Convection in fluid and porous media

The subject of convection in fluid and porous media is investigated. Particular attention is paid to penetrative convection. The first two chapters are devoted to penetrative convection when fluid overlies and saturates a porous medium. Penetrative convection is described by a quadratic equation of state in the first instance and via internal heating in the second. Linear instability analyses are performed in both cases. A surprising and striking array of streamlines are presented at the onset of convection. The streamlines exhibit novel behaviour when physical parameters of the problem are varied. Penetrative convection in a horizontally isotropic porous layer is discussed next. Again penetrative convection is described by a quadratic equation of state and internal heating. The internally heated model is dealt with primarily as it yields a global nonlinear stability bound. The two models are shown to be mathematically adjoint and the nonlinear stability results compared with previously published linear ones. Good agreement between the two is seen. The effect of convection on the evolution of under-ice meltponds is investigated next. Linear and nonlinear analyses are employed to yield instability and global stability results respectively. Discrepancy between the two is found and the region of possible subcritical instabilities is presented. Finally convection in a porous medium is investigated via a cubic equation of state. It is found that unconditional nonlinear stability results can be established if Forchheimer theory is introduced. The results are compared to previously published linear ones and it is shown that the linear theory essentially captures the physics involved

Shear induced breaking of large internal solitary waves

The stability properties of 24 experimentally generated internal solitary waves (ISWs) of extremely large amplitude, all with minimum Richardson number less than 1/4, are investigated. The study is supplemented by fully nonlinear calculations in a three-layer fluid. The waves move along a linearly stratified pycnocline (depth h2) sandwiched between a thin upper layer (depth h1) and a deep lower layer (depth h3), both homogeneous. In particular, the wave-induced velocity profile through the pycnocline is measured by particle image velocimetry (PIV) and obtained in computation. Breaking ISWs were found to have amplitudes (a1) in the range a1>2.24 √h1h2(1+h2/h1), while stable waves were on or below this limit. Breaking ISWs were investigated for 0.27 0.86 and stable waves for Lx/λ < 0.86. The results show a sort of threshold-like behaviour in terms of Lx/λ. The results demonstrate that the breaking threshold of Lx/λ = 0.86 was sharper than one based on a minimum Richardson number and reveal that the Richardson number was found to become almost antisymmetric across relatively thick pycnoclines, with the minimum occurring towards the top part of the pycnoclinePostprintPeer reviewe

A conformal mapping approach to modelling two-dimensional stratified flow

Funding: This research received support from the UK Engineering and Physical Sciences Research Council (Impact Acceleration Account, both at the University of St Andrews and Newcastle University). This research received support from the UK Engineering and Physical Sciences Research Council (grants EP/R511778/1 and EP/R511584/1).Herein we describe a new approach to modelling inviscid two-dimensional stratified flows in a general domain. The approach makes use of a conformal map of the domain to a rectangle. In this transformed domain, the equations of motion are largely unaltered, and in particular Laplace's equation remains unchanged. This enables one to construct exact solutions to Laplace's equation and thereby enforce all boundary conditions. An example is provided for two-dimensional flow under the Boussinesq approximation, though the approach is much more general (albeit restricted to two-dimensions). This example is motivated by flow under a weir in a tidal estuary. Here, we discuss how to use a dynamically-evolving conformal map to model changes in the water height on either side of the weir, though the example presented keeps these heights fixed due to limitations in the computational speed to generate the conformal map. The numerical approach makes use of contour advection, wherein material buoyancy contours are advected conservatively by the local fluid velocity, while a dual contour-grid representation is used for the vorticity in order to account for vorticity generation from horizontal buoyancy gradients. This generation is accurately estimated by using the buoyancy contours directly, rather than a gridded version of the buoyancy field. The result is a highly-accurate, efficient numerical method with extremely low levels of numerical damping.Publisher PDFPeer reviewe

The characteristics of billows generated by internal solitary waves

The spatial and temporal development of shear-induced overturning billows associated with breaking internal solitary waves is studied by means of a combined laboratory and numerical investigation. The waves are generated in the laboratory by a lock exchange mechanism and they are simulated numerically via a contour-advective semi-Lagrangian method. The properties of individual billows (maximum height attained, time of collapse, growth rate, speed, wavelength, Thorpe scale) are determined in each case, and the billow interaction processes are studied and classified. For broad flat waves, similar characteristics are seen to those in parallel shear flow, but, for waves not at the conjugate flow limit, billow characteristics are affected by the spatially varying wave-induced shear flow. Wave steepness and wave amplitude are shown to have a crucial influence on determining the type of interaction that occurs between billows and whether billow overturning can be arrested. Examples are given in which billows (i) evolve independently of one another, (ii) pair with one another, (iii) engulf/entrain one another and (iv) fail to completely overturn. It is shown that the vertical extent a billow can attain (and the associated Thorpe scale of the billow) is dependent on wave amplitude but that its value saturates once a given amplitude is reached. It is interesting to note that this amplitude is less than the conjugate flow limit amplitude. The number of billows that form on a wave is shown to be dependent on wavelength; shorter waves support fewer but larger billows than their long-wave counterparts for a given stratification.PostprintPeer reviewe

