account for the observed wavelengths, there must be turbulence, fast turbulent eddies, and the attendant eddy viscosity. 13. G. A. Valentine, K. H. Wohletz, J. Geophys. Res. 94, 1867 (1989). 14. K. H. Wohletz estimated an eddy velocity of 10 m/s for the Plinian column at Mount St. Helens and used equation (5) in (13) to obtain the lower bound of 200 m 2 /s (personal communication, 2005). 15. A common example is afforded by a meteorological cloud, which can be thought of as a vast umbrella that remains neutrally buoyant for extended periods of time (but may on accasion undergo a turbulent RT instability leading to the formation of mammatus pouches; see (7)). 16. We thank Steve Marshak for calling our attention to a photograph of Reventador s fascinating column. 8

9 Figure 1: The larger Reventador volcanic column at 09:12 hours November 03, 2002, reaching km high, viewed from Lago Agrio, 90 km to the east of the eruption site on which this column grew. Photographer unknown. Note the light-colored, steam-rich column. 9

10 (a) D H (b) (c) h (d) Figure 2: Reventador co-ignimbrite column with scalloped umbrella. The co-ignimbrite cloud on which this column fed was just forming at the base of the larger column of figure 1. (a) Photograph by Armando Alvarez Sánchez, Cruz Roja Ecuatoriana. (Permission to publish under request.) FOR ENLARGED VERSION SEE PAGE 12. (b) Photograph by R. Saca, taken from a construction camp approximately 8 km from the erupting cone. (Permission to publish under request.) FOR ENLARGED VERSION SEE PAGE 13. (c) Photograph by John Fisher, at (Permission to publish under request.) We use the segments marked D, H and h to perform measurements; see (4). (d) Scallop. Photographer unknown. 10

11 (a) (c) (b) (d) Figure 3: (a) Plinian volcanic column over Mount St. Helens. Photographer unknown. (b) Nuclear-test column, Ivy-Mike, Photograph U.S. Government. Photographer unknown. (c) Classical lithograph titled The Eruption of Vesuvius as Seen from Naples, October 1822, from V. Day & Son. (d) Toroidal circulation. Adapted from (3). 11

12 Enlarged version of figure 2a. 12

13 Enlarged version of figure 2b. 13

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17 List of Recent TAM Reports No. Authors Title Date 989 Riahi, D. N. On stationary and oscillatory modes of flow instabilities in a rotating porous layer during alloy solidification Journal of Porous Media 6, 1 11 (2003) 990 Okhuysen, B. S., and Effect of Coriolis force on instabilities of liquid and mushy regions D. N. Riahi during alloy solidification Physics of Fluids (submitted) 991 Christensen, K. T., and R. J. Adrian Measurement of instantaneous Eulerian acceleration fields by particle-image accelerometry: Method and accuracy Experimental Fluids (submitted) 992 Liu, M., and K. J. Hsia Interfacial cracks between piezoelectric and elastic materials under in-plane electric loading Journal of the Mechanics and Physics of Solids 51, (2003) 993 Panat, R. P., S. Zhang, Bond coat surface rumpling in thermal barrier coatings Acta and K. J. Hsia Materialia 51, (2003) 994 Aref, H. A transformation of the point vortex equations Physics of Fluids 14, (2002) 995 Saif, M. T. A, S. Zhang, A. Haque, and K. J. Hsia 996 Fried, E., and M. E. Gurtin Effect of native Al 2 O 3 on the elastic response of nanoscale aluminum films Acta Materialia 50, (2002) A nonequilibrium theory of epitaxial growth that accounts for surface stress and surface diffusion Journal of the Mechanics and Physics of Solids 51, (2003) 997 Aref, H. The development of chaotic advection Physics of Fluids 14, (2002); see also Virtual Journal of Nanoscale Science and Technology, 11 March Christensen, K. T., and The velocity and acceleration signatures of small-scale vortices in R. J. Adrian turbulent channel flow Journal of Turbulence, in press (2002) 999 Riahi, D. N. Flow instabilities in a horizontal dendrite layer rotating about an inclined axis Journal of Porous Media, in press (2003) 1000 Kessler, M. R., and S. R. White Cure kinetics of ring-opening metathesis polymerization of dicyclopentadiene Journal of Polymer Science A 40, (2002) Point defects in nematic gels: The case for hedgehogs Archive for Rational Mechanics and Analysis 177, (2005) 1001 Dolbow, J. E., E. Fried, and A. Q. Shen 1002 Riahi, D. N. Nonlinear steady convection in rotating mushy layers Journal of Fluid Mechanics 485, (2003) 1003 Carlson, D. E., E. Fried, The totality of soft-states in a neo-classical nematic elastomer and S. Sellers Journal of Elasticity 69, (2003) with revised title 1004 Fried, E., and Normal-stress differences and the detection of disclinations in R. E. Todres nematic elastomers Journal of Polymer Science B: Polymer Physics 40, (2002) 1005 Fried, E., and B. C. Roy Gravity-induced segregation of cohesionless granular mixtures Lecture Notes in Mechanics, in press (2002) 1006 Tomkins, C. D., and Spanwise structure and scale growth in turbulent boundary R. J. Adrian layers Journal of Fluid Mechanics (submitted) 1007 Riahi, D. N. On nonlinear convection in mushy layers: Part 2. Mixed oscillatory and stationary modes of convection Journal of Fluid Mechanics 517, (2004) 1008 Aref, H., P. K. Newton, M. A. Stremler, T. Tokieda, and D. L. Vainchtein 1009 Bagchi, P., and S. Balachandar 1010 Zhang, S., R. Panat, and K. J. Hsia Nov Dec Dec Dec Jan Jan Jan Jan Jan Jan Feb Feb Feb Mar Mar June 2002 July 2002 Aug Sept Vortex crystals Advances in Applied Mathematics 39, in press (2002) Oct Effect of turbulence on the drag and lift of a particle Physics of Fluids, in press (2003) Influence of surface morphology on the adhesive strength of aluminum/epoxy interfaces Journal of Adhesion Science and Technology 17, (2003) Oct Oct. 2002

