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860 References

Howard LN (1966) Convection at high Rayleigh number. In: Görtler H (ed) Proc 11th int cong

appl mech. Springer, Berlin, pp 1109–1115

Howard LN, Kopell N (1977) Slowly varying waves and shock structures in reaction-diffusion

equations. Stud Appl Math 56:95–145

Howell PD (1996) Models for thin viscous sheets. Eur J Appl Math 7:321–343

Howison SD (2005) Practical applied mathematics: modelling, analysis, approximation. Cam-

bridge University Press, Cambridge

Hubbard BP, Sharp MJ, Willis IC, Nielsen MK, Smart CC (1995) Borehole water-level varia-

tions and the structure of the subglacial hydrological system of Haut Glacier d’Arolla, Valais,

Switzerland. J Glaciol 41:572–583

Hughes TJ (1973) Is the West Antarctic ice sheet disintegrating? J Geophys Res 78:7884–7910

Hunt JCR, Leibovich S, Richards KJ (1988) Turbulent shear ﬂows over low hills. Q J R Meteorol

Soc 114:1435–1470

Hunt JM (1990) Generation and migration of petroleum from abnormally pressured ﬂuid compart-

ments. Am Assoc Pet Geol Bull 74:1–12

Huppert HE (1986) The intrusion of ﬂuid mechanics into geology. J Fluid Mech 173:557–594

Huppert HE (1990) The ﬂuid mechanics of solidiﬁcation. J Fluid Mech 212:209–240

Huppert HE (2000) Geological ﬂuid mechanics. In: Batchelor GK, Moffatt HK, Worster MG (eds)

Perspectives in ﬂuid dynamics. Cambridge University Press, Cambridge, pp 447–506

Huppert HE, Sparks RSJ (1980) The ﬂuid dynamics of a basaltic magma chamber replenished by

inﬂux of hot, dense, ultrabasic magma. Contrib Mineral Petrol 75:279–289

Huppert HE, Sparks RSJ (1988) The ﬂuid dynamics of crustal melting by injection of basaltic sills.

Trans R Soc Edinb 79:237–243

Hutter K (1983) Theoretical glaciology. Reidel, Dordrecht

Hutter K, Olunloyo VOS (1980) On the distribution of stress and velocity in an ice strip, which is

partly sliding over and partly adhering to its bed, by using a Newtonian viscous approximation.

Proc R Soc Lond A 373:385–403

Hutter K, Yakowitz S, Szidarovsky F (1986) A numerical study of plane ice sheet ﬂow. J Glaciol

32:139–160

Hüttmann A, Wilson RD, Thornton SF, Lerner DN (2003) Natural attenuation of ammonium at

a former coal carbonisation plant (Mansﬁeld, UK): conceptual model for biodegradation pro-

cesses. In: Consoil 2003, Gent, Conference Proceedings CD, pp 1542–1547

Hyde WT, Crowley TJ, Baum SK, Peltier WR (2000) Neoproterozoic ‘snowball Earth’ simulations

with a coupled climate/ice sheet model. Nature 405:425–429

Iken A (1981) The effect of subglacial water pressure on the sliding velocity of a glacier in an

idealized numerical model. J Glaciol 27:407–422

Imbrie J, Imbrie KP (1979) Ice ages; solving the mystery. Harvard University Press, Cambridge

Innes R (1732) Miscellaneous letters on several subjects in philosophy and astronomy, I, p 4. S Birt,

London

Irvine TN (1987) Layering and related structures in the Duke Island and Skaergaard intrusions:

similarities, differences, and origins. In: Parsons I (ed) Origins of igneous layering. NATO ASI

series C, vol 196. Reidel, Dordrecht, pp 185–245

Ishii M (1975) Thermo-ﬂuid dynamic theory of two-phase ﬂow. Eyrolles, Paris

Ivanov AB, Muhleman DO (2000) The role of sublimation for the formation of the Northern ice

cap: results from the Mars Orbiter Laser Altimeter. Icarus 144:436–448

Iverson NR, Baker RW, Hooyer TS (1997) A ring-shear device for the study of till deformation:

tests on tills with contrasting clay contents. Quat Sci Rev 16(9):1057–1066

Izumi N, Parker G (1995) Inception of channelization and drainage basin formation: upstream-

driven theory. J Fluid Mech 283:341–363

Izumi N, Parker G (2000) Linear stability analysis of channel inception: downstream-driven theory.

J Fluid Mech 419:239–262

Jackson PS, Hunt JCR (1975) Turbulent wind ﬂow over a low hill. Q J R Meteorol Soc 101:929–

955

Jarvis GT, McKenzie D (1982) Mantle convection as a boundary layer phenomenon. Geophys J R

Astron Soc 68:389–427

References 861

Jaupart C, Labrosse S, Mareschal J-C (2009) Temperatures, heat and energy in the mantle of the

Earth. In: Bercovici D (ed) Mantle dynamics. Treatise on geophysics, vol 7. Elsevier, Amster-

dam, pp 253–303

Jeffrey A (2004) Handbook of mathematical formulas and integrals, 3rd edn. Elsevier, Amsterdam

Jeffreys H (1925) The ﬂow of water in an inclined channel of rectangular section. Philos Mag

49:793–807

Jeffreys H, Jeffreys B (1953) Methods of mathematical physics. Cambridge University Press, Cam-

bridge

Jimenez J, Zuﬁria JA (1987) A boundary layer analysis of Rayleigh-Bénard convection at large

Rayleigh number. J Fluid Mech 178:53–71

Jóhannesson T (2002a) The initiation of the 1996 jökulhlaup from Lake Grímsvötn, Iceland. In:

Snorrason Á, Finnsdóttir HP, Moss ME (eds) The extremes of the extremes: extraordinary

ﬂoods. IASH publ, vol 271, pp 57–64

Jóhannesson T (2002b) Propagation of a subglacial ﬂood wave during the initiation of a jökulhlaup.

Hydrol Sci J 47:417–434

Johnsen SJ, Clausen HB, Dansgaard W, Fuhrer K, Gundestrup N, Hammer CU, Iversen P, Jouzel

J, Stauffer B, Steffensen JP (1992) Irregular glacial interstadials recorded in a new Greenland

ice core. Nature 359:311–313

Jones M (1994) Mechanical principles of sediment deformation. In: Maltman A (ed) The geologi-

cal deformation of sediments. Chapman and Hall, London, pp 37–71

Julien PY (1995) Erosion and sedimentation. Cambridge University Press, Cambridge

Kalnay E (2003) Atmospheric modeling, data assimilation and predictability. Cambridge Univer-

sity Press, Cambridge

Kamb B (1987) Glacier surge mechanism based on linked cavity conﬁguration of the basal water

conduit system. J Geophys Res 92:9083–9100

Kamb B (1991) Rheological nonlinearity and ﬂow instability in the deforming bed mechanism of

ice stream motion. J Geophys Res 96(B10):16585–16595

Kamb B, Raymond CF, Harrison WD, Engelhardt H, Echelmeyer KA, Humphrey N, Brugman

MM, Pfeffer T (1985) Glacier surge mechanism: 1982–1983 surge of Variegated Glacier,

Alaska. Science 227:469–479

Kamb WB (1970) Sliding motion of glaciers: theory and observation. Rev Geophys Space Phys

8:673–728

Kardar M, Parisi G, Zhang YC (1986) Dynamic scaling of growing interfaces. Phys Rev Lett

56:889–892

Kargel JS (2004) Mars—a warmer, wetter planet. Springer, Berlin

Kasting JF (1989) Long-term stability of the Earth’s climate. Palaeogeogr Palaeoclimatol

Palaeoecol 75:83–95

Kasting JF, Ackermann TP (1986) Climatic consequences of very high carbon dioxide levels in

Earth’s early atmosphere. Science 234:1383–1385

Kaye GWC, Laby TH (1960) Physical and chemical constants, 12th edn. Longman, Harlow

Keener JP (1980) Waves in excitable media. SIAM J Appl Math 39:528–548

Keener JP (1986) A geometrical theory for spiral waves in excitable media. SIAM J Appl Math

46:1039–1056

Keller JB, Rubinow SI (1981) Recurrent precipitation and Liesegang rings. J Chem Phys 74:5000–

5007

Kennedy JF (1963) The mechanics of dunes and anti-dunes in erodible-bed channels. J Fluid Mech

16:521–544

Kern R, Weisbrod A (1967) Thermodynamics for geologists. Translation from French by D McKie.

Freeman Cooper and Co, San Francisco

Kevorkian J, Cole JD (1981) Perturbation methods in applied mathematics. Springer, Berlin

Kinahan GH, Close MH (1872) The general glaciation of Iar-Connaught and its neighbourhood, in

the counties of Galway and Mayo. Hodges, Foster and Co, Dublin

Kleman J, Hättestrand C (1999) Frozen-bed Fennoscandian and Laurentide ice sheets during the

Last Glacial Maximum. Nature 402:63–66

862 References

Knighton D (1998) Fluvial forms and processes: a new perspective. Arnold, London

Knittle E, Jeanloz R (1991) Earth’s core–mantle boundary: results of experiments at high pressures

and temperatures. Science 251:1438–1443

Koestler A (1964) The sleepwalkers. Penguin Books, London

Köhler P, Fischer H (2006) Simulating low frequency changes in atmospheric CO

during the last

740000 years. Clim Past 2:57–78

Köhler P, Fischer H, Munhoven G, Zeebe RE (2005) Quantitative interpretation of atmospheric

carbon records over the last glacial termination. Glob Biogeochem Cycles 19:GB4020.

doi:10.1029/2004GB002345

Kopell N, Howard LN (1973) Plane wave solutions to reaction-diffusion equations. Stud Appl

Math 42:291–328

Korteweg DJ, de Vries G (1895) On the change of form of long waves advancing in a rectangular

canal, and on a new type of long stationary waves. Philos Mag Ser 5 39:422–443

Kramer S, Marder M (1992) Evolution of river networks. Phys Rev Lett 68:205–208

Krauskopf KB, Bird DK (1995) Introduction to geochemistry. McGraw-Hill, New York

Kroy K, Sauermann G, Herrmann HJ (2002a) Minimal model for sand dunes. Phys Rev Lett

88:054301

Kroy K, Sauermann G, Herrmann HJ (2002b) Minimal model for aeolian sand dunes. Phys Rev E

66:031302

Kurz W, Fisher DJ (1998) Fundamentals of solidiﬁcation, 4th edn. Trans Tech, Zurich

Lakin WD, Ng BS, Reid WH (1978) Approximations to the eigenvalue relation for the Orr-

Sommerfeld problem. Philos Trans R Soc 289:347–371

Lamb, Sir Horace (1945) Hydrodynamics, 6th edn. Dover reprint of the 1932 sixth edition. Dover,

