Variations in the abundances of elements and radiogenic isotopes in mantle derived peridotites and volcanic rocks are chemical integrals over time, space, and process, which ultimately contain information about the role of convection in the earth's mantle in creating, maintaining, and destroying geochemical heterogeneities. Successful inversion of these integrals requires extensive knowledge of the geochemical behavior of elements, the length scales of chemical variability, the evolution with time of geologic systems, the physical properties of mantle rocks, and the driving forces of phenomena which govern heat and mass transport in a dynamic earth. This dissertation attempts to add to this knowledge by examining the trace element and isotope geochemistry of mantle peridotites and oceanic island basalts, and by studying aspects of the flow of viscous fluids driven by thermal buoyancy. The trace element and isotopic systematics of peridotites and associated mafic layers from the Ronda Ultramafic Complex, southern Spain (Chapter 2), provides information bearing on the geochemical behavior of the highly incompatible elements U, Th, and Pb in the mantle, and on the length scales of geochemical variability in a well exposed peridotite massif. Garnet is demonstrated to be a significant host for U in the mantle, and together with clinopyroxene, these two minerals control the abundances and partitioning relationships of U and Th during the melting of anhydrous peridotite. Clinopyroxene, plagioclase, and to a lesser extent garnet are hosts for Pb in mantle peridotite; however, the role of trace sulfide may exert some control over the abundance and partitioning of Pb in some samples. Due to the possibility that Pb is partitioned into sulfide, the U/Pb, Th/Pb, and Ce/Pb ratios measured in clinopyroxene are likely to be higher than the bulk rock. U-Pb age systematics of garnet-clinopyroxene pairs from Ronda peridotites and mafic layers indicate Pb isotopic equilibrium in these samples up to 20-50 Ma ago. The Pb-Pb systematics of garnet- and spinel-facies peridotites and mafic layers indicate a heterogeneity on the order of 3 Ga old. This Pb isotope signature may have been created within the massif 3 Ga ago, or may have been metasomatically imprinted on the massif 1.3 Ga ago by basaltic melts with island arc affinities. The isotopic evolution of Ronda is consistent with at 1.3 Ga ago, and was subsequently incorporated into the subcontinental lithosphere. The very low U, Th, and Pb concentrations in depleted peridotite indicate that recycled crustal materials, with U-Th-Pb concentrations 102-104 times higher than peridotite, will have a larger influence on the isotopic composition of Pb in the mantle than on the Sr and Nd isotopic composition. An investigation of the trace element and isotopic compositions of clinopyroxenes in peridotite xenoliths from Savaii, Western Samoa and Tubuai, Austral Islands (Chapter 3) reveals geochemical signatures which are not present in basalts from these islands, due to the inherent averaging of melting processes. The data indicate similarities in the melting and melt segregation processes beneath these isotopically extreme islands. Samples with LREE depleted clinopyroxenes, with positive Zr and negative Ti anomalies, are the result of poly baric fractional melting of peridotite in the garnet- and spinel lherzolite stability fields, with the Savaii samples having experienced a larger mean degree of melting than the Tubuai samples. The extreme fractionation of HREE in the Savaii samples requires that they have melted to the clinopyroxene-out point (about 20%) while retaining residual garnet; the low concentrations ofHREE in these same samples requires a further 10-20% melting in the spinel lherzolite stability field. The extremely high total degrees of melting experienced by the Savaii samples (33-42%), as well as the high degree of melting in the garnet lherzolite stability field, suggests a mantle plume origin for these xenoliths. A large majority of the xenolith clinopyroxenes from both Savaii and Tubuai are LREE enriched to varying degrees, and many samples display significant intergrain trace element heterogeneity. This highly variable yet systematic heterogeneity was the result of metasomatism by percolating melts undergoing chromatographic trace element fractionation. The trace element compositions of some LREE enriched clinopyroxenes are consistent with the percolating melt being typical oceanic island basalt. The clinopyroxenes with the highest LREE concentrations from both islands, which also have very low Ti and Zr concentrations and large amounts of grain-boundary hosted Ba, require that the percolating melt in these cases had the trace element signature of carbonatite melt. The isotopic composition of one of these "carbonatitic" samples