scholarly journals Thermomechanically coupled modelling for land-terminating glaciers: a comparison of two-dimensional, first-order and three-dimensional, full-Stokes approaches

2015 ◽  
Vol 61 (228) ◽  
pp. 702-712 ◽  
Author(s):  
Tong Zhang ◽  
Lili Ju ◽  
Wei Leng ◽  
Stephen Price ◽  
Max Gunzburger
Keyword(s):  
Initial Conditions ◽  
Three Dimensional ◽  
Integration Time ◽  
Two Dimensional ◽  
Shape Factors ◽  
Coupled Modelling ◽  
First Order ◽  
Glacier Changes ◽  
Basal Sliding ◽  
Long Time

AbstractFor many regions, glacier inaccessibility results in sparse geometric datasets for use as model initial conditions (e.g. along the central flowline only). In these cases, two-dimensional (2-D) flowline models are often used to study glacier dynamics. Here we systematically investigate the applicability of a 2-D, first-order Stokes approximation flowline model (FLM), modified by shape factors, for the simulation of land-terminating glaciers by comparing it with a 3-D, ‘full’-Stokes ice-flow model (FSM). Based on steady-state and transient, thermomechanically uncoupled and coupled computational experiments, we explore the sensitivities of the FLM and FSM to ice geometry, temperature and forward model integration time. We find that, compared to the FSM, the FLM generally produces slower horizontal velocities, due to simplifications inherent to the FLM and to the underestimation of the shape factor. For polythermal glaciers, those with temperate ice zones, or when basal sliding is important, we find significant differences between simulation results when using the FLM versus the FSM. Over time, initially small differences between the FLM and FSM become much larger, particularly near cold/temperate ice transition surfaces. Long time integrations further increase small initial differences between the two models. We conclude that the FLM should be applied with caution when modelling glacier changes under a warming climate or over long periods of time.

Upstream motions in stratified flow

1988 ◽  
Vol 187 ◽  
pp. 487-506 ◽  
Author(s):  
I. P. Castro ◽  
W. H. Snyder
Keyword(s):  
Body Height ◽  
Three Dimensional ◽  
Time Dependent ◽  
Experimental Measurements ◽  
Two Dimensional ◽  
Towing Tank ◽  
First Order ◽  
Density Perturbations ◽  
Small Obstacle ◽  
Obstacle Height

In this paper experimental measurements of the time-dependent velocity and density perturbations upstream of obstacles towed through linearly stratified fluid are presented. Attention is concentrated on two-dimensional obstacles which generate turbulent separated wakes at Froude numbers, based on velocity and body height, of less than 0.5. The form of the upstream columnar modes is shown to be largely that of first-order unattenuating disturbances, which have little resemblance to the perturbations described by small-obstacle-height theories. For two-dimensional obstacles the disturbances are similar to those found by Wei, Kao & Pao (1975) and it is shown that provided a suitable obstacle drag coefficient is specified, the lowest-order modes (at least) are quantitatively consistent with the results of the Oseen inviscid model.Discussion of some results of similar measurements upstream of three-dimensional obstacles, the importance of towing tank endwalls and the relevance of the Foster & Saffman (1970) theory for the limit of zero Froude number is also included.

scholarly journals Three-Dimensional Coordination Number from Two-Dimensional Measurements: A New Method

1986 ◽  
Vol 32 (112) ◽  
pp. 391-396 ◽  
Author(s):  
Richard B. Alley
Keyword(s):  
Coordination Number ◽  
Three Dimensional ◽  
New Method ◽  
Two Dimensional ◽  
Shape Factors ◽  
Important Measure ◽  
Dimensional Measurements ◽  
Average Bond

AbstractThe average three-dimensional coordination number, n3, is an important measure of firn structure. The value of n3 can be estimated from n2, the average measured two-dimensional coordination number, and from a function, Γ, that depends only on the ratio of average bond radius to grain radius in the sample. This method is easy to apply and does not require the use of unknown shape factors or tunable parameters.

scholarly journals Penerapan Teknologi Augmented Reality Sebagai Informasi Dan Navigasi Pada Taman Rekreasi Sengkaling

Repositor ◽  
2020 ◽  
Vol 2 (5) ◽  
pp. 553
Author(s):  
Tirto Adhi Triambodo ◽  
Ali Sofyan Kholimi ◽  
Lailatul Husniah
Keyword(s):  
Augmented Reality ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Application System ◽  
Virtual Objects ◽  
Existing Problems ◽  
Information Center ◽  
Long Time ◽  
Augmented Reality Technology ◽  
Vehicle Information