18 List of Recent TAM Reports (cont d) No. Authors Title Date 1011 Carlson, D. E., E. Fried, On internal constraints in continuum mechanics Journal of and D. A. Tortorelli Elasticity 70, (2003) 1012 Boyland, P. L., Topological fluid mechanics of point vortex motions Physica D M. A. Stremler, and 175, (2002) H. Aref 1013 Bhattacharjee, P., and Computational studies of the effect of rotation on convection D. N. Riahi during protein crystallization International Journal of Mathematical Sciences, in press (2004) 1014 Brown, E. N., In situ poly(urea-formaldehyde) microencapsulation of M. R. Kessler, dicyclopentadiene Journal of Microencapsulation (submitted) N. R. Sottos, and S. R. White 1015 Brown, E. N., S. R. White, and N. R. Sottos 1016 Kuznetsov, I. R., and D. S. Stewart 1017 Dolbow, J., E. Fried, and H. Ji Microcapsule induced toughening in a self-healing polymer composite Journal of Materials Science (submitted) Burning rate of energetic materials with thermal expansion Combustion and Flame (submitted) Chemically induced swelling of hydrogels Journal of the Mechanics and Physics of Solids, in press (2003) 1018 Costello, G. A. Mechanics of wire rope Mordica Lecture, Interwire 2003, Wire Association International, Atlanta, Georgia, May 12, Wang, J., N. R. Sottos, Thin film adhesion measurement by laser induced stress waves and R. L. Weaver Journal of the Mechanics and Physics of Solids (submitted) 1020 Bhattacharjee, P., and Effect of rotation on surface tension driven flow during protein D. N. Riahi crystallization Microgravity Science and Technology 14, (2003) 1021 Fried, E. The configurational and standard force balances are not always statements of a single law Proceedings of the Royal Society (submitted) 1022 Panat, R. P., and K. J. Hsia 1023 Fried, E., and M. E. Gurtin Experimental investigation of the bond coat rumpling instability under isothermal and cyclic thermal histories in thermal barrier systems Proceedings of the Royal Society of London A 460, (2003) A unified treatment of evolving interfaces accounting for small deformations and atomic transport: grain-boundaries, phase transitions, epitaxy Advances in Applied Mechanics 40, (2004) On similarity waves in compacting media Horizons in World Physics 244, (2004) 1024 Dong, F., D. N. Riahi, and A. T. Hsui 1025 Liu, M., and K. J. Hsia Locking of electric field induced non-180 domain switching and phase transition in ferroelectric materials upon cyclic electric fatigue Applied Physics Letters 83, (2003) 1026 Liu, M., K. J. Hsia, and M. Sardela Jr. In situ X-ray diffraction study of electric field induced domain switching and phase transition in PZT-5H Journal of the American Ceramics Society (submitted) 1027 Riahi, D. N. On flow of binary alloys during crystal growth Recent Research Development in Crystal Growth, in press (2003) 1028 Riahi, D. N. On fluid dynamics during crystallization Recent Research Development in Fluid Dynamics, in press (2003) 1029 Fried, E., V. Korchagin, Biaxial disclinated states in nematic elastomers Journal of Chemical and R. E. Todres Physics 119, (2003) 1030 Sharp, K. V., and Transition from laminar to turbulent flow in liquid filled R. J. Adrian microtubes Physics of Fluids (submitted) 1031 Yoon, H. S., D. F. Hill, Reynolds number scaling of flow in a Rushton turbine stirred tank: S. Balachandar, Part I Mean flow, circular jet and tip vortex scaling Chemical R. J. Adrian, and Engineering Science (submitted) M. Y. Ha Oct Oct Feb Feb Feb Mar Mar Mar Apr Apr Apr May 2003 May 2003 May 2003 May 2003 May 2003 May 2003 July 2003 July 2003 July 2003 Aug. 2003

