Computation of multi-region, relaxed magnetohydrodynamic equilibria with prescribed toroidal current profile

The stepped-pressure equilibrium code (SPEC) (Hudson et al., Phys. Plasmas, vol. 19, issue 11, 2012, 112502) is extended to allow the computation of multi-region, relaxed magnetohydrodynamics (MRxMHD) equilibria at prescribed toroidal current profile. Toroidal currents are expressed in the framework of the MRxMHD theory, exhibiting spatial separation between pressure driven and externally driven currents. Additionally, analytical force balance derivatives at constant toroidal current are deployed in order to maintain SPEC's advantageous speed. The newly implemented capability is verified in screw pinch and classical stellarator geometries, and is applied to obtain the equilibrium $\beta$ -limit of a classical stellarator without net toroidal currents. This new capability opens the possibility to study the effect of toroidal current on three-dimensional equilibria with the SPEC code.

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Harmonic Analysis on Low Quality Tidal Data

Volume 8B: Ocean Engineering ◽

10.1115/omae2014-24014 ◽

2014 ◽

Author(s):

Joost den Haan

Keyword(s):

Harmonic Analysis ◽

Three Dimensional ◽

Measurement Data ◽

Tidal Energy ◽

Energy Yield ◽

Profile Measurement ◽

Current Profile ◽

Tidal Power ◽

Data Set ◽

Tidal Forcing

The aim of the study is to devise a method to conservatively predict a tidal power generation based on relatively short current profile measurement data sets. Harmonic analysis on a low quality tidal current profile measurement data set only allowed for the reliable estimation of a limited number of constituents leading to a poor prediction of tidal energy yield. Two novel, but very different approaches were taken: firstly a quasi response function is formulated which combines the currents profiles into a single current. Secondly, a three dimensional vectorial tidal forcing model was developed aiming to support the harmonic analysis with upfront knowledge of the actual constituents. The response based approach allowed for a reasonable prediction. The vectorial tidal forcing model proved to be a viable start for a full featuring numerical model; even in its initial simplified form it could provide more insight than the conventional tidal potential models.

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Experimental study of a pressure-driven, three-dimensional, turbulent boundary layer

10.2514/6.1986-211 ◽

1986 ◽

Cited By ~ 5

Author(s):

S. ANDERSON ◽

J. EATON

Keyword(s):

Boundary Layer ◽

Experimental Study ◽

Turbulent Boundary Layer ◽

Three Dimensional ◽

Pressure Driven

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Obstacle drag in stratified flow

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1990.0054 ◽

1990 ◽

Vol 429 (1876) ◽

pp. 119-140 ◽

Cited By ~ 22

Keyword(s):

Experimental Study ◽

Linear Density ◽

Three Dimensional ◽

Inviscid Flow ◽

Force Balance ◽

Video Recordings ◽

Lee Waves ◽

Time Variations ◽

Obstacle Height ◽

Stable Linear

This paper describes an experimental study of the drag of two- and three-dimensional bluff obstacles of various cross-stream shapes when towed through a fluid having a stable, linear density gradient with Brunt-Vaisala frequency, N . Drag measurements were made directly using a force balance, and effects of obstacle blockage ( h / D , where h and D are the obstacle height and the fluid depth, respectively) and Reynolds number were effectively eliminated. It is shown that even in cases where the downstream lee waves and propagating columnar waves are of large amplitude, the variation of drag with the parameter K ( = ND /π U ) is qualitatively close to that implied by linear theories, with drag minima existing at integral values of K . Under certain conditions large, steady, periodic variations in drag occur. Simultaneous drag measurements and video recordings of the wakes show that this unsteadiness is linked directly with time-variations in the lee and columnar wave amplitudes. It is argued that there are, therefore, situations where the inviscid flow is always unsteady even for large times; the consequent implications for atmospheric motions are discussed.

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ESTRUCTURA DE LA COMUNIDAD EPIFAUNAL ASOCIADA A COLONIAS DE VIDA LIBRE DEL HIDROCORAL MILLEPORA ALCICORNIS LINNAEUS 1758 EN BAHÍA PORTETE, CARIBE COLOMBIANO

Bulletin of Marine and Coastal Research ◽

10.25268/bimc.invemar.2006.35.0.223 ◽

2016 ◽

Vol 35 ◽

Author(s):

Carolina Castro S. ◽

Mario Monroy L. ◽

Oscar David Solano

Keyword(s):