New York

Lambe TW, Whitman RV (1979) Soil mechanics, SI version. Wiley, New York

Lang C, Leuenberger M, Schwander J, Johnsen S (1999) 16°C rapid temperature variation in cen-

tral Greenland 70000 years ago. Science 286:934–937

Lasaga AC, Berner RA, Garrels RM (1985) An improved geochemical model of atmospheric CO

ﬂuctuations over the past 100 million years. In: Sundquist ET, Broecker WS (eds) The carbon

cycle and atmospheric CO

: natural variations Archaen to present. AGU, Washington, pp 397–

411

Le Grand HE (1988) Drifting continents and shifting theories. Cambridge University Press, Cam-

bridge

Leuenberger MC, Lang C, Schwander J (1999) Delta

N measurements as a calibration tool for

the paleothermometer and gas–ice age differences: a case study for the 8200 BP event on GRIP

ice. J Geophys Res 104(D18):22163–22170

Li M, Richmond O (1997) Intrinsic instability and non-uniformity of plastic deformation. Int J

Plast 13:765–784

Lighthill MJ, Whitham GB (1955a) On kinematic waves. I. Flood movement in long rivers. Proc

R Soc Lond A 229:281–316

Lighthill MJ, Whitham GB (1955b) On kinematic waves. II. A theory of trafﬁc ﬂow on long,

crowded roads. Proc R Soc Lond A 229:317–345

Lin CC, Segel LA (1974) Mathematics applied to deterministic problems in the natural sciences.

MacMillan, New York

Liñán A, Williams FA (1993) Fundamental aspects of combustion. Oxford University Press, Ox-

ford

Liou KN (2002) An introduction to atmospheric radiation, 2nd edn. Academic Press, San Diego

Lister JR, Kerr RC (1991) Fluid-mechanical models of crack propagation and their application to

magma transport in dykes. J Geophys Res 96:10049–10077

Lliboutry LA (1956) La mécanique des glaciers en particulier au voisinage de leur front. Ann

Geophys 12:245–276

Lliboutry LA (1958a) La dynamique de la Mer de Glace et la vague de 1891–95 d’après les mésures

de Joseph Vallot. In: Physics of the movement of ice (Chamonix symposium). IAHS publ,

vol 47. IAHS Press, Wallingford, pp 125–138. Available to download at http://www.iahs.info/

redbooks/047.htm

References 863

Lliboutry LA (1958b) Glacier mechanics in the perfect plasticity theory. J Glaciol 3:162–169

Lliboutry LA (1964) Traité de glaciologie, vol I. Glace, neige, hydrologie nivale. Masson, Paris

Lliboutry LA (1965) Traité de glaciologie, vol II. Glaciers, variations du climat, sols gelés. Masson,

Paris

Lliboutry LA (1968) General theory of subglacial cavitation and sliding of temperate glaciers.

J Glaciol 7:21–58

Lliboutry LA (1979) Local friction laws for glaciers: a critical review and new openings. J Glaciol

23:67–95

Lliboutry LA (1987) Very slow ﬂows of solids. Basics of modeling in geodynamics and glaciology.

Martinus Nijhoff, Dordrecht

Loewenherz DS (1991) Stability and the initiation of channelized surface drainage: a reassessment

of the short wavelength limit. J Geophys Res 96:8453–8464

Loewenherz-Lawrence DS (1994) Hydrodynamic description for advective sediment transport pro-

cesses and rill initiation. Water Resour Res 30:3203–3212

Loper DE (ed) (1987) Structure and dynamics of partially solidiﬁed systems. Martinus Nijhoff,

Dordrecht

Lorenz EN (1963) Deterministic non-periodic ﬂow. J Atmos Sci 20:130–141

Lynch DK (1982) Tidal bores. Sci Am 247:131–143

Lynch P (2006) The emergence of numerical weather prediction: Richardson’s dream. Cambridge

University Press, Cambridge

Maaløe S (1978) The origin of rhythmic layering. Mineral Mag 42:337–345

MacAyeal DR (1989) Large-scale ice ﬂow over a viscous basal sediment. J Geophys Res 94:4071–

4087

MacAyeal DR (1993) Binge/purge oscillations of the Laurentide ice sheet as a cause of the North

Atlantic’s Heinrich events. Paleoceanography 8:775–784

Malkus WVR, Veronis G (1958) Finite amplitude cellular convection. J Fluid Mech 4:225–260

Manabe S, Stouffer RJ (1995) Simulation of abrupt climate change induced by freshwater input to

the North Atlantic Ocean. Nature 378:165–167

Marsh BD (1982) On the mechanics of igneous diapirism, stoping, and zone melting. Am J Sci

282:808–855

Marsh SP, Glicksman ME (1996) Overview of geometric effects on coarsening of mushy zones.

Metall Mater Trans 27A:557–567

Marshall HG, Walker JCG, Kuhn WR (1988) Long term climate change and the geochemical cycle

of carbon. J Geophys Res 93:791–801

Mason B, Moore CB (1982) Principles of geochemistry, 4th edn. Wiley, Chichester

Massey BS (1986) Measures in science and engineering. Ellis Horwood, Chichester

Matson LE (2007) The Malkus–Lorenz water wheel revisited. Am J Phys 75:1114–1122

Matuszkiewicz A, Flamand JC, Bouré JA (1987) The bubble-slug ﬂow pattern transition and insta-

bilities of void-fraction waves. Int J Multiph Flow 13:199–217

Mayer KU, Benner SG, Frind EO, Thornton SF, Lerner DN (2001) Reactive transport modeling of

processes controlling the distribution and natural attenuation of phenolic compounds in a deep

sandstone aquifer. J Contam Hydrol 53:341–368

McBirney AR (1984) Igneous petrology. Freeman Cooper and Co, San Francisco

McBirney AR, Noyes RM (1979) Crystallisation and layering of the Skaergaard intrusion. J Pet

20:487–554

McCoy RM (2006) Ending in ice: the revolutionary idea and tragic expedition of Alfred Wegener.

Oxford University Press, Oxford

McKenzie DP (1984) The generation and compaction of partially molten rock. J Pet 25:713–765

McNutt MK (2006) Another nail in the plume cofﬁn? Science 313:1394

Meinhardt H (1982) Models of biological pattern formation. Academic Press, New York

Meinhardt H (1995) The algorithmic beauty of sea shells. Springer, Berlin

Melnik O (2000) Dynamics of two-phase conduit ﬂow of high-viscosity gas-saturated magma:

large variations of sustained explosive eruption intensity. Bull Volcanol 62:153–170

Menzies J (1984) Drumlins: a bibliography. Geo Books, Norwich

864 References

Meyer-Peter E, Müller R (1948) Formulas for bed-load transport. In: Proc int assoc hydraul res,

3rd annual conference, Stockholm, pp 39–64

Miller RN (2007) Numerical modelling of ocean circulation. Cambridge University Press, Cam-

bridge

Millero FJ (1995) Thermodynamics of the carbon dioxide system in the oceans. Geochim Cos-

mochim Acta 59:661–677

Monod J (1949) The growth of bacterial cultures. Annu Rev Microbiol 3:371–394

Moore DR, Weiss NO (1973) Two-dimensional Rayleigh-Bénard convection. J Fluid Mech

58:289–312

Moore PL, Iverson NR (2002) Slow episodic shear of granular materials regulated by dilatant

strengthening. Geology 30:843–846

Moresi L-N, Solomatov VS (1995) Numerical investigation of 2D convection with extremely large

viscosity variations. Phys Fluids 7:2154–2162

Moresi L-N, Solomatov VS (1998) Mantle convection with a brittle lithosphere: thoughts on the

global tectonic styles of the Earth and Venus. Geophys J Int 133:669–682

Morgan JP, Blackman DK, Sinton JM (eds) (1992) Mantle ﬂow and melt generation at mid-ocean

ridges. Geophysical monograph, vol 71. AGU, Washington

Morgan WJ (1971) Convection plumes in the lower mantle. Nature 230:42–43

Morland LW (1976a) Glacier sliding down an inclined wavy bed. J Glaciol 17:447–462

Morland LW (1976b) Glacier sliding down an inclined wavy bed with friction. J Glaciol 17:463–

477

Morland LW (1984) Thermo-mechanical balances of ice sheet ﬂow. Geophys Astrophys Fluid Dyn

29:237–266

Morland LW, Johnson IR (1980) Steady motion of ice sheets. J Glaciol 25:229–246

Morland LW, Shoemaker EM (1982) Ice shelf balances. Cold Reg Sci Technol 5:235–251

Morris S (1982) The effects of strongly temperature-dependent viscosity on slow ﬂow past a hot

sphere. J Fluid Mech 124:1–26

Morris S, Canright D (1984) A boundary layer analysis of Bénard convection in a ﬂuid of strongly

temperature-dependent viscosity. Phys Earth Planet Inter 29:320–329

Munhoven G, François LM (1996) Glacial–interglacial variability of atmospheric CO

due to

changing continental silicate rock weathering: a model study. J Geophys Res 101:21423–21437

Murray JD (2002) Mathematical biology, 2 volumes. Springer, Berlin

Muskhelishvili NI (1953) Singular integral equations (Translation edited by JRM Radok). Noord-

hoff, Groningen

Nataf H-C, Richter FM (1982) Convection experiments in ﬂuids with highly temperature-

dependent viscosity and the thermal evolution of the planets. Phys Earth Planet Inter 29:320–

329

Nayfeh AH (1973) Perturbation methods. Wiley-Interscience, New York

Needham DJ, Merkin JH (1984) On roll waves down an open inclined channel. Proc R Soc Lond

A 394:259–278

Newell AC (1985) Solitons in mathematics and physics. Society for Industrial and Applied Math-

ematics, Philadelphia

Newell AC, Whitehead JA (1969) Finite bandwidth, ﬁnite amplitude convection. J Fluid Mech

38:279–303

Ng FSL (1998) Mathematical modelling of subglacial drainage and erosion. DPhil thesis, Oxford

University

Ng F, Björnsson H (2003) On the Clague-Mathews relation for jökulhlaups. J Glaciol 49:161–172

Ng FSL, Zuber MT (2003) Albedo feedback in the patterning mechanisms of Martian polar caps.

In: 3rd international conference on Mars polar science and exploration, abstract #8061, Lunar

and Planetary Science Institute, Houston (CD-ROM)

Ng FSL, Zuber MT (2006) Patterning instability on the Mars polar ice caps. J Geophys Res

111:E02005. doi:10.1029/2005JE002533

Nicolas A (1986) A melt extraction model based on structural studies in mantle peridotites. J Pet

27:999–1022

References 865

Nicolussi K (1990) Bilddokumente zur Geschichte des Vernagtferners im 17. Jahrhundert. Zeit

Gletschkd Glazialgeol 26(2):97–119

Nienow P, Sharp M, Willis I (1998) Seasonal changes in the morphology of the subglacial drainage

system, Haut Glacier d’Arolla. Switz Earth Surf Process Landf 23:825–843

Noble B (1988) Methods based on the Wiener–Hopf technique, 2nd (unaltered) edn. Chelsea, New

Yor k

Nockolds SR, O’B Knox RW, Chinner GA (1978) Petrology for students. Cambridge University

Press, Cambridge

Nordstrom DK, Munoz JL (1994) Geochemical thermodynamics, 2nd edn. Blackwell Scientiﬁc

Publications, Cambridge

North GR (1975a) Analytical solution to a simple climate model with diffusive heat transport.

J Atmos Sci 32:1301–1307

North GR (1975b) Theory of energy-balance climate models. J Atmos Sci 32:2033–2043

North GR, Mengel JG, Short DA (1983) Simple energy balance model resolving the season and

continents: applications to astronomical theory of ice ages. J Geophys Res 88:6576–6586

Nowicki SMJ, Wingham DJ (2008) Conditions for a steady ice sheet–ice shelf junction. Earth

Planet Sci Lett 265:246–255

Nye JF (1953) The ﬂow law of ice from measurements in glacier tunnels, laboratory experiments

and the Jungfrauﬁrn borehole experiment. Proc R Soc Lond A 219:477–489

Nye JF (1957) Glacier mechanics; comments on Professor L Lliboutry’s paper. J Glaciol 3:91–93

Nye JF (1958) Comments on Professor Lliboutry’s paper. J Glaciol 3:170–172

Nye JF (1959) The motion of ice sheets and glaciers. J Glaciol 3:493–507

Nye JF (1960) The response of glaciers and ice sheets to seasonal and climatic changes. Proc R

Soc Lond A 256:559–584

Nye JF (1963) The response of a glacier to changes in the rate of nourishment and wastage. Proc

R Soc Lond A 275:87–112

Nye JF (1967) Theory of regelation. Philos Mag Ser 8 16(144):1249–1266

Nye JF (1969) A calculation on the sliding of ice over a wavy surface using a Newtonian viscous

approximation. Proc R Soc Lond A 311:445–477

Nye JF (1970) Glacier sliding without cavitation in a linear viscous approximation. Proc R Soc

Lond A 315:381–403

Nye JF (1973) Water at the bed of a glacier. IASH Publ 95:189–194

Nye JF (1976) Water ﬂow in glaciers: jökulhlaups, tunnels, and veins. J Glaciol 17:181–207

Ockendon H, Ockendon JR (2004) Waves and compressible ﬂow. Springer, New York

Olbers D (2001) A gallery of simple models from climate physics. Prog Probab 49:3–63

Olson P, Corcos GM (1980) A boundary layer model for mantle convection with surface plates.

Geophys J R Astron Soc 62:195–219

Olver FWJ (1974) Asymptotics and special functions. Academic Press, New York

O’Malley K, Fitt AD, Jones TV, Ockendon JR, Wilmott P (1991) Models for high-Reynolds-

number ﬂow down a step. J Fluid Mech 222:139–155

Oreskes N (1999) The rejection of continental drift. Oxford University Press, New York

Orme AR (2007) The rise and fall of the Davisian cycle of erosion: prelude, fugue, coda, and

sequel. Phys Geogr 28:474–506

Orszag SA, Patera AT (1983) Secondary instability of wall-bounded shear ﬂows. J Fluid Mech

128:347–385

Ortoleva P (1994) Geochemical self-organisation. Oxford University Press, Oxford

Parker G (1975) Sediment inertia as a cause of river antidunes. J Hydraul Div ASCE 101:211–221

Parker G (1978) Self-formed straight rivers with equilibrium banks and mobile bed. Part 1. The

sand-silt river. J Fluid Mech 89:109–125

Parker G (2004) 1D sediment transport morphodynamics with applications to rivers and turbidity

currents. http://vtchl.uiuc.edu/people/parkerg/morphodynamics_e-book.htm

Parsons B, Sclater JG (1977) An analysis of the variation of ocean ﬂoor depth and heat ﬂow with

age. J Geophys Res 82:803–827

Parsons DR, Walker IJ, Wiggs GFS (2004) Numerical modelling of ﬂow structures over idealized

transverse aeolian dunes of varying geometry. Geomorphology 59:149–164

866 References

Parsons I (ed) (1987) Origins of igneous layering. NATO ASI series C, vol 196. Reidel, Dordrecht

Parteli EJR, Durán O, Herrmann HJ (2007) Minimal size of a barchan dune. Phys Rev E 75:011301

Parteli EJR, Durán O, Tsoar H, Schwämmle V, Herrmann HJ (2009) Dune formation under bi-

modal winds. Proc Natl Acad Sci 106:22085–22089

Paterson WSB (1994) The physics of glaciers, 3rd edn. Pergamon, Oxford

Pattyn F, de Smedt B, Souchez R (2004) Inﬂuence of subglacial Vostok lake on the regional ice

dynamics of the Antarctic ice sheet: a model study. J Glaciol 50:583–589

Payne AJ, Dongelmans PW (1997) Self-organization in the thermomechanical ﬂow of ice sheets.

