Modelling dispersion and mixing in geophysical flows

This thesis is concerned with modelling geophysical flows. The problems considered in this work include dispersion in flows through heterogeneous porous rocks, turbulent mixing in the surface layer of the ocean, and mixing in turbulent starting plumes. In chapters 2, 3 and 4, we study the longitudinal dispersion of a passive tracer by a two-dimensional pressure-driven flow through a layer of heterogeneous porous rock which is bounded above and below by impermeable seal rock. In chapters 2 and 3, we assume that the heterogeneity of the rock is due to localised regions of different permeability located at randomly assigned vertical positions within the otherwise uniform permeability layer. It is well known that in a porous layer of large cross-flow extent, such heterogeneity leads to Fickian-type dispersion. However, many porous rocks consist of relatively thin, laterally extensive layers. As a result, streamlines in the centre of the channel can be diverted upwards or downwards into regions of higher permeability, while streamlines near the boundaries are more restricted. We demonstrate that this results in a net cross-layer shear in the mean flow. We develop a depth-averaged model for the dispersal of a pulse of tracer by the flow, which shows that although at early times the Fickian dispersion dominates, at large distances downstream the spreading of the pulse of tracer is controlled by the shear. In chapter 4, we demonstrate this shear in a cross-bedded formation, focusing on the flow across an interface between two neighbouring zones of the rock. We explore the strength of this shear as a function of the permeability ratio across the interface and the interface angle. Finally, in chapters 5 and 6, we focus our attention on mixing in turbulent flows, considering two classes of problems -- turbulent mixing of a passive tracer in the ocean mixed layer and mixing in turbulent starting plumes. In chapter 5, we present results from high resolution numerical simulations of the ocean mixed layer to estimate an exact functional relationship between the turbulent fluxes and the gradients of a passive tracer. This functional form of the eddy diffusivity does not use any closure assumptions, and it highlights both local and non-local effects of mixing of a passive tracer. For simplicity, we restrict our focus to convection-driven mixing in an idealised two-dimensional surface layer of the ocean. In chapter 6, we explore the dynamics of turbulent starting plumes by analysis of a series of new small-scale laboratory experiments to describe the mixing and interaction between the plume head, the following steady plume, and the ambient. We find that the head of the plume ascends with a speed which is approximately 0.6 times the characteristic speed of the fluid in the following steady plume, and so the fluid released from the source eventually catches the head of the flow. On reaching the top of the plume, it recirculates and mixes in the plume head. We present results from new experiments to visualise the dispersion of the source fluid in the plume head, and propose a theoretical model to describe the dynamics of the plume head. We present our conclusions and discuss directions for future work in chapter 7.Cambridge Trust, Total SA studentship (Department of Earth Sciences

Shear generation in a confined, composite layer of cross-bedded porous rock

We study the longitudinal spreading of a passive tracer by a two-dimensional pressure-driven flow through a composite layer of porous rock which is bounded above and below by impermeable seal rock. We focus on the flow across the interface between two neighbouring zones of the rock. First, we show that, with isotropic permeability, if the interface between the two zones is tilted relative to the boundaries, then this results in a difference in travel times across the formation which in turns leads to a net shear flow. We explore the strength of this shear as a function of (a) the permeability ratio across the interface, and (b) the interface angle. Second, we show that if one zone of the rock is cross-bedded, then with uniform flow, the pressure gradient is directed at an angle to the boundary. As a result, there is a transition zone across the interface, which again leads to a net shear, even if the interface is normal to the boundaries of the layer. We explore the competition between these effects, showing how they may combine constructively to produce a larger shear, or may negate one another, reducing or reversing the sign of the shear, depending on the angle of the interface, the degree of anisotropy and the change in effective downstream permeability across the interface. We discuss some of the implications of this shear for modelling flow in such composite rocks

The ventilation of buildings and other mitigating measures for COVID-19: a focus on wintertime.

The year 2020 has seen the emergence of a global pandemic as a result of the disease COVID-19. This report reviews knowledge of the transmission of COVID-19 indoors, examines the evidence for mitigating measures, and considers the implications for wintertime with a focus on ventilation.This work was undertaken as a contribution to the Rapid Assistance in Modelling the Pandemic (RAMP) initiative, coordinated by the Royal Society

Shear generation in a confined, composite layer of cross-bedded porous rock

Abstract Cambridge Trust, Total SA studentshi

NeverWorld2: an idealized model hierarchy to investigate ocean mesoscale eddies across resolutions

© The Author(s), 2022. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Marques, G. M., Loose, N., Yankovsky, E., Steinberg, J. M., Chang, C.-Y., Bhamidipati, N., Adcroft, A., Fox-Kemper, B., Griffies, S. M., Hallberg, R. W., Jansen, M. F., Khatri, H., & Zanna, L. NeverWorld2: an idealized model hierarchy to investigate ocean mesoscale eddies across resolutions. Geoscientific Model Development, 15(17), (2022): 6567–6579, https://doi.org/10.5194/gmd-15-6567-2022.We describe an idealized primitive-equation model for studying mesoscale turbulence and leverage a hierarchy of grid resolutions to make eddy-resolving calculations on the finest grids more affordable. The model has intermediate complexity, incorporating basin-scale geometry with idealized Atlantic and Southern oceans and with non-uniform ocean depth to allow for mesoscale eddy interactions with topography. The model is perfectly adiabatic and spans the Equator and thus fills a gap between quasi-geostrophic models, which cannot span two hemispheres, and idealized general circulation models, which generally include diabatic processes and buoyancy forcing. We show that the model solution is approaching convergence in mean kinetic energy for the ocean mesoscale processes of interest and has a rich range of dynamics with circulation features that emerge only due to resolving mesoscale turbulence.This research has been supported by the US Department of Commerce (grant no. NA18OAR4320123), the Division of Ocean Sciences (grant nos. 1912420, 1912332, 1912357, 1912163, and 1912302), the Division of Atmospheric and Geospace Sciences (grant no. 1852977), and the Climate Program Office (grant nos. NA19OAR4310364, NA19OAR4310365, and NA19OAR4310366)

NeverWorld2: an idealized model hierarchy to investigate ocean mesoscale eddies across resolutions

Abstract. We describe an idealized primitive-equation model for studying mesoscale turbulence and leverage a hierarchy of grid resolutions to make eddy-resolving calculations on the finest grids more affordable. The model has intermediate complexity, incorporating basin-scale geometry with idealized Atlantic and Southern oceans and with non-uniform ocean depth to allow for mesoscale eddy interactions with topography. The model is perfectly adiabatic and spans the Equator and thus fills a gap between quasi-geostrophic models, which cannot span two hemispheres, and idealized general circulation models, which generally include diabatic processes and buoyancy forcing. We show that the model solution is approaching convergence in mean kinetic energy for the ocean mesoscale processes of interest and has a rich range of dynamics with circulation features that emerge only due to resolving mesoscale turbulence. </jats:p