Coral Species ◽

Three Dimensional ◽

Spatial Separation ◽

Juvenile Stage ◽

Living Tissue ◽

Free Living ◽

Invertebrate Species ◽

Epifaunal Community ◽

Dimensional Growth ◽

Petrolisthes Armatus

The epifaunal community associated with free-living colonies of Millepora alcicornis, the dominant coral species in Portete Bay, was characterized from twenty living colonies randomly collected within a shallow Thalassia testudinum seabed. The three-dimensional growth colonies sheltered 15 families, 15 genera and 18 mobile invertebrate species. The 97% of individuals was represented by decapods crustaceans specially adapted as to live in association with the host. Within them, the porcelanid Petrolisthes armatus, representing 79% of the epifauna (961 individuals), was exclusively found in a juvenile stage suggesting that M. alcicornis is mainly used by this species as a nursery zone. The epifaunal composition is partially related to coral living tissue whereas the principal simbionts size is correlated with the spatial separation of coral branches. In spite of being slightly diverse in comparison with the epifaunal community found in other coral species, the epifauna found in M. alcicornis is of great interest and peculiarity by their association with the free-living form of this coral.

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Improved convergence and stability properties in a three-dimensional higher-order ice sheet model

Geoscientific Model Development Discussions ◽

10.5194/gmdd-4-1569-2011 ◽

2011 ◽

Vol 4 (3) ◽

pp. 1569-1610

Author(s):

J. J. Fürst ◽

O. Rybak ◽

H. Goelzer ◽

B. De Smedt ◽

P. de Groen ◽

...

Keyword(s):

Velocity Field ◽

Finite Difference ◽

Three Dimensional ◽

Ice Sheet ◽

Higher Order ◽

Velocity Fields ◽

Force Balance ◽

Staggered Grid ◽

Comparison Results ◽

Resultant Velocity

Abstract. We present a novel finite difference implementation of a three-dimensional higher-order ice sheet model that performs well both in terms of convergence rate and numerical stability. In order to achieve these benefits the discretisation of the governing force balance equation makes extensive use of information on staggered grid points. Using the same iterative solver, an existing discretisation that operates exclusively on the regular grid serves as a reference. Participation in the ISMIP-HOM benchmark indicates that both discretisations are capable of reproducing the higher-order model inter-comparison results. This allows a direct comparison not only of the resultant velocity fields but also of the solver's convergence behaviour which holds main differences. First and foremost, the new finite difference scheme facilitates convergence by a factor of up to 7 and 2.6 in average. In addition to this decrease in computational costs, the precision for the resultant velocity field can be chosen higher in the novel finite difference implementation. For high precisions, the old discretisation experiences difficulties to converge due to large variation in the velocity fields of consecutive Picard iterations. Finally, changing discretisation prevents build-up of local field irregularites that occasionally cause divergence of the solution for the reference discretisation. The improved behaviour makes the new discretisation more reliable for extensive application to real ice geometries. Higher precision and robust numerics are crucial in time dependent applications since numerical oscillations in the velocity field of subsequent time steps are attenuated and divergence of the solution is prevented. Transient applications also benefit from the increased computational efficiency.

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Sheared free-surface flow over three-dimensional obstructions of finite amplitude

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.657 ◽

2019 ◽

Vol 878 ◽

pp. 740-767

Author(s):

Andreas H. Akselsen ◽

Simen Å. Ellingsen

Keyword(s):

Perturbation Technique ◽

Three Dimensional ◽

Free Surface Flow ◽

Radiation Condition ◽

Finite Amplitude ◽

Higher Order ◽

Surface Flow ◽

Current Profile ◽

Bottom Boundary Condition ◽

Lord Kelvin

When shallow water flows over uneven bathymetry, the water surface is modulated. This type of problem has been revisited numerous times since it was first studied by Lord Kelvin in 1886. Our study analytically examines currents whose unperturbed velocity profile $U(z)$ follows a power law $z^{q}$, flowing over a three-dimensional uneven bed. This particular form of $U$, which can model a miscellany of realistic flows, allows explicit analytical solutions. Arbitrary bed shapes can readily be imposed via Fourier’s theorem provided their steepness is moderate. Three-dimensional vorticity–bathymetry interaction effects are evident when the flow makes an oblique angle with a sinusoidally corrugated bed. Streamlines are found to twist and the fluid particle drift is redirected away from the direction of the unperturbed current. Furthermore, a perturbation technique is developed which satisfies the bottom boundary condition to arbitrary order also for large-amplitude obstructions which penetrate well into the current profile. This introduces higher-order harmonics of the bathymetry amplitude. States of resonance for first- and higher-order harmonics are readily calculated. Although the method is theoretically restricted to bathymetries of moderate inclination, a wide variety of steeper obstructions are satisfactorily represented by the method, even provoking occurrences of recirculation. All expressions are analytically explicit and sequential fast Fourier transformations ensure quick and easy computation for arbitrary three-dimensional bathymetries. A method for separating near and far fields ensures computational convergence under the appropriate radiation condition.

