Stable Split Time Stepping Schemes for Large-Scale Ocean Modeling

ABSTRACT We present a method for efficiently modelling Braginskii viscosity on an unstructured, moving mesh. Braginskii viscosity, i.e. anisotropic transport of momentum with respect to the direction of the magnetic field, is thought to be of prime importance for studies of the weakly collisional plasma that comprises the intracluster medium (ICM) of galaxy clusters. Here, anisotropic transport of heat and momentum has been shown to have profound consequences for the stability properties of the ICM. Our new method for modelling Braginskii viscosity has been implemented in the moving mesh code arepo. We present a number of examples that serve to test the implementation and illustrate the modified dynamics found when including Braginskii viscosity in simulations. These include (but are not limited to) damping of fast magnetosonic waves, interruption of linearly polarized Alfvén waves by the firehose instability, and the inhibition of the Kelvin–Helmholtz instability by Braginskii viscosity. An explicit update of Braginskii viscosity is associated with a severe time-step constraint that scales with (Δx)2, where Δx is the grid size. In our implementation, this restrictive time-step constraint is alleviated by employing second-order accurate Runge–Kutta–Legendre super-time-stepping. We envision including Braginskii viscosity in future large-scale simulations of Kelvin–Helmholtz unstable cold fronts in cluster mergers and AGN-generated bubbles in central cluster regions.

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On the use of Schwarz–Christoffel conformal mappings to the grid generation for global ocean models

Geoscientific Model Development ◽

10.5194/gmd-8-3471-2015 ◽

2015 ◽

Vol 8 (10) ◽

pp. 3471-3485 ◽

Cited By ~ 2

Author(s):

S. Xu ◽

B. Wang ◽

J. Liu

Keyword(s):

General Circulation ◽

Large Scale ◽

Grid Cell ◽

Grid Generation ◽

General Circulation Models ◽

Conformal Mappings ◽

Ocean Modeling ◽

Global Ocean ◽

Ocean General Circulation Models ◽

Ocean General Circulation

Abstract. In this article we propose two grid generation methods for global ocean general circulation models. Contrary to conventional dipolar or tripolar grids, the proposed methods are based on Schwarz–Christoffel conformal mappings that map areas with user-prescribed, irregular boundaries to those with regular boundaries (i.e., disks, slits, etc.). The first method aims at improving existing dipolar grids. Compared with existing grids, the sample grid achieves a better trade-off between the enlargement of the latitudinal–longitudinal portion and the overall smooth grid cell size transition. The second method addresses more modern and advanced grid design requirements arising from high-resolution and multi-scale ocean modeling. The generated grids could potentially achieve the alignment of grid lines to the large-scale coastlines, enhanced spatial resolution in coastal regions, and easier computational load balance. Since the grids are orthogonal curvilinear, they can be easily utilized by the majority of ocean general circulation models that are based on finite difference and require grid orthogonality. The proposed grid generation algorithms can also be applied to the grid generation for regional ocean modeling where complex land–sea distribution is present.

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Three-Dimensional Hydrostatic Curved Channel Flow Simulations Using Non-Staggered Triangular Grids

Water ◽

10.3390/w14020174 ◽

2022 ◽

Vol 14 (2) ◽

pp. 174

Author(s):

Wei Zhang ◽

Miguel Uh Uh Zapata ◽

Damien Pham Van Pham Van Bang ◽

Kim Dan Nguyen

Keyword(s):

Finite Volume Method ◽

Finite Volume ◽

Channel Flow ◽

Large Scale ◽

Three Dimensional ◽

Ocean Modeling ◽

Curved Channel ◽

Triangular Grids ◽

Vortex Pattern ◽

Volume Method

Non-staggered triangular grids have many advantages in performing river or ocean modeling with the finite-volume method. However, horizontal divergence errors may occur, especially in large-scale hydrostatic calculations with centrifugal acceleration. This paper proposes an unstructured finite-volume method with a filtered scheme to mitigate the divergence noise and avoid further influencing the velocities and water elevation. In hydrostatic pressure calculations, we apply the proposed method to three-dimensional curved channel flows. Approximations reduce the numerical errors after filtering the horizontal divergence operator, and the approximation is second-order accurate. Numerical results for the channel flow accurately calculate the velocity profile and surface elevation at different Froude numbers. Moreover, secondary flow features such as the vortex pattern and its movement along the channel sections are also well captured.

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Rossby Wave Instability and Apparent Phase Speeds in Large Ocean Basins

Journal of Physical Oceanography ◽

10.1175/jpo3054.1 ◽

2007 ◽

Vol 37 (5) ◽

pp. 1177-1191 ◽

Cited By ~ 25

Author(s):

P. E. Isachsen ◽

J. H. LaCasce ◽

J. Pedlosky

Keyword(s):

Large Scale ◽

Initial Conditions ◽

Water System ◽

Local Deformation ◽

Equation Model ◽

Ocean Modeling ◽

High Latitudes ◽

Regional Ocean Modeling System ◽

Latitude Range ◽

The Stability

Abstract The stability of baroclinic Rossby waves in large ocean basins is examined, and the quasigeostrophic (QG) results of LaCasce and Pedlosky are generalized. First, stability equations are derived for perturbations on large-scale waves, using the two-layer shallow-water system. These equations resemble the QG stability equations, except that they retain the variation of the internal deformation radius with latitude. The equations are solved numerically for different initial conditions through eigenmode calculations and time stepping. The fastest-growing eigenmodes are intensified at high latitudes, and the slower-growing modes are intensified at lower latitudes. All of the modes have meridional scales and growth times that are comparable to the deformation radius in the latitude range where the eigenmode is intensified. This is what one would expect if one had applied QG theory in latitude bands. The evolution of large-scale waves was then simulated using the Regional Ocean Modeling System primitive equation model. The results are consistent with the theoretical predictions, with deformation-scale perturbations growing at rates inversely proportional to the local deformation radius. The waves succumb to the perturbations at the mid- to high latitudes, but are able to cross the basin at low latitudes before doing so. Also, the barotropic waves produced by the instability propagate faster than the baroclinic long-wave speed, which may explain the discrepancy in speeds noted by Chelton and Schlax.

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