Automating Finite Element Methods for Geodynamics via Firedrake

Firedrake is an automated system for solving partial differential equations using the finite element method. By applying sophisticated performance optimisations through automatic code-generation techniques, it provides a means to create accurate, efficient, flexible, easily extensible, scalable, transparent and reproducible research software, that is ideally suited to simulating a wide-range of problems in geophysical fluid dynamics. Here, we demonstrate the applicability of Firedrake for geodynamical simulation, with a focus on mantle dynamics. The accuracy and efficiency of the approach is confirmed via comparisons against a suite of analytical and benchmark cases of systematically increasing complexity, whilst parallel scalability is demonstrated up to 12288 compute cores, where the problem size and the number of processing cores are simultaneously increased. In addition, Firedrake's flexibility is highlighted via straightforward application to different physical (e.g. complex nonlinear rheologies, compressibility) and geometrical (2-D and 3-D Cartesian and spherical domains) scenarios. Finally, a representative simulation of global mantle convection is examined, which incorporates 230 Myr of plate motion history as a kinematic surface boundary condition, confirming its suitability for addressing research problems at the frontiers of global mantle dynamics research.

Overlapping boundary layers in coastal oceans

Boundary layer turbulence in coastal regions differs from that in deep ocean because of bottom interactions. In this paper, we focus on the merging of surface and bottom boundary layers in a finite-depth coastal ocean by numerically solving the wave-averaged equations using a large eddy simulation method. The ocean fluid is driven by combined effects of wind stress, surface wave, and a steady current in the presence of stable vertical stratification. The resulting flow consists of two overlapping boundary layers, i.e. surface and bottom boundary layers, separated by an interior stratification. The overlapping boundary layers evolve through three phases, i.e. a rapid deepening, an oscillatory equilibrium and a prompt merger, separated by two transitions. Before the merger, internal waves are observed in the stratified layer, and they are excited mainly by Langmuir turbulence in the surface boundary layer. These waves induce a clear modulation on the bottom-generated turbulence, facilitating the interaction between the surface and bottom boundary layers. After the merger, the Langmuir circulations originally confined to the surface layer are found to grow in size and extend down to the sea bottom (even though the surface waves do not feel the bottom), reminiscent of the well-organized Langmuir supercells. These full-depth Langmuir circulations promote the vertical mixing and enhance the bottom shear, leading to a significant enhancement of turbulence levels in the vertical column.

The Influence of a Suspended Cage Aquaculture Farm on the Hydrodynamic Environment in a Semienclosed Bay, SE China

Hydrodynamic responses of the aquaculture farm structures have been increasingly studied because of their importance in informing the aquaculture carrying capacity and ecological sustainability. The hydrodynamical effect of the suspended cage farm on flow structures and vertical mixing in the Sansha Bay, SE China, is examined using observational data of two comparative stations inside and outside the cage farm. The results show that current velocities are relatively uniform in the vertical except a bottom boundary layer outside the cage farm. Within the cage farm, the surface boundary layer produced by the cage-induced friction is obvious with current velocities decreasing upward, combining the classic bottom boundary layer to form a “double-drag layers” structure in the water column. The cage-induced drag decreases with water depth in the surface boundary layer with a maximum thickness of 3/4 the water column, and the current velocities can be reduced by 54%. The cage-induced friction can also significantly hinder the horizontal water exchange in the farm. Periodic stratification phenomena exist at both stations under the influence of lateral circulation. However, the subsurface (5–10 m below the sea surface) water column below the cage facilities is well-mixed as indicated by the vertical density profile, where the velocity shear (10–3 m–2) is about 10 times higher than that of the subsurface layer outside the cage farm. Therefore, we speculate that the well-mixing of the subsurface water column results from the local turbulence induced by the velocity shear, which in turn is produced by the friction of cage structures.

Interaction Between Waves and Turbulence Within the Nocturnal Boundary Layer

The presence of waves is proven to be ubiquitous within nocturnal stable boundary layers over complex terrain, where turbulence is in a continuous, although weak, state of activity. The typical approach based on Reynolds decomposition is unable to disaggregate waves from turbulence contributions, thus hiding any information about the production/destruction of turbulence energy injected/subtracted by the wave motion. We adopt a triple-decomposition approach to disaggregate the mean, wave, and turbulence contributions within near-surface boundary-layer flows, with the aim of unveiling the role of wave motion as a source and/or sink of turbulence kinetic and potential energies in the respective explicit budgets. By exploring the balance between buoyancy (driving waves) and shear (driving turbulence), a simple interpretation paradigm is introduced to distinguish two layers, namely the near-ground and far-ground sublayer, estimating where the turbulence kinetic energy can significantly feed or be fed by the wave. To prove this paradigm, a nocturnal valley flow is used as a case study to detail the role of wave motions on the kinetic and potential energy budgets within the two sublayers. From this dataset, the explicit kinetic and potential energy budgets are calculated, relying on a variance–covariance analysis to further comprehend the balance of energy production/destruction in each sublayer. With this investigation, we propose a simple interpretation scheme to capture and interpret the extent of the complex interaction between waves and turbulence in nocturnal stable boundary layers.

Numerical simulation of a tropical Storm boundary layer

A model has been designed to study the surface boundary layer of a tropical storm. The numerical method consists of solving a two point boundary value problem for two systems of simultaneous non-linear differential equations by finite differences. A Stoke's stream function suitable to represent the flow both in interior and exterior regions of a tropical storm boundary layer has been developed. The advantage of the method is that the, boundary layer of the tropical storm can be studied starting from the outer region to the centre of the storm without neglecting non-linear terms. In addition, there IS no need for assumptions on the vertical profiles for tangential and radial velocities. The method is stable and converges within a few iterations. The flow above the friction layer is represented by a steady axisymmetric vortex in gradient balance. To investigate the effect of turbulence- on boundary layer characteristics, turbulence has been represented by four different variations of the eddy coefficient of viscosity with no slip boundary conditions. Computations have been performed 1aking 40-grid points in the vertical direction. It is observed that, if the eddy coefficient of viscosity is assumed to vary with the superimposed flow above the boundary layer, the solutions compare favourably well with observations. The solution also shows an outflow from the Inner core of the boundary layer which is necessary for creation of an eye of the storm.

Past monsoons : A review of proxy data and modelling

Recent modelling studies have given insight into the role of internal feedback processes among components of the climate system on the evolution of monsoon strength since the Last Glacial Maximum (21,000 years ago). Here we present an overview of these modelling studies related to the summer monsoon over India and northern Africa. These studies indicate that the seasonal insolation changes alone do not explain the observed extent of hydrological changes during the early and middle Holocene over northern Africa. To simulate the extent of observed changes during this period incorporation of vegetation as an active component in climate models appears to be necessary. Over the Indian region, model results show that precipitation-soil moisture feedbacks play an important role in determining the response of the monsoon to changes in insolation and glacial-age surface boundary conditions. Indian monsoon strength from proxy records during the early and middle. Holocene have also been used in conjunction with coupled ocean atmosphere general circulation model experiments to refute the suggestion that semi-permanent warm surface conditions prevailed over equatorial Pacific ocean from 11 to 5ka.

Confined self-propulsion of an isotropic active colloid

To spontaneously break their intrinsic symmetry and self-propel at the micron scale, isotropic active colloidal particles and droplets exploit the nonlinear convective transport of chemical solutes emitted/consumed at their surface by the surface-driven fluid flows generated by these solutes. Significant progress was recently made to understand the onset of self-propulsion and nonlinear dynamics. Yet, most models ignore a fundamental experimental feature, namely the spatial confinement of the colloid, and its effect on propulsion. In this work the self-propulsion of an isotropic colloid inside a capillary tube is investigated numerically. A flexible computational framework is proposed based on a finite-volume approach on adaptative octree grids and embedded boundary methods. This method is able to account for complex geometric confinement, the nonlinear coupling of chemical transport and flow fields, and the precise resolution of the surface boundary conditions, that drive the system's dynamics. Somewhat counterintuitively, spatial confinement promotes the colloid's spontaneous motion by reducing the minimum advection-to-diffusion ratio or Péclet number, ${Pe}$ , required to self-propel; furthermore, self-propulsion velocities are significantly modified as the colloid-to-capillary size ratio $\kappa$ is increased, reaching a maximum at fixed ${Pe}$ for an optimal confinement $0<\kappa <1$ . These properties stem from a fundamental change in the dominant chemical transport mechanism with respect to the unbounded problem: with diffusion now restricted in most directions by the confining walls, the excess solute is predominantly convected away downstream from the colloid, enhancing front-back concentration contrasts. These results are confirmed quantitatively using conservation arguments and lubrication analysis of the tightly confined limit, $\kappa \rightarrow 1$ .

The dynamics of surface boundary layer during total Solar eclipse 1995

A microclimatological tower of 1.6 m height with six instrumented booms at different heights carrying wind speed, temperature and humidity sensors was set up at Robertsgun 24° 42'N, 83°4'E, 3l2m amsl) to study the implication of the total Solar eclipse on the dynamics of Atmospheric Boundary Layer (ABL). Apart from this, the soil temperature and heat flux were also measured during the same time. The observations were taken with a one minute average interval and recorded continuously with the data logger and then transferred to a PC for later use. The data were collected during 2l –26 October 1995. During the eclipse period decrease of surface temperature and soil temperature by 6.2°C and 3.5°C respectively and increase of humidity by nearly 60% were observed. Due to the decrease in velocity fluctuations, the mean wind speed showed the sharp increase compared to other days. The setting of stable atmosphere before the total solar eclipse was observed.