Hydrodynamic and hydromagnetic stability

Multiple abiotic and biotic factors combine in nature to influence the formation of calcium carbonate limestone deposits. Systems Geobiology studies of how micro-organisms respond to, or sometimes even control, the coupled effects of environmental change and mineralization will permit more accurate interpretation of the fossil record of ancient microbial life. Mammoth Hot Springs in Yellowstone National Park, USA, serves as a natural laboratory for tracking how the dynamic interplay of physical, chemical and biological factors come together to form hot-spring limestone (called ‘travertine’). Systematic downstream correlations occur at Mammoth Hot Springs between travertine deposition (geomorphology, crystalline structure and geochemistry), microbial communities (mat morphology, pigmentation, and phylogenetic and metabolic diversity) and spring-water conditions (temperature, pH, geochemistry and flow). Field-based microscale and mesoscale experimentation indicates that microbes directly influence travertine growth rate and crystalline structure. At the macroscale, time-lapse field photography and numerical modelling suggest that travertine terrace geomorphology is influenced strongly by hydrology, heat dispersion and geochemistry. These results from Mammoth Hot Springs allow establishment of a conceptual framework across broad spatial and temporal scales in which to track how multiple geological and biological factors combine to control CaCO3 crystal precipitation and the resulting formation of travertine deposits.

Hot‐spring Systems Geobiology: abiotic and biotic influences on travertine formation at Mammoth Hot Springs, Yellowstone National Park, USA

Heat transfer—A review of 2005 literature

Bödewadt flow and heat transfer over a stretching stationary disk

Effects of uniform radial electric field on the MHD heat and fluid flow due to a rotating disk

We consider the gravity-driven laminar flow of a shallow fluid layer down an uneven incline with the principal objective of investigating the effect of bottom topography and surface tension on the stability of the flow. The equations of motion are approximations to the Navier–Stokes equations which exploit the assumed relative shallowness of the fluid layer. Included in these equations are diffusive terms that are second order relative to the shallowness parameter. These terms, while small in magnitude, represent an important dependence of the flow dynamics on the variation in bottom topography and play a significant role in theoretically capturing important aspects of the flow. Some of the second-order terms include normal shear contributions, while others lead to a nonhydrostatic pressure distribution. The explicit dependence on the cross-stream coordinate is eliminated from the equations of motion by means of a weighted residual approach. The resulting mathematical formulation constitutes an extension ...

Instability in gravity-driven flow over uneven surfaces

The two-dimensional problem of gravity-driven laminar flow of a thin layer of fluid down a heated wavy inclined surface is discussed. The coupled effect of bottom topography, variable surface tension and heating has been investigated both analytically and numerically. A stability analysis is conducted while nonlinear simulations are used to validate the stability predictions and also to study thermocapillary effects. The governing equations are based on the Navier–Stokes equations for a thin fluid layer with the cross-stream dependence eliminated by means of a weighted residual technique. Comparisons with experimental data and direct numerical simulations have been carried out and the agreement is good. New interesting results regarding the combined role of surface tension and sinusoidal topography on the stability of the flow are presented. The influence of heating and the Marangoni effect are also deduced.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112010004003

Film flow over heated wavy inclined surfaces

Absolute and convective instabilities in the incompressible boundary layer on a rotating disk with temperature-dependent viscosity

The stability of a conducting fluid flow over a rotating disk with a uniform magnetic field applied normal to the disk, is investigated. It is assumed that the magnetic field is unaffected by the motion of the fluid. The mean flow and linear stability equations are solved for a range of magnetic field-strength parameters and the absolute/convective nature of the stability is investigated. It is found that increasing the magnetic field parameter is in general stabilizing.

Convective and absolute instability in the incompressible boundary layer on a rotating disk in the presence of a uniform magnetic field

The stability of a family of boundary-layer flows, which includes the von Karman, Bodewadt and Ekman flows for a rotating incompressible fluid between a rotating disc and a stationary lid, is investigated. Numerical computations with the use of a spectral method are carried out to analyse absolute and convective instability. It is shown that the stability of the system is enhanced with a decrease in distance between the disc and the lid.

H. A. Jasmine

Papers

Instability in gravity-driven flow over uneven surfaces

Film flow over heated wavy inclined surfaces

Absolute and convective instabilities in the incompressible boundary layer on a rotating disk with temperature-dependent viscosity

Convective and absolute instability in the incompressible boundary layer on a rotating disk in the presence of a uniform magnetic field

Absolute instability of the von Karman, Bodewadt and Ekman flows between a rotating disc and a stationary lid