Interaction of a mode-2 internal solitary wave with narrow isolated topography

This research was supported by the Natural Sciences and Engineering Research Council of Canada through a Discovery Grant (MS), and the Government of Ontario through a Queen Elizabeth II Graduate Scholarship in Science and Technology (DD). The experimental work was conducted at The University of Dundee by DD and MC with the aid of grants provided by The University of Dundee, the University of St Andrews, and the University of Waterloo.Numerical and experimental studies of the transit of a mode-2 internal solitary wave over an isolated ridge are presented. All studies used a quasi-two-layer fluid with a pycnocline centred at the mid-depth. The wave amplitude and total fluid depth were both varied, while the topography remained fixed. The strength of the interaction between the internal solitary waves and the hill was found to be characterized by three regimes: weak, moderate, and strong interactions. The weak interaction exhibited negligible wave modulation and bottom surface stress. The moderate interaction generated weak and persistent vorticity in the lower layer, in addition to negligible wave modulation. The strong interaction clearly showed material from the trapped core of the mode-2 wave extracted in the form of a thin filament while generating a strong vortex at the hill. A criterion for the strength of the interaction was found by non-dimensionalizing the wave amplitude by the lower layer depth, a/ℓ. A passive tracer was used to measure the conditions for resuspension of boundary material due to the interaction. The speed and prevalence of cross boundary layer transport increased with a/ℓ.PostprintPeer reviewe

Laboratory Experiments on Internal Solitary Waves in Ice-Covered Waters

Internal solitary waves (ISWs) propagating in a stably-stratified two-layer fluid in which the upper boundary condition changes from open water to ice are studied for cases of grease, level and nilas ice. The ISW-induced current at the surface is capable of trans-porting the ice in the horizontal direction. In the level ice case, the transport speed of, relatively long ice floes, non-dimensionalised by the wave speed is linearly dependent on the length of the ice floe non-dimensionalised by the wave length. Measures of turbulent kinetic energy dissipation under the ice are comparable to those at the wave density interface. Moreover, in cases where the ice floe protrudes into the pycnocline, interaction with the ice edge can cause the ISW to break or even be destroyed by the process. The results suggest that interaction between ISWs and sea ice may be an important mechanism for dissipation of ISW energy in the Arctic Ocean

Blockage of saline intrusions in restricted, two-layer exchange flows across a submerged sill obstruction

The work has been supported by European Community’s Seventh Framework Programme through the grant to the budget of the Integrating Activity HYDRALAB IV within the Transnational Access Activities, Contract No. 261520.Results are presented from a series of large-scale experiments investigating the internal and near-bed dynamics of bi-directional stratified flows with a net-barotropic component across a submerged, trapezoidal, sill obstruction. High-resolution velocity and density profiles are obtained in the vicinity of the obstruction to observe internal-flow dynamics under a range of parametric forcing conditions (i.e. variable saline and fresh water volume fluxes; density differences; sill obstruction submergence depths). Detailed synoptic velocity fields are measured across the sill crest using 2D particle image velocimetry, while the density structure of the two-layer exchange flows is measured using micro-conductivity probes at several sill locations. These measurements are designed to aid qualitative and quantitative interpretation of the internal-flow processes associated with the lower saline intrusion layer blockage conditions, and indicate that the primary mechanism for this blockage is mass exchange from the saline intrusion layer due to significant interfacial mixing and entrainment under dominant, net-barotropic, flow conditions in the upper freshwater layer. This interfacial mixing is quantified by considering both the isopycnal separation of vertically-sorted density profiles across the sill, as well as calculation of corresponding Thorpe overturning length scales. Analysis of the synoptic velocity fields and density profiles also indicates that the net exchange flow conditions remain subcritical (G < 1) across the sill for all parametric conditions tested. An analytical two-layer exchange flow model is then developed to include frictional and entrainment effects, both of which are needed to account for turbulent stresses and saline entrainment into the upper freshwater layer. The experimental results are used to validate two key model parameters: (1) the internal-flow head loss associated with boundary friction and interfacial shear; and (2) the mass exchange from the lower saline layer into the upper fresh layer due to entrainment.Publisher PDFPeer reviewe

Phase 1 clinical study of an embryonic stem cell-derived retinal pigment epithelium patch in age-related macular degeneration

Age-related macular degeneration (AMD) remains a major cause of blindness, with dysfunction and loss of retinal pigment epithelium (RPE) central to disease progression. We engineered an RPE patch comprising a fully differentiated, human embryonic stem cell (hESC)-derived RPE monolayer on a coated, synthetic basement membrane. We delivered the patch, using a purpose-designed microsurgical tool, into the subretinal space of one eye in each of two patients with severe exudative AMD. Primary endpoints were incidence and severity of adverse events and proportion of subjects with improved best-corrected visual acuity of 15 letters or more. We report successful delivery and survival of the RPE patch by biomicroscopy and optical coherence tomography, and a visual acuity gain of 29 and 21 letters in the two patients, respectively, over 12 months. Only local immunosuppression was used long-term. We also present the preclinical surgical, cell safety and tumorigenicity studies leading to trial approval. This work supports the feasibility and safety of hESC-RPE patch transplantation as a regenerative strategy for AMD