19 List of Recent TAM Reports (cont d) No. Authors Title Date 1032 Raju, R., S. Balachandar, D. F. Hill, and R. J. Adrian 1033 Hill, K. M., G. Gioia, and V. V. Tota Reynolds number scaling of flow in a Rushton turbine stirred tank: Part II Eigen-decomposition of fluctuation Chemical Engineering Science (submitted) Structure and kinematics in dense free-surface granular flow Physical Review Letters 91, (2003) 1034 Fried, E., and S. Sellers Free-energy density functions for nematic elastomers Journal of the Mechanics and Physics of Solids 52, (2004) 1035 Kasimov, A. R., and On the dynamics of self-sustained one-dimensional detonations: D. S. Stewart A numerical study in the shock-attached frame Physics of Fluids (submitted) 1036 Fried, E., and B. C. Roy Disclinations in a homogeneously deformed nematic elastomer Nature Materials (submitted) 1037 Fried, E., and The unifying nature of the configurational force balance Mechanics M. E. Gurtin of Material Forces (P. Steinmann and G. A. Maugin, eds.), in press 1038 Panat, R., K. J. Hsia, and J. W. Oldham 1039 Cermelli, P., E. Fried, and M. E. Gurtin 1040 Yoo, S., and D. S. Stewart 1041 Dienberg, C. E., S. E. Ott-Monsivais, J. L. Ranchero, A. A. Rzeszutko, and C. L. Winter 1042 Kasimov, A. R., and D. S. Stewart 1043 Kasimov, A. R., and D. S. Stewart 1044 Panat, R., K. J. Hsia, and D. G. Cahill (2003) Rumpling instability in thermal barrier systems under isothermal conditions in vacuum Philosophical Magazine, in press (2004) Sharp-interface nematic isotropic phase transitions without flow Archive for Rational Mechanics and Analysis 174, (2004) A hybrid level-set method in two and three dimensions for modeling detonation and combustion problems in complex geometries Combustion Theory and Modeling (submitted) Proceedings of the Fifth Annual Research Conference in Mechanics (April 2003), TAM Department, UIUC (E. N. Brown, ed.) Asymptotic theory of ignition and failure of self-sustained detonations Journal of Fluid Mechanics (submitted) Theory of direct initiation of gaseous detonations and comparison with experiment Proceedings of the Combustion Institute (submitted) Evolution of surface waviness in thin films via volume and surface diffusion Journal of Applied Physics (submitted) 1045 Riahi, D. N. Steady and oscillatory flow in a mushy layer Current Topics in Crystal Growth Research, in press (2004) 1046 Riahi, D. N. Modeling flows in protein crystal growth Current Topics in Crystal Growth Research, in press (2004) 1047 Bagchi, P., and Response of the wake of an isolated particle to isotropic turbulent S. Balachandar cross-flow Journal of Fluid Mechanics (submitted) 1048 Brown, E. N., Fatigue crack propagation in microcapsule toughened epoxy S. R. White, and Journal of Materials Science (submitted) N. R. Sottos 1049 Zeng, L., S. Balachandar, and P. Fischer 1050 Dolbow, J., E. Fried, and H. Ji Wall-induced forces on a rigid sphere at finite Reynolds number Journal of Fluid Mechanics (submitted) A numerical strategy for investigating the kinetic response of stimulus-responsive hydrogels Computer Methods in Applied Mechanics and Engineering 194, (2005) 1051 Riahi, D. N. Effect of permeability on steady flow in a dendrite layer Journal of Porous Media, in press (2004) 1052 Cermelli, P., E. Fried, Transport relations for surface integrals arising in the formulation and M. E. Gurtin of balance laws for evolving fluid interfaces Journal of Fluid Mechanics (submitted) 1053 Stewart, D. S., and A. R. Kasimov Theory of detonation with an embedded sonic locus SIAM Journal on Applied Mathematics (submitted) Aug Aug Sept Nov Nov Dec Dec Dec Feb Feb Feb Mar Mar Mar Mar Mar Apr May 2004 June 2004 July 2004 Sept Oct. 2004