J Geophys Res 102:12219–12233

Pearson JRA (1958) On convection cells induced by surface tension. J Fluid Mech 4:489–500

Pedlosky J (1987) Geophysical ﬂuid dynamics, 2nd edn. Springer, Berlin

Pelletier JD (2004) How do spiral troughs form on Mars? Geology 32(4):365–367

Pelletier JD (2008) Quantitative modeling of Earth surface processes. Cambridge University Press,

Cambridge

Peregrine DH (1966) Calculations of the development of an undular bore. J Fluid Mech 25:321–

330

Petford N, Lister JR, Kerr RC (1994) The ascent of felsic magmas in dykes. Lithos 32:161–168

Petit JR, Jouzel J, Raynaud D, Barkov NI, Barnola J-M, Basile I, Bender M, Chappellaz J, Davis

M, Delaygue G, Delmotte M, Kotlyakov VM, Legrand M, Lipenkov VY, Lorius C, Pépin L,

Ritz C, Saltzman E, Stievenard M (1999) Climate and atmospheric history of the past 420000

years from the Vostok ice core, Antarctica. Nature 399:429–436

Picioreanu C, van Loosdrecht MCM, Heijnen JJ (1998) Mathematical modeling of bioﬁlm

structure with a hybrid differential-discrete cellular automaton approach. Biotechnol Bioeng

58:101–116

Pierrehumbert RT (2004) High atmospheric carbon dioxide necessary for the termination of global

glaciation. Nature 429:646–648

Pillow AF (1952) The free convection cell in two dimensions. Dept of Supply, Aeronautical Re-

search Laboratories, Report A.79 [Dept of Mathematics, University of Queensland, St Lucia,

Queensland 4067, Australia]

Pitcher WS (1997) The nature and origin of granite, 2nd edn. Chapman and Hall, London

Polubarinova-Kochina PYa (1962) Theory of ground water movement. Princeton University Press,

Princeton

Price M (1985) Introducing groundwater. George Allen and Unwin, London

Prosperetti A, Satrape JV (1990) Stability of two-phase ﬂow models. In: Joseph DD, Schaeffer DG

(eds) Two-phase ﬂow models and waves. Springer, New York, pp 98–117

Pugh DT (1987) Tides, surges and mean sea-level. Wiley, Chichester

Pye K, Tsoar H (1990) Aeolian sand and sand dunes. Unwin Hyman, London

Quareni F, Yuen DA, Sewell G, Christensen UR (1985) High Rayleigh number convection with

strongly variable viscosity: a comparison between mean ﬁeld and two-dimensional solutions.

J Geophys Res 90:12633–12644

Rahmstorf S (1995) Bifurcations of the Atlantic thermohaline circulation in response to changes

in the hydrological cycle. Nature 378:145–149

Rahmstorf S (2002) Ocean circulation and climate during the past 120000 years. Nature 419:207–

214

Rathbun AP, Marone C, Alley RB, Anandakrishnan S (2008) Laboratory study of the frictional

rheology of sheared till. J Geophys Res 113:F02020. doi:10.1029/2007JF000815

Rayleigh, Lord (1908) Note on tidal bores. Proc R Soc Lond A 81:448–449

Rayleigh, Lord (1916) On convective currents in a horizontal layer of ﬂuid when the higher tem-

perature is on the under side. Philos Mag 32:529–546

Reese CC, Solomatov VS (2002) Mean ﬁeld heat transfer scaling for non-Newtonian stagnant lid

convection. J Non-Newton Fluid Mech 107:39–49

Reese CC, Solomatov VS, Moresi L-N (1999) Non-Newtonian stagnant lid convection and mag-

matic resurfacing on Venus. Icarus 139:67–80

Reid WH (1972) Composite approximations to the solutions of the Orr-Sommerfeld equation. Stud

Appl Math 51:341–368

References 867

Rempel AW, Wettlaufer JS, Worster MG (2004) Premelting dynamics in a continuum model of

frost heave. J Fluid Mech 498:227–244

Reynolds AJ (1965) Waves on the erodible bed of an open channel. J Fluid Mech 22:113–133

Reynolds O (1895) On the dynamical theory of incompressible viscous ﬂuids and the determination

of the criterion. Philos Trans R Soc Lond A 186:123–164

Ribe NM (2009) Analytical approaches to mantle dynamics. In: Bercovici D (ed) Mantle dynamics.

Treatise on geophysics, vol 7. Elsevier, Amsterdam, pp 167–226

Richards K (1982) Rivers: form and process in alluvial channels. Methuen, London

Richards KJ (1980) The formation of ripples and dunes on an erodible bed. J Fluid Mech 99:597–

618

Richardson CN, Lister JR, McKenzie D (1996) Melt conduits in a viscous porous matrix. J Geo-

phys Res 101:20423–20432

Rittmann BE, McCarty PL (1980) Model of steady-state-bioﬁlm kinetics. Biotechnol Bioeng

22:2343–2357

Roberts GO (1977) Fast viscous convection. Geophys Astrophys Fluid Dyn 8:197–233

Roberts GO (1979) Fast viscous Bénard convection. Geophys Astrophys Fluid Dyn 12:235–272

Roberts MJ (2005) Jökulhlaups: a reassessment of ﬂoodwater ﬂow through glaciers. Rev Geophys

43:RG1002

Robin G de Q (1955) Ice movement and temperature distribution in glaciers and ice sheets.

J Glaciol 2:523–532

Robinson JR (1967) Finite amplitude convection cells. J Fluid Mech 30:577–600

Rodríguez-Iturbe I, Rinaldo A (1997) Fractal river basins. Cambridge University Press, Cambridge

Röthlisberger H (1972) Water pressure in intra- and subglacial channels. J Glaciol 11:177–203

Rowbotham F (1970) The Severn bore, 2nd edn. David and Charles, Newton Abbot

Rubinstein J, Mauri R (1986) Dispersion and convection in periodic porous media. SIAM J Appl

Math 46:1018–1023

Ruddiman WF (2001) Earth’s climate: past and future. Freeman, New York

Ryan MP (ed) (1990) Magma transport and storage. Wiley, Chichester

Saffman PG (1959) A theory of dispersion in a porous medium. J Fluid Mech 6:321–349

Sahimi M (1995) Flow and transport in porous media and fractured rock. VCH, Weinheim

Samarskii AA, Galaktionov VA, Kurdyumov SP, Mikhailov AP (1995) Blow-up in quasilinear

parabolic equations. de Gruyter expositions in mathematics, vol 19. de Gruyter, Berlin

Sanchez-Palencia E (1983) Homogenization method for the study of composite media. Springer,

Berlin

Sass BM, Rosenberg PE, Kittrick JA (1987) The stability of illite/smectite during diagenesis: an

experimental study. Geochim Cosmochim Acta 51:2103–2115

Sauermann G, Kroy K, Herrmann HJ (2001) Continuum saltation model for sand dunes. Phys Rev

E 64:031305

Sayag R, Tziperman E (2008) Spontaneous generation of pure ice streams via ﬂow insta-

bility: role of longitudinal shear stresses and subglacial till. J Geophys Res 113:B05411.

doi:10.1029/2007JB005228

Schlichting H (1979) Boundary layer theory. McGraw-Hill, New York

Schmidt MW, Vautravers MJ, Spero HJ (2006) Rapid subtropical North Atlantic salinity oscilla-

tions across Dansgaard–Oeschger cycles. Nature 443:561–564

Schoof C (2005) The effect of cavitation on glacier sliding. Proc R Soc Lond A 461:609–627

Schoof C (2007a) Pressure-dependent viscosity and interfacial instability in coupled ice-sediment

ﬂow. J Fluid Mech 570:227–252

Schoof C (2007b) Marine ice-sheet dynamics. Part 1. The case of rapid sliding. J Fluid Mech

573:27–55

Schoof C (2007c) Ice sheet grounding line dynamics: steady states, stability and hysteresis. J Geo-

phys Res 112:F03S28. doi:10.1029/2006JF000664

Schoof C, Hindmarsh RCA (2010) Thin-ﬁlm ﬂows with wall slip: an asymptotic analysis of higher

order glacier ﬂow models. Q J Mech Appl Math 63:73–114

Schubert G, Turcotte DL, Olson P (2001) Mantle convection in the Earth and planets. Cambridge

University Press, Cambridge

868 References

Schulte P et al (2010) The Chicxulub asteroid impact and mass extinction at the Cretaceous-

Paleogene boundary. Science 327:1214–1218

Schwämmle V, Herrmann H (2004) Modelling transverse dunes. Earth Surf Process Landf 29:769–

784

Scott DR, Stevenson DJ (1984) Magma solitons. Geophys Res Lett 11:1161–1164

Scott DR, Stevenson DJ, Whitehead JA (1986) Observations of solitary waves in a viscously de-

formable pipe. Nature 319:759–761

Segel LA (1969) Distant side-walls cause slow amplitude modulation of cellular convection.

J Fluid Mech 38:203–224

Selby MJ (1993) Hillslope materials and processes, 2nd edn. Oxford University Press, Oxford

Sellers WD (1969) A climate model based on the energy balance of the Earth-atmosphere system.

J Appl Meteorol 8:392–400

Sellmeijer JB, Koenders MA (1991) A mathematical model for piping. Appl Math Model 15:646–

651

Severinghaus JP, Brook EJ (1999) Abrupt climate change at the end of the last glacial period

inferred from trapped air in polar ice. Science 286:930–934

Shapiro MA, Keyser DA (1990) Fronts, jet streams and the tropopause. In: Newton CW,

Holopainen EO (eds) Extratropical cyclones. The Erik Palmén memorial volume. Amer Met

Soc, Boston, pp 167–191

Sharpe D (2005) Comments on: “Paleohydraulics of the last outburst ﬂood from glacial Lake Agas-

siz and the 8200 BP cold event” by Clarke et al. [Quat Sci Rev 23:389–407 (2004)]. Quat Sci

Revs 24:1529–1532

Shaw J (1983) Drumlin formation related to inverted meltwater erosional marks. J Glaciol 29:461–

479

Shaw J, Kvill D, Rains B (1989) Drumlins and catastrophic subglacial ﬂoods. Sediment Geol

62:177–202

Shields A (1936) Anwendung der Ähnlichkeits mechanik und der Turbulenzforschung auf die

Geschiebebewegung. Mitteilung der Preussischen Versuchanstalt für Wasserbau und Schiffbau,

Heft 26, Berlin

Shreve RL (1985) Esker characteristics in terms of glacier physics, Katahdin esker system, Maine.

Geol Soc Amer Bull 96:639–646

Siegert MJ (2005) Lakes beneath the ice sheet: the occurrence, analysis, and future exploration of

Lake Vostok and other Antarctic subglacial lakes. Annu Rev Earth Planet Sci 33:215–245

Siegert MJ, Dowdeswell JA, Gorman MR, McIntyre NF (1996) An inventory of Antarctic sub-

glacial lakes. Antarct Sci 8:281–286

Siegert MJ, Ellis-Evans JC, Tranter M, Mayer C, Petit J-R, Salamatin A, Priscu JC (2001) Physical,

chemical and biological processes in Lake Vostok and other Antarctic subglacial lakes. Nature

414:603–608

Sigurdsson H (ed) (2000) Encyclopedia of volcanoes. Academic Press, San Diego

Sih GC (ed) (1973) Methods of analysis and solutions of crack problems. Noordhoff, Leyden

Sinclair, Sir John (ed) (1791–1799) The statistical account of Scotland: drawn up from the com-

munications of the ministers of the different parishes, 21 vols. William Creech, Edinburgh

Smith JD (1970) Stability of a sand bed subjected to a shear ﬂow of low Froude number. J Geophys

Res 75:5928–5940

Smith JD, McLean SR (1977) Spatially averaged ﬂow over a wavy surface. J Geophys Res

83:1735–1745

Smith JE (1971) The dynamics of shale compaction and evolution in pore-ﬂuid pressures. Math

Geol 3:239–263

Smith TR (2010) A theory for the emergence of channelized drainage. J Geophys Res 115:F02023.

doi:10.1029/2008JF001114

Smith TR, Bretherton FP (1972) Stability and the conservation of mass in drainage basin evolution.

