A new nested boundary condition for a primitive equation

Nested boundary techniques are developed based on the results of Perkins [1993] and Blake [1991]. We focus on the numerical and physical consistency needs across the nested boundary. These techniques replace the transition zone used by other researchers with a numerically and a physically based correction step. We demonstrate our method using a nested, reduced gravity version of the Naval Research Laboratory (NRL) primitive equation ocean model and a two-layