Dynamics of Laboratory Diapir and Plume Models
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VOL. 80, NO. 5 JOURNAL OF GEOPHYSICALRESEARCH FEBRUARY 10, 1975 Dynamics of Laboratory Diapir and Plume Models JOHN A. WHITEHEAD, JR. Departmentof Physical Oceanography, Woods Hole Oceanographic Instituiion Woods Hole, Massachusetts 02543 DOUGLAS S. LUTHER WoodsHole OceanographicInstitution, WoodsHole, Massachusetts02543 MassachusettsInstitute of Technology,Cambridge, Massachusetts 02139 The low Reynoldsnumber dynamicsof a thin layer of fluid boundedbelow by a flat horizontal boundaryand movingbuoyantly through a fluid of anotherviscosity and densityis observedby meansof modelexperiments and is describedtheoretically. Three distinct stages of growthwere observed. The first stageis describedby a linearizedRayleigh-Taylor instability, for whichprevious literature, present theory, and experimentsexhibit closeagreement. In this stage,disturbances of one specificwave numberare foundto grow mostrapidly. In the secondstage, distortion of the interfaceis largeenough to invalidate the linearizedanalysis. It is found experimentallythat the fluid movesupward as circularcolumns sur- rounded by relatively broad regions of descendingmaterial. A theory is advancedthat attributes an acceleratedgrowth to a structureof thiskind througha resonanttriad interaction.In the third stage,fully matured structuresare formed. If the upwellingmaterial has greaterviscosity than the surrounding material,the structureis a long verticalcolumn with graduallydecreasing diameter; if the upwelling material has lessviscosity than the surroundingmaterial, the structuredevelops a rim synclineand a pronouncedoverhang and eventuallyascends as a sphericalpocket of fluid fed by a pipe. Dynamicex- planationsfor thesefeatures are advanced,and somepossible implications for geologicaland geophysical processesare discussed. , A number of theories about the internal horizontal structure laboratories,the greatestnumber were aimed specifically at the of the mantleinvolve hot spots,mantle plumes, pipes, ascend- salt dome problem. ing sheetsof fluid under ridges,ascending blobs of fluid un- The investigation.s have utilized essentially two approaches. der island arc chains, and the like. More needs to be done to In the first the materials have been assumed to be Newtonian reconcilethe possibilityof suchstructures with what is known fluids. Analytical resultswere then obtainedfor the growth of flow in a deformable material. ratesof disturbancesin a fluid that is initiallyalmost perfectly Likewise, on a smaller scale,various types of diapirs are flat. This problem has been formulatedby, among others, believedto be formed from a densityin.version. Perhaps the Dane• [1964], solvedtheoretically by Selig [1965], solvedalso most highly studied example is salt domes, a considerable by Blotand Odb [1965] and Blot [1966],and solved numericaH, y amount being known about the structureof the domesand the for many layers by Ramberg [1968a, b]. In all cases the fluid propertiesof salt at elevatedtemperature. However, a equationscould be solvedanalytically as a linearizedproblem, variety of other diapiric structurespossibly have similar and recourseto a computerwas necessaryonly to avoid heavy dynamic origins, such as granitic batholiths, mud volcanoes, algebraicmanipulation. Recently, Berner et al. [1972] have mud lumps, and clay diapirs. Survey papers and a recent used finite differencemethods to study more matured struc- bibliographyare given by Braunsteinand O'Brien [1968]. turesthat cannotbe studiedanalytically. Emphasis in all the As an attemptto understandsuch structures, this paperis paperswas confinedto the rangeof parametersbelieved to be concernedwith the qualitativeshape and quantitative important in salt domes. dynamicsthat occur Whena fluid of a given large viscosity Experimental observationsof such a Newtonian fluid were movesbuoyantly up or downthrough a fluidof anotherlarge made by Nettleton [1934] and Dobrin [194'1]in which clear viscosityand density in a fieldof gravity.We reporton experi- photographsand detailedqualitative discussion revealed that mentsin which a thin horizontallayer of fluid is observedto suchdomes possess many features of realsalt domes, although go unstableand deform to a matrix of upwellingspouts that no theorieswere advanced to explainthe featuresof the struc- rise through a denserfluid of anotherviscosity. It is observed tures. that the structuralfeatures are stronglydependent on which Thesecond approach has been to studythe instability of fluid is more viscous.The dynamicsof sucha processis dis- materials whose rheology is felt to be somewhat more cussed.Experiments in which a fluid is fed from a continuous earthlike.Because of uncertaintyin the rheOlogicalequations, sourceare described,and it is again noted that the structural very little theoreticalor quantitativework is possible,and the featuresare stronglydependent on which fluid is more viscous. articlesare confinedto describingqualitative features of the in- Theoriesfor the formationof the structuresare advancedby trusions.An extensivework of this nature is by Parker and usingNewtonian fluid dynamics.Lastly, a comparisonwith McDowell [1955], which also contains an excellent some diapiric formations will be made. bibliographyof earlier work. A secondset of qualitativeex- Of the theoretical and laboratory studiesof diastrophic perimental studieshas been done by Ramberg [1963, 1967, movementsthat have beenpreviously modeled by theory or in 1970], who subjectedspecimens of pasty material to cen- trifugal forces.This approachhas the distinctadvantage that Copyright¸ 1975by the AmericanGeophysical Union. relativelycomplex and realisticgeometries are easilystudied, 705 706 WHITEHEAD AND LUTHER: DYNAMICS OF LABORATORYDIAPIR AND PLUME MODELS and specimenscan be stored and studied for a relatively long neck of fluid feedingthese pockets almost pinchedoff and left period of time. a tiny pipe of fluid trailing the main pocket of fluid, which The presentpaper differs from theseearlier works in that a descendedthrough the viscousfluid as almost perfectspheres. large range of viscosities is studied theoretically, and ex- This sequenceis shown in Figure 2. The picturesare inverted periments are conducted for the limiting cases. for clarity. It appears that the unstableflows proceededthrough three OBSERVATIONS OF UNSTABLE LAYERS distinctphysical flow stages,which will be discussedin the next This sectionwill describesome simple experimentsthat were three sections.Initially, the surfacewas nearly flat, while small performed in order to visualizethe problem. The experiments distortions to the interface grew by a Rayleigh-Taylor in- were suggestedby D. Griggs after a seminar given by D. stability. During this stage the assumptionof an almost flat Chappell at the Institute of Geophysicsand Planetary Physics, surface allows the equations to be linearized, and the University of California at Los Angeles, in 1969. A container equations that describe the growing flow have long been was almost completely filled with glycerin with a kinematic known. Such a study predicts the wavelength of maximum viscosityof 1400cm•'/s and a densityof 1.25 g/cm 3, to which a growth and the exponential time constant of growth. The small amount of immisciblesilicone oil with a viscosityof 60,- predicted rates, which will be describedin the next section, 000 cm•'/sand a densityof 0.92 g/cm 3 was added. This formed agree with various observationsin the literature as well as with a layer on top of the glycerinapproximately 5 mm thick. The observationsin the experiment described here. container was then carefully coveredso that no air was left in The second stage occurred when the interface became dis- it. After being left overnight, the container was inverted. In torted enoughto violate the linearizingassumptions of the first about 30 s the layer of viscousoil (which was on the bottom of stage. More complicated physical processesthat generally the tank) was observedto develop protrusionsthat buoyantly have not been identified began to occur at this stage.A few of pushedupward through' the glycerin as long buoyancy-driven the things that can happen are enhancedgrowth rate (super- columns,shown in the seriesof photographsin Figure 1. We exponential),nonlinear interactions among the variousgrow- found in particular, that if the containerwas left carefully ing modes,and a consequentialnarrowing of the classof the leveledfor a number of days so that the oil interfacewas very fastestgrowing modes. A work discussingthis stage will be flat before inversion,the columnsthat developedwere spaced briefly describedin the sectionon the initiation of spouts. quite uniformly throughout the tank and were very nearly In the third stagethe interfacewas greatly distorted,and the equal in size, volume, and growth rate. The wave number of intrusions had developeda matured structure. The linearized the columns, defined as 2;rH/L, where L is the distance solutions now are completely inadequate for describing the between columns and H is the depth of the fluid, was flow. The experimentsindicated that this final state is also a 2.5. strong function of the ratios of the viscositiesof the two fluids. The same experimentwas performed with another container The dynamics of these structures will be hypothesized and filled almost completelywith siliconeoil and with a thin layer tested against experiment. These will be describedin the sec- of glycerin on the bottom. Again, after the container was tion on rim synclines,overhang, and 'necking.' carefully leveled and left