Water Resour Res 8:1506–1529

Smith TR, Birnir B, Merchant GE (1997a) Towards an elementary theory of drainage basin evolu-

tion: I. The theoretical basis. Comput Geosci 23:811–822

References 869

Smith TR, Birnir B, Merchant GE (1997b) Towards an elementary theory of drainage basin evolu-

tion: II. A computational evaluation. Comput Geosci 23:823–849

Sneddon IN, Lowengrub M (1969) Crack problems in the classical theory of elasticity. Wiley, New

Yor k

Solomatov VS (1996) Stagnant lid convection on Venus. J Geophys Res 101:4737–4753

Solomon S (1999) Stratospheric ozone depletion: a review of concepts and history. Rev Geophys

37:275–316

Sparks RSJ, Huppert HE, Koyaguchi T, Hallworth MA (1993) Origin of modal and rhythmic ig-

neous layering by sedimentation in a convecting magma chamber. Nature 361:246–249

Sparks RSJ, Bursik MI, Carey SN, Gilbert JS, Glaze LS, Sigurdsson H, Woods AW (1997) Volcanic

plumes. Wiley, Chichester

Sparrow C (1982) The Lorenz equations: bifurcations, chaos, and strange attractors. Springer, New

Yor k

Sparrow EM, Cess RD (1978) Radiation heat transfer. Hemisphere, Belmont

Spence DA, Turcotte DL (1985) Magma driven propagation of cracks. J Geophys Res 90:575–580

Spence DA, Sharp PW, Turcotte DL (1987) Buoyancy-driven crack propagation: a mechanism for

magma migration. J Fluid Mech 174:135–153

Spiegelman M, Kelemen PB, Aharonov E (2001) Causes and consequences of ﬂow organization

during melt transport: the reaction inﬁltration instability in compactible media. J Geophys Res

106:2061–2078

Spohn T, Hort M, Fischer H (1988) Numerical simulation of the crystallization of multicomponent

melts in thin dikes or sills. 1. The liquidus phase. J Geophys Res 93:4880–4894

Spring U, Hutter K (1981) Numerical studies of jökulhlaups. Cold Reg Sci Technol 4:227–244

Spring U, Hutter K (1982) Conduit ﬂow of a ﬂuid through its solid phase and its application to

intraglacial channel ﬂow. Int J Eng Sci 20:327–363

Starostin AB, Barmin AA, Melnik OE (2005) A transient model for explosive and phreatomag-

matic eruptions. J Volcanol Geotherm Res 143:133–151

Stern ME (1960) The ‘salt fountain’ and thermohaline convection. Tellus 12:172–175

Stevenson DJ (1989) Spontaneous small-scale melt segregation in partial melts undergoing defor-

mation. Geophys Res Lett 16:1067–1070

Stocker TF, Johnsen SJ (2003) A minimum thermodynamic model for the bipolar seesaw. Pale-

oceanography 18:1087. doi:10.1029/2003PA000920

Stocker TF, Wright DG (1991) Rapid transitions of the ocean’s deep circulation induced by changes

in surface water ﬂuxes. Nature 351:729–732

Stoker JJ (1957) Water waves: the mathematical theory with applications. Interscience, New York

Stommel H (1961) Thermohaline convection with two stable régimes of ﬂow. Tellus 13:224–230

Strahler AN (1952) Hypsometric (area altitude) analysis of erosional topography. Geol Soc Amer

Bull 63:1117–1142

Strutt JW (Lord Rayleigh) (1871) On the light from the sky, its polarization and colour. Phil Mag

41:107–120

Su MD, Xu X, Zhu JL, Hon YC (2001) Numerical simulation of tidal bore in Hangzhou Gulf and

Qiantangjiang. Int J Numer Methods Fluids 36:205–247

Sugden D, Denton G (2004) Cenozoic landscape evolution of the Convoy Range to Mackay Glacier

area, Transantarctic Mountains: onshore to offshore synthesis. Geol Soc Am Bull 116:840–857

Sugden DE, John BS (1976) Glaciers and landscape: a geomorphological approach. Edward

Arnold, London

Sumer BM, Bakioglu M (1984) On the formation of ripples on an erodible bed. J Fluid Mech

144:177–190

Sykes RI (1980) An asymptotic theory of incompressible turbulent boundary-layer ﬂow over a

small hump. J Fluid Mech 101:647–670

Tackley P (1998) Self-consistent generation of tectonic plates in three-dimensional mantle convec-

tion. Earth Planet Sci Lett 157:9–22

Tackley P (2000a) Self-consistent generation of tectonic plates in time-dependent, three-

dimensional mantle convection simulations. 1. Pseudoplastic yielding. Geochem Geophys

Geosyst 1(8):1021. doi:10.1029/2000GC000036