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It is a general problem in geoscience to estimate the time-series of velocity and temperature fields for a fluid based on limited observations, such as the flow velocity at the fluid surface and/or a temperature snapshot after flow. In this study, an adjoint-based data assimilation method (also known as 4-D variational data assimilation) was used to reconstruct the thermal convection in a highly viscous fluid (e.g. Earth's mantle) to investigate which observations constrain the thermal convection and how accurately the convection can be reconstructed for different wavelengths. The data assimilated to the adjoint-based model were generated synthetically from forward models with convecting cells of different length-scales. Based on the surface velocity and temperature snapshot, our simulations successfully reconstructed thermal convection over 50 Myr in the case that the wavelength of the convective cells is sufficiently large. We obtained two main results from this parametric study. (1) When we only considered instantaneous thermal structure fitting in the cost function, the convection reconstruction tended to fail. However, there are some cases where the laminar thermal convection can be reconstructed by assimilating only the velocity along the fluid surface. (2) There is a limit to the reconstruction of thermal convection in the case that the convecting cells are small (∼1000 km for a 50 Myr reconstruction). We propose that (1) is related to the balance of forces due to the thermal buoyancy and viscous stress around the thermal anomalies and (2) is related to how information is preserved (i.e. how the previous thermal structure is maintained in the observable state throughout the convection process). The results enable the use of geological records to estimate time-series of velocity and temperature in Earth's deep interior, even though the records may only contain information from shallow parts of Earth. [ABSTRACT FROM AUTHOR]

Cellular structures are hydrodynamically interconnected, such that force generation in one location can move distal structures. One example of this phenomenon is cytoplasmic streaming, whereby active forces at the cell cortex induce streaming of the entire cytoplasm. However, it is not known how the spatial distribution and magnitude of these forces move distant objects within the cell. To address this issue, we developed a computational method that used cytoplasm hydrodynamics to infer the spatial distribution of shear stress at the cell cortex induced by active force generators from experimentally obtained flow field of cytoplasmic streaming. By applying this method, we determined the shear-stress distribution that quantitatively reproduces in vivo flow fields in Caenorhabditis elegans embryos and mouse oocytes during meiosis II. Shear stress in mouse oocytes were predicted to localize to a narrower cortical region than that with a high cortical flow velocity and corresponded with the localization of the cortical actin cap. The predicted patterns of pressure gradient in both species were consistent with species-specific cytoplasmic streaming functions. The shear-stress distribution inferred by our method can contribute to the characterization of active force generation driving biological streaming. [ABSTRACT FROM AUTHOR]