Maximum principle preserving high order schemes for convection-dominated diffusion equations

The maximum principle is an important property of solutions to PDE. Correspondingly, it's of great interest for people to design a high order numerical scheme solving PDE with this property maintained. In this thesis, our particular interest is solving convection-dominated diffusion equation. We first review a nonconventional maximum principle preserving(MPP) high order finite volume(FV) WENO scheme, and then propose a new parametrized MPP high order finite difference(FD) WENO framework, which is generalized from the one solving hyperbolic conservation laws. A formal analysis is presented to show that a third order finite difference scheme with this parametrized MPP flux limiters maintains the third order accuracy without extra CFL constraint when the low order monotone flux is chosen appropriately. Numerical tests in both one and two dimensional cases are performed on the simulation of the incompressible Navier-Stokes equations in vorticity stream-function formulation and several other problems to show the effectiveness of the proposed method.

Thermal Convection and the Origin of Ice Streams

Ice streams are a fact of ice-sheet dynamics, draining up to 90% of the ice. Thermal convection in ice below the density inversion is a speculation. An attempt is made to meld the two in such a way that the speculation becomes an explanation for the fact.

Reactive mass transport modelling of a three-dimensional vertical fault zone with a finger-like convective flow regime

For a three-dimensional vertically-oriented fault zone, we consider the coupled effects of fluid flow, heat transfer and reactive mass transport, to investigate the patterns of fluid flow, temperature distribution, mineral alteration and chemically induced porosity changes. We show, analytically and numerically, that finger-like convection patterns can arise in a vertically-oriented fault zone. The onset and patterns of convective fluid flow are controlled by the Rayleigh number which is a function of the thermal properties of the fluid and the rock, the vertical temperature gradient, and the height and the permeability of the fault zone. Vigorous fluid flow causes low temperature gradients over a large region of the fault zone. In such a case, flow across lithological interfaces becomes the most important mechanism for the formation of sharp chemical reaction fronts. The degree of rock buffering, the extent and intensity of alteration, the alteration mineralogy and in some cases the formation of ore deposits are controlled by the magnitude of the flow velocity across these compositional interfaces in the rock. This indicates that alteration patterns along compositional boundaries in the rock may provide some insights into the convection pattern. The advective mass and heat exchanges between the fault zone and the wallrock depend on the permeability contrast between the fault zone and the wallrock. A high permeability contrast promotes focussed convective flow within the fault zone and diffusive exchange of heat and chemical reactants between the fault zone and the wallrock. However, a more gradual permeability change may lead to a regional-scale convective flow system where the flow pattern in the fault affects large-scale fluid flow, mass transport and chemical alteration in the wallrocks

A laboratory-scale experiment and a numerical simulation of unusual spiral plumes in a High-Prandtl-number fluid, links supplementary material

We experimentally and numerically investigated the generation of plumes from a local heat source (LHS) and studied the interaction of these plumes with cellular convective motion (CCM) in a rectangular cavity filled with silicon oil at a Prandtl number (Pr) of approximately two thousand. The LHS is generated using a 0.2-W green laser beam. A roll-type CCM is generated by vertically heating one side of the cavity. The CCM may lead to the formation of an unusual spiral convective plume that resembles a vertical Archimedes spiral. A similar plume is obtained in a direct numerical simulation. We discuss the physical mechanism for the formation of a spiral plume and the application of the results to mantle convection problems. We also estimate the Reynolds (Re) and Rayleigh (Ra) numbers and apply self-similarity theory to convection in the Earth's mantle. Spiral plumes can be used to interpret mantle tomography results over the last decade.

Underway physical oceanography and carbonate chemistry measured during the EURO-BASIN cruise M87/1 (Deep Convection Cruise)

The track of the cruise, and the location of the different stations cover a large range of water masses, many of which take part in the exchange across the Greenland-Scotland Ridge, and of importance for the biogeochemical fluxes in the region. These water masses are of very different origins, which can be observed in the concentration of the different biogeochemical parameters. The concentrations are a result of the combination of the physical and biogeochemical environment in each formation region, and the processes acting on the water masses as they are transported away from the formation areas. The aim of the biogeochemistry measurements was to achieve a better understanding of the strength and variability of the biological carbon pump in the North Atlantic and Nordic Seas.

High frequency high-order Rayleigh modes in ZnO/GaAs

Strong high-order Rayleigh or Sezawa modes, in addition to the fundamental Rayleigh mode, have been observed in ZnO/GaAs(001) systems along the [110] propagation direction of GaAs. The dispersion of the different acoustic waves has been calculated and compared to the experimental data. The bandwidth and impedance matching characteristics of the multimode SAW delay lines operating at high frequencies (2.5-3.5 GHz regime) have been investigated.

On the onset of turbulence in natural convection on inclined plates

The problem of determination of the turbulence onset in natural convection on heated inclined plates in an air environment has been experimentally revisited. The transition has been detected by using hot wire velocity measurements. The onset of turbulence has been considered to take place where velocity fluctuations (measured through turbulence intensity) start to grow. Experiments have shown that the onset depends not only on the Grashof number defined in terms of the temperature difference between the heated plate and the surrounding air. A correlation between dimensionless Grashof and Reynolds numbers has been obtained, fitting quite well the experimental data.

Self-consistent numerical dispersion relation of the ablative Rayleigh-Taylor instability of double ablation fronts in inertial confinement fusion

The linear stability analysis of accelerated double ablation fronts is carried out numerically with a self-consistent approach. Accurate hydrodynamic profiles are taken into account in the theoretical model by means of a fitting parameters method using 1D simulation results. Numerical dispersión relation is compared to an analytical sharp boundary model [Yan˜ez et al., Phys. Plasmas 18, 052701 (2011)] showing an excellent agreement for the radiation dominated regime of very steep ablation fronts, and the stabilization due to smooth profiles. 2D simulations are presented to validate the numerical self-consistent theory.

Reentrant and whirling hexagons in non-Boussinesq convection

We review recent computational results for hexagon patterns in non- Boussinesq convection. For sufficiently strong dependence of the fluid parameters on the temperature we find reentrance of steady hexagons, i.e. while near onset the hexagon patterns become unstable to rolls as usually, they become again stable in the strongly nonlinear regime. If the convection apparatus is rotated about a vertical axis the transition from hexagons to rolls is replaced by a Hopf bifurcation to whirling hexagons. For weak non-Boussinesq effects they display defect chaos of the type described by the two-dimensional (2D) complex Ginzburg-andau equation. For stronger non-Boussinesq effects the Hopf bifurcation becomes subcritical and localized bursting of the whirling amplitude is found. In this regime the cou- pling of the whirling amplitude to (small) deformations of the hexagon lattice becomes important. For yet stronger non-Boussinesq effects this coupling breaks up the hexagon lattice and strongly disordered states characterized by whirling and lattice defects are obtained.

Hydrothermal waves and corotating rolls in laterally heated convection in simple liquids.

The stability of a liquid layer with an undeformable interface open to the atmo- sphere, subjected to a horizontal temperature gradient, is theoretically analysed. Buoyancy and surface tension forces give rise to a basic flow for any temperature dif- ference applied on the system. Depending on the liquid depth, this basic flow is desta- bilised either by an oscillatory instability, giving rise to the so-called hydrothermal waves, or by a stationary instability leading to corotating rolls. Oscillatory perturba- tions are driven by the basic flow and therefore one must distinguish between convec- tive and absolute thresholds. The instability mechanisms as well as the di¿erent re- gimes observed in experiments are discussed. The calculations are performed for a fluid used in recent experiments, namely silicone oil of 0.65 cSt ðPr 1?4 10Þ. In partic- ular, it is shown that two branches of absolute instability exist, which may be related to the two types of hydrothermal waves observed experimentally

Hexagonal patterns in a model for rotating convection

We study a model equation that mimics convection under rotation in a fluid with temperature- dependent properties (non-Boussinesq (NB)), high Prandtl number and idealized boundary conditions. It is based on a model equation proposed by Segel [1965] by adding rotation terms that lead to a Kuppers-Lortz instability [Kuppers & Lortz, 1969] and can develop into oscillating hexagons. We perform a weakly nonlinear analysis to find out explicitly the coefficients in the amplitude equation as functions of the rotation rate. These equations describe hexagons and os- cillating hexagons quite well, and include the Busse?Heikes (BH) model [Busse & Heikes, 1980] as a particular case. The sideband instabilities as well as short wavelength instabilities of such hexagonal patterns are discussed and the threshold for oscillating hexagons is determined.