20 List of Recent TAM Reports (cont d) No. Authors Title Date 1054 Stewart, D. S., K. C. Tang, S. Yoo, M. Q. Brewster, and I. R. Kuznetsov 1055 Ji, H., H. Mourad, E. Fried, and J. Dolbow 1056 Fulton, J. M., S. Hussain, J. H. Lai, M. E. Ly, S. A. McGough, G. M. Miller, R. Oats, L. A. Shipton, P. K. Shreeman, D. S. Widrevitz, and E. A. Zimmermann Multi-scale modeling of solid rocket motors: Time integration methods from computational aerodynamics applied to stable quasi-steady motor burning Proceedings of the 43rd AIAA Aerospace Sciences Meeting and Exhibit (January 2005), Paper AIAA (2005) Kinetics of thermally induced swelling of hydrogels International Journal of Solids and Structures (submitted) Final reports: Mechanics of complex materials, Summer 2004 (K. M. Hill and J. W. Phillips, eds.) 1057 Hill, K. M., G. Gioia, and D. R. Amaravadi Radial segregation patterns in rotating granular mixtures: Waviness selection Physical Review Letters 93, (2004) 1058 Riahi, D. N. Nonlinear oscillatory convection in rotating mushy layers Journal of Fluid Mechanics (submitted) 1059 Okhuysen, B. S., and On buoyant convection in binary solidification Journal of Fluid D. N. Riahi Mechanics (submitted) 1060 Brown, E. N., Retardation and repair of fatigue cracks in a microcapsule S. R. White, and toughened epoxy composite Part I: Manual infiltration N. R. Sottos Composites Science and Technology (submitted) 1061 Brown, E. N., S. R. White, and N. R. Sottos 1062 Berfield, T. A., R. J. Ong, D. A. Payne, and N. R. Sottos 1063 Anderson, D. M., P. Cermelli, E. Fried, M. E. Gurtin, and G. B. McFadden 1064 Fried, E., and M. E. Gurtin 1065 Gioia, G., and F. A. Bombardelli Retardation and repair of fatigue cracks in a microcapsule toughened epoxy composite Part II: In situ self-healing Composites Science and Technology (submitted) Residual stress effects on piezoelectric response of sol-gel derived PZT thin films Journal of Applied Physics (submitted) General dynamical sharp-interface conditions for phase transformations in viscous heat-conducting fluids Journal of Fluid Mechanics (submitted) Oct Dec Dec Dec Dec Jan Jan Jan Apr Apr Second-gradient fluids: A theory for incompressible flows at small Apr length scales Journal of Fluid Mechanics (submitted) Localized turbulent flows on scouring granular beds Physical May 2005 Review Letters, in press (2005) 1066 Fried, E., and S. Sellers Orientational order and finite strain in nematic elastomers Journal May 2005 of Chemical Physics 123, (2005) 1067 Chen, Y.-C., and Uniaxial nematic elastomers: Constitutive framework and a simple June 2005 E. Fried application Proceedings of the Royal Society of London A (submitted) 1068 Fried, E., and S. Sellers Incompatible strains associated with defects in nematic Aug elastomers Physical Review Letters (submitted) 1069 Gioia, G., and X. Dai Surface stress and reversing size effect in the initial yielding of Aug ultrathin films Journal of Applied Mechanics, in press (2005) 1070 Gioia, G., and Turbulent friction in rough pipes and the energy spectrum of the Aug P. Chakraborty phenomenological theory arxiv:physics v1 8 Jul Keller, M. W., and Mechanical properties of capsules used in a self-healing polymer Sept N. R. Sottos Experimental Mechanics (submitted) 1072 Chakraborty, P., Volcán Reventador s unusual umbrella Sept G. Gioia, and S. Kieffer