Open Boundary Conditions in Numerical Ocean Models

1986 ◽  
pp. 411-436 ◽  
Author(s):  
L. P. Røed ◽  
C. K. Cooper
Keyword(s):  
Boundary Conditions ◽  
Open Boundary ◽  
Open Boundary Conditions ◽  
Ocean Models

scholarly journals Considerations on Open Boundary Conditions for Regional and Coastal Ocean Models

2006 ◽  
Vol 23 (11) ◽  
pp. 1604-1613 ◽  
Author(s):  
P. Marsaleix ◽  
F. Auclair ◽  
C. Estournel
Keyword(s):  
Energy Conservation ◽  
Boundary Conditions ◽  
Radiation Condition ◽  
Coastal Ocean ◽  
Open Boundary ◽  
External Information ◽  
Advection Equation ◽  
Open Boundary Conditions ◽  
Ocean Models ◽  
Mass And Energy Conservation

Abstract This paper reviews the usual open boundary conditions (OBCs) for coastal ocean models and proposes a complete set of open boundaries based on stability criteria, on mass and energy conservation arguments, and on the ability to enforce external information. This set includes a radiation condition for barotropic variables, an equation of wave propagation for baroclinic velocities, and an advection equation for tracers. Considerations on mass and energy conservation properties suggest a suitable numerical treatment of the barotropic scheme, which is different from what is commonly used. Restoring terms, when classically added in the Sommerfeld OBCs, are not consistent with external fields. It is shown that this can be avoided if proper numerical schemes are used or if OBCs are applied on differences between the model and forcing rather than on absolute variables. Finally, this paper shows that simplistic advection-type methods for temperature and salinity should not be used in sigma coordinate models because this introduces errors in the computation of the horizontal pressure gradient.

scholarly journals Impurity induced scale-free localization

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Linhu Li ◽  
Ching Hua Lee ◽  
Jiangbin Gong
Keyword(s):  
Boundary Conditions ◽  
Skin Effect ◽  
Reciprocal Lattice ◽  
Periodic Boundary Conditions ◽  
Open Boundary ◽  
Open Boundary Conditions ◽  
Translational Invariance ◽  
Scale Free ◽  
Special Cases ◽  
Simulation Results

AbstractNon-Hermitian systems have been shown to have a dramatic sensitivity to their boundary conditions. In particular, the non-Hermitian skin effect induces collective boundary localization upon turning off boundary coupling, a feature very distinct from that under periodic boundary conditions. Here we develop a full framework for non-Hermitian impurity physics in a non-reciprocal lattice, with periodic/open boundary conditions and even their interpolations being special cases across a whole range of boundary impurity strengths. We uncover steady states with scale-free localization along or even against the direction of non-reciprocity in various impurity strength regimes. Also present are Bloch-like states that survive albeit broken translational invariance. We further explore the co-existence of non-Hermitian skin effect and scale-free localization, where even qualitative aspects of the system’s spectrum can be extremely sensitive to impurity strength. Specific circuit setups are also proposed for experimentally detecting the scale-free accumulation, with simulation results confirming our main findings.

scholarly journals Measuring Chern numbers in Hofstadter strips

2017 ◽  
Vol 3 (2) ◽  
Author(s):  
Samuel Mugel ◽  
Alexandre Dauphin ◽  
Pietro Massignan ◽  
Leticia Tarruell ◽  
Maciej Lewenstein ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary Conditions ◽  
Chern Number ◽  
Open Boundary ◽  
Topological Invariants ◽  
Transverse Displacement ◽  
Open Boundary Conditions ◽  
Open Questions ◽  
Chern Numbers ◽  
Spatial Dimensions

Topologically non-trivial Hamiltonians with periodic boundary conditions are characterized by strictly quantized invariants. Open questions and fundamental challenges concern their existence, and the possibility of measuring them in systems with open boundary conditions and limited spatial extension. Here, we consider transport in Hofstadter strips, that is, two-dimensional lattices pierced by a uniform magnetic flux which extend over few sites in one of the spatial dimensions. As we show, an atomic wave packet exhibits a transverse displacement under the action of a weak constant force. After one Bloch oscillation, this displacement approaches the quantized Chern number of the periodic system in the limit of vanishing tunneling along the transverse direction. We further demonstrate that this scheme is able to map out the Chern number of ground and excited bands, and we investigate the robustness of the method in presence of both disorder and harmonic trapping. Our results prove that topological invariants can be measured in Hofstadter strips with open boundary conditions and as few as three sites along one direction.

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