AbstrakTaman Rekreasi Sengkaling memiliki luas keseluruhan  9 hektar yang terdiri dari 6 hektar  diantaranya ada taman dan pepohonan hijau. Mengingat luasnya Taman Rekreasi Sengkaling, disana tidak ada peta dan tempat lokasi pusat informasi wahana berada di pintu masuk yang tentu akan membuat pengunjung bingung ketika sudah berada didalam Taman Rekreasi Sengkaling ingin mengetahui informasi wahana dan membutuhkan waktu lama dalam mencapai tujuan wahana yang diinginkan. Berdasarkan dari permasalahan yang ada, maka dibutuhkan suatu aplikasi yang bisa memberikan informasi dan navigasi sehingga pengunjung dapat dengan mudah mengetahui informasi wahana dan navigasi menuju lokasi wahana. Augmented Reality adalah teknologi yang menggabungkan benda maya dua dimensi dan ataupun tiga dimensi ke dalam lingkungan nyata tiga dimensi. Teknologi Augmented Reality ini digunakan untuk pembuatan aplikasi untuk informasi dan navigasi pada Taman Rekreasi Sengkaling. Pada pengujian sistem berdasarkan hasil kuesioner dengan 5 pertanyaan kepada 30 responden untuk memakai aplikasi AR Taman Rekreasi Sengkaling. Dari pengujian sistem aplikasi AR kepada user yang memilih setuju dengan presentase 91%. Maka hasil yang didapatkan, penggunaan aplikasi Augmented Reality direspon baik oleh pengunjung Taman Rekreasi Sengkaling.Abstract  Sengkaling Recreation Park has a total area of 9 hectares consisting of 6 hectares of which there are parks and green trees. Given the breadth of the Sengkaling Recreation Park, there is no map and location of the information center where the vehicle is located at the entrance which would make visitors confused when already in the Sengkaling Recreation Park wants to know vehicle information and takes a long time to reach the desired destination. Based on the existing problems, it requires an application that can provide information and navigation so that visitors can easily find information on vehicle and navigation to the location of the vehicle. Augmented Reality is a technology that combines two-dimensional and / or three-dimensional virtual objects into a real three-dimensional environment. This Augmented Reality technology is used for making applications for information and navigation in Sengkaling Recreation Park. On testing the system based on the results of the questionnaire with 5 questions to 30 respondents to use the AR Sengkaling Recreational Park application. From testing the AR application system to users who choose to agree with a percentage of 91%. Then the results obtained, the use of Augmented Reality applications responded well by visitors to the Sengkaling Recreation Park.

scholarly journals Steady-State Three-Dimensional Ice Flow over an Undulating Base: First-Order Theory with Linear Ice Rheology

1987 ◽  
Vol 33 (114) ◽  
pp. 177-185 ◽  
Author(s):  
Niels Reeh
Keyword(s):  
Three Dimensional ◽  
Steady Motion ◽  
Simple Shear Flow ◽  
Finite Width ◽  
Two Dimensional ◽  
Internal Layers ◽  
Ice Flow ◽  
Depth Variation ◽  
First Order ◽  
First Order Theory

AbstractThe problem of ice flow over threedimensional basal irregularities is studied by considering the steady motion of a fluid with a linear constitutive equation over sine-shaped basal undulations. The undisturbed flow is simple shear flow with constant depth. Using the ratio of the amplitude of the basal undulations to the ice thickness as perturbation parameter, equations to the first order for the velocity and pressure perturbations are set up and solved.The study shows that when the widths of the basal undulations are larger than 2–3 times their lengths, the finite width of the undulations has only a minor influence on the flow, which to a good approximation may be considered two-dimensional. However, as the ratio between the longitudinal and the transverse wavelengthL/Wincreases, the three-dimensional flow effects becomes substantial. If, for example, the ratio ofLtoWexceeds 3, surface amplitudes are reduced by more than one order of magnitude as compared to the two-dimensional case. TheL/Wratio also influences the depth variation of the amplitudes of internal layers and the depth variation of perturbation velocities and strain-rates. With increasingL/Wratio, the changes of these quantities are concentrated in a near-bottom layer of decreasing thickness. Furthermore, it is shown, that the azimuth of the velocity vector may change by up to 10° between the surface and the base of the ice sheet, and that significant transverse flow may occur at depth without manifesting itself at the surface to any significant degree.

scholarly journals Steady-State Three-Dimensional Ice Flow over an Undulating Base: First-Order Theory with Linear Ice Rheology

1987 ◽  
Vol 33 (114) ◽  
pp. 177-185 ◽  
Author(s):  
Niels Reeh
Keyword(s):  
Three Dimensional ◽  
Steady Motion ◽  
Simple Shear Flow ◽  
Finite Width ◽  
Two Dimensional ◽  
Internal Layers ◽  
Ice Flow ◽  
Depth Variation ◽  
First Order ◽  
First Order Theory

AbstractThe problem of ice flow over threedimensional basal irregularities is studied by considering the steady motion of a fluid with a linear constitutive equation over sine-shaped basal undulations. The undisturbed flow is simple shear flow with constant depth. Using the ratio of the amplitude of the basal undulations to the ice thickness as perturbation parameter, equations to the first order for the velocity and pressure perturbations are set up and solved.The study shows that when the widths of the basal undulations are larger than 2–3 times their lengths, the finite width of the undulations has only a minor influence on the flow, which to a good approximation may be considered two-dimensional. However, as the ratio between the longitudinal and the transverse wavelength L/W increases, the three-dimensional flow effects becomes substantial. If, for example, the ratio of L to W exceeds 3, surface amplitudes are reduced by more than one order of magnitude as compared to the two-dimensional case. The L/W ratio also influences the depth variation of the amplitudes of internal layers and the depth variation of perturbation velocities and strain-rates. With increasing L/W ratio, the changes of these quantities are concentrated in a near-bottom layer of decreasing thickness. Furthermore, it is shown, that the azimuth of the velocity vector may change by up to 10° between the surface and the base of the ice sheet, and that significant transverse flow may occur at depth without manifesting itself at the surface to any significant degree.

On the Hysteresis of Adsorption on Solid Surfaces

1952 ◽  
Vol 5 (2) ◽  
pp. 288
Author(s):  
RG Wylie
Keyword(s):  
Phase Transitions ◽  
Solid Surface ◽  
Three Dimensional ◽  
Solid Surfaces ◽  
Two Dimensional ◽  
Capillary Effects ◽  
First Order ◽  
Adsorption Of Gases ◽  
First Order Phase ◽  
Hysteresis Phenomena

Hysteresis phenomena associated with the adsorption of gases on solid surfaces are usually explained in terms of three-dimensional capillary effects or with more or less unspecific reference to phase transitions. It is shown that hysteresis effects are to be expected when two dimensional phase transitions occur on solids. In the connection, the thermodynamic equation governing the equilibrium of small, incompressible two-dimensional phases is derived. Such phases can form on an imperfect solid surface in an irreversible manner and, as calculation shows, can contribute significantly to the hysteresis of adsorption. In some cases the phase change may be responsible for the whole effect. The diffuseness of first-order phase transitions may be due to the same mechanism.

Three-dimensional impulsive vortex formation from slender orifices

2011 ◽  
Vol 666 ◽  
pp. 506-520 ◽  
Author(s):  
F. DOMENICHINI
Keyword(s):  
Stokes Equations ◽  
Intermediate Phase ◽  
Vortex Formation ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Vortex Ring Formation ◽  
Long Time ◽  
Definition Of

The vortex formation behind an orifice is a widely investigated phenomenon, which has been recently studied in several problems of biological relevance. In the case of a circular opening, several works in the literature have shown the existence of a limiting process for vortex ring formation that leads to the concept of critical formation time. In the different geometric arrangement of a planar flow, which corresponds to an opening with straight edges, it has been recently outlined that such a concept does not apply. This discrepancy opens the question about the presence of limiting conditions when apertures with irregular shape are considered. In this paper, the three-dimensional vortex formation due to the impulsively started flow through slender openings is studied with the numerical solution of the Navier–Stokes equations, at values of the Reynolds number that allow the comparison with previous two-dimensional findings. The analysis of the three-dimensional results reveals the two-dimensional nature of the early vortex formation phase. During an intermediate phase, the flow evolution appears to be driven by the local curvature of the orifice edge, and the time scale of the phenomena exhibits a surprisingly good agreement with those found in axisymmetric problems with the same curvature. The long-time evolution shows the complete development of the three-dimensional vorticity dynamics, which does not allow the definition of further unifying concepts.

Long-time symplectic integration: the example of four-vortex motion

1991 ◽  
Vol 432 (1886) ◽  
pp. 481-494 ◽  
Keyword(s):  
Fourth Order ◽  
Initial Conditions ◽  
Hamiltonian Formulation ◽  
Superior Performance ◽  
Integration Time ◽  
Characteristic Time Scale ◽  
Symplectic Integration ◽  
Time Step ◽  
Long Time ◽  
Runge Kutta

Detailed comparisons are made between long-time numerical integration of the motion of four identical point vortices obtained using both a fourth-order symplectic integration method of the implicit Runge-Kutta type and a standard fourth-order explicit Runge-Kutta scheme. We utilize the reduced hamiltonian formulation of the four-vortex problem due to Aref & Pomphrey. Initial conditions which give both fully chaotic and also quasi-periodic motions are considered over integration times of order 10 6 -10 7 times the characteristic time scale of the evolution. The convergence, as the integration time step is decreased, of the Poincaré section is investigated. When smoothness of the section compared to the converged image, and the fractional change in the hamiltonian H are used as diagnostic indicators, it is found that the symplectic scheme gives substantially superior performance over the explicit scheme, and exhibits only an apparent qualitative degrading in results up to integration time steps of order the minimum timescale of the evolution. It is concluded that this performance derives from the symplectic rather than the implicit character of the method.

Vortex merger in rotating stratified flows

2002 ◽  
Vol 455 ◽  
pp. 83-101 ◽  
Author(s):  
DAVID G. DRITSCHEL
Keyword(s):  
Aspect Ratio ◽  
Initial Conditions ◽  
Random Noise ◽  
Three Dimensional ◽  
Separation Distance ◽  
Two Dimensional ◽  
Initial Separation ◽  
Weak Exchange ◽  
First Results ◽  
Asymmetric Vortices

This paper describes the interaction of symmetric vortices in a three-dimensional quasi-geostrophic fluid. The initial vortices are taken to be uniform-potential-vorticity ellipsoids, of height 2h and width 2R, and with centres at (±d/2; 0, 0), embedded within a background flow having constant background rotational and buoyancy frequencies, f/2 and N respectively. This problem was previously studied by von Hardenburg et al. (2000), who determined the dimensionless critical merger distance d/R as a function of the height-to-width aspect ratio h/R (scaled by f/N). Their study, however, was limited to small to moderate values of h/R, as it was anticipated that merger at large h/R would reduce to that for two columnar two-dimensional vortices, i.e. d/R ≈ 3.31. Here, it is shown that no such two-dimensional limit exists; merger is found to occur at any aspect ratio, with d ∼ h for h/R [Gt ] 1.New results are also found for small to moderate values of h/R. In particular, our numerical simulations reveal that asymmetric merger is predominant, despite the initial conditions, if one includes a small amount of random noise. For small to moderate h/R, decreasing the initial separation distance d first results in a weak exchange of material, with one vortex growing at the expense of the other. As d decreases further, this exchange increases and leads to two dominant but strongly asymmetric vortices. Finally, for yet smaller d, rapid merger into a single dominant vortex occurs – in effect the initial vortices exchange nearly all of their material with one another in a nearly symmetrical fashion.

Self-Organization in Three-Dimensional Hydrodynamic Turbulence Self-Organization in Three-Dimensional Hydrodynamic Turbulence

1990 ◽  
Vol 45 (9-10) ◽  
pp. 1059-1073 ◽  
Author(s):  
G. Knorr ◽  
J. P. Lynov ◽  
H. L. Pécseli
Keyword(s):  
Euler Equations ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Self Organization ◽  
Two Dimensional ◽  
Hydrodynamic Turbulence ◽  
Available Energy ◽  
Wave Numbers ◽  
Negative Helicity ◽  
Incompressible Euler

Abstract The three-dimensional incompressible Euler equations are expanded in eigenflows of the curl operator, which represent positive and negative helicity flows in a particularly simple and convenient way. Four different basic types of interactions between eigenflows are found. Two represent an "inverse cascade", the interaction familiar from the two-dimensional Euler equations, in which only modes of the same sign of the helicity interact. The other two interactions mix positive and negative helicity modes. Only these interactions can transport all of the available energy to higher wave numbers. Initial conditions, which lead to the appearance of structures and self-organization, are discussed.

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