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A Spatial Filter Approach to Evaluating the Role of Convection on the Evolution of a Mesoscale Vortex

Journal of the Atmospheric Sciences ◽

10.1175/jas-d-12-0186.1 ◽

2013 ◽

Vol 70 (7) ◽

pp. 1954-1976 ◽

Cited By ~ 3

Author(s):

Glenn A. Creighton ◽

Robert E. Hart ◽

Philip Cunningham

Keyword(s):

Three Dimensional ◽

Spatial Separation ◽

Spatial Filter ◽

Tropical Cyclogenesis ◽

Moist Convection ◽

Mesoscale Vortex ◽

Convective Scale ◽

Vortical Hot Towers ◽

Order Of Magnitude ◽

Deep Moist Convection

Abstract A new spatial filter is proposed that exploits a spectral gap in power between the convective scale and the system (“vortex”) scale during tropical cyclone (TC) genesis simulations. Using this spatial separation, this study analyzes idealized three-dimensional numerical simulations of deep moist convection in the presence of a symmetric midlevel vortex to quantify and understand the energy cascade between the objectively defined convective scale and system scale during the early stages of tropical cyclogenesis. The simulations neglect surface momentum, heat, and moisture fluxes to focus on generation and enhancement of vorticity within the interior to more completely close off the energy budget and to be consistent for comparison with prior benchmark studies of modeled TC genesis. The primary contribution to system-scale intensification comes from the convergence of convective-scale vorticity that is supplied by vortical hot towers (VHTs). They contribute more than the convergence of system-scale vorticity to the spinup of vorticity in these simulations by an order of magnitude. Analysis of the change of circulation with time shows an initial strengthening of the surface vortex, closely followed by a growth of the mid- to upper-level circulation. This evolution precludes any possibility of a stratiform precipitation–induced top-down mechanism as the primary contributor to system-scale spinup in this simulation. Instead, an upscale cascade of rotational kinetic energy during vortex mergers is responsible for spinup of the simulated mesoscale vortex. The spatial filter employed herein offers an alternative approach to the traditional symmetry–asymmetry paradigm, acknowledges the highly asymmetric evolution of the system-scale vortex itself, and may prove useful to future studies on TC genesis.

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Three-dimensional reconstructed glomerular capillary network: blood flow distribution and local filtration

AJP Renal Physiology ◽

10.1152/ajprenal.1992.263.3.f562 ◽

1992 ◽

Vol 263 (3) ◽

pp. F562-F572 ◽

Cited By ~ 6

Author(s):

A. Remuzzi ◽

B. M. Brenner ◽

V. Pata ◽

G. Tebaldi ◽

R. Mariano ◽

...

Keyword(s):

Blood Flow ◽

Theoretical Model ◽

Three Dimensional ◽

Capillary Network ◽

Rheological Parameters ◽

Image Analysis System ◽

Heterogeneous Distribution ◽

Filtration Pressure ◽

Pressure Equilibrium ◽

Topological Organization

We developed a mathematical model to simulate blood flow and filtration in individual capillary segments of a glomerular network reconstructed from a normal Munich-Wistar (MW) rat. Three-dimensional geometric reconstruction was obtained by semithin serial sections (1 micron) of one glomerulus after perfusion fixation of kidney. Photomicrographs of each section were digitized and processed, using a computer-based image-analysis system, to derive the topological organization of the capillary network and mean diameter and length of individual capillary segments. Blood flow rate in capillary segments was calculated using a theoretical model that considers apparent viscosity of blood in small capillaries as a function of local rheological parameters, partition of cells at bifurcations, and local filtration dependent on transmembrane hydraulic and oncotic pressure gradients along the network. In accord with previous observations, the topological organization of the capillary network disclosed a three-lobular structure. The ultrafiltration coefficient (Kf) calculated for the euvolemic MW rat with the present network approach was compared with that derived from a theoretical model that assumes identical capillaries in parallel. The latter model is shown to underestimate Kf, particularly under conditions in which filtration pressure equilibrium is approached. Calculation of local blood flow and filtration along the network indicates a heterogeneous distribution of these parameters and that some parts of the capillary network operate at filtration pressure equilibrium even if the overall network operates at filtration disequilibrium.

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