from Tubuai is similar to basalts from this island. The isotopic composition of clinopyroxene in a "carbonatitic" sample from Savaii records 87Sr/86Sr and l43Nd/l44Nd values of .71284 and .512516 respectively, far in excess of the most extreme Samoa basalt values (87Sr/86Sr=.70742, 143Nd/l44Nd=.51264). These "carbonatitic" signatures indicate the presence of volatilerich, isotopically extreme components in the mantle beneath Tubuai and Savaii, which likely have their origins in recycled crustal materials. The Re-Os isotope systematics of oceanic island basalts from Rarotonga, Savaii, Tahaa, Rurutu, Tubuai, and Mangaia are examined (Chapter 4). Os concentration variations suggest that olivine, or a low Re/Os phase associated with olivine, controls the Os concentration in basaltic magmas. The Savaii and Tahaa samples, with high 87Sr/86Sr and 207Pb/204Pb ratios (EMII), as well as basalts from Rarotonga, have 1870s/1860s ratios of 1.026-1.086, within the range of estimates of bulk silicate earth and depleted upper mantle. The basalts from Rurutu, Tubuai, and Mangaia (Macdonald hotspot), characterized by high Pb isotope ratios (HIMU), have 1870sfl860s ratios of 1.117-1.248, higher than any estimates for bulk silicate earth, and higher than Os isotope ratios of metasomatized peridotites. The high 1870s/1860s ratios indicate the presence of recycled oceanic crust in the mantle sources of Rurutu, Tubuai, and Mangaia. Inversion of the isotopic data for Mangaia (endmember HIMU) indicate that the recycled crustal component has Rb/Sr, Sm/Nd, Lu/Hf, and Th/U ratios which are very similar to fresh MORB glasses, and U/Pb and Th/Pb ratios which are within the range of MORB values, but slightly higher than average N-MORB. These results indicate that the low-temperature alteration signature of altered oceanic crust may be largely removed during subduction, and that oceanic crust was recycled into to the lower mantle source of the Macdonald hotspot plume. Furthennore, the high 187Os/l86Os ratios of the Tubuai and Mangaia basalts indicates that percolation through depleted mantle peridotite (187Os/186Qs=1.00-1.08), observed to occur in the Tubuai xenoliths, had little influence on the composition of the erupted basalts. A fluid dynamic model for mantle plumes is developed (Chapter 5) by examining a vertical, axisymmetric boundary layer originating from a point source of heat, and incorporating experimentally constrained rheological and physical properties of the mantle. Comparison of linear (n=l) and non-Newtonian (olivine, n=3) rheologies reveals that non-Newtonian plumes have narrower radii and higher vertical velocities than corresponding Newtonian plumes. The non-Newtonian plumes also exhibit "plug flow" at the conduit axis, providing a mechanism for the transport of deep mantle material, through the full depth of the mantle, in an unmixed state. Plumes are demonstrated to entrain ambient mantle via the horizontal conduction of heat, which increases the buoyancy and lowers the viscosity of mantle at the plume boundary. Streamlines calculated from the fluid dynamic model demonstrate that most of the entrained mantle originates from below 1500 km depth. Parameterization of the entrainment mechanism indicates that the factional amount of entrained mantle is lower in stronger, hotter plumes due to their higher vertical velocities. Examination of the global isotopic database for oceanic island basalts reveals the presence of a mantle component (FOZO), common to many hotspots worldwide, characterized by depleted 87Sr/86Sr and 143Nd/l44Nd, radiogenic 206,207,208Pb/204Pb, and high 3He/4He. This component is isotopically distinct from the source of MORB; thus, with the exception of ridge centered hotspots such as Iceland and the Galapagos, upper mantle does not appear to be a component in most hotspots, in agreement with entrainment theory. The combined fluid dynamic and isotopic results indicate that both FOZO and the enriched mantle components (EMI, EMil, and HIMU) are located in the lower mantle. Furthermore, high 3He/4He in FOZO precludes an origin for FOZO-bearing plumes in a thermal boundary layer at 670 km depth in the mantle. Since a 670 km thermal boundary layer would be replenished by the downward motion of the upper mantle, an origin for FOZO at 670 km would require either 1) a high 3He/4He signature in the MORB source, or 2) entrainment of MORB mantle into intraplate plumes, neither of which is observed in the OIB isotope data. This indicates that the 670 km discontinuity is not a barrier to mantle convection. The preservation of isotopically different upper and lower mantles does not require layered convection, but is probably the result of an increasing residence time with depth in the mantle, possibly caused by an increase in the mean viscosity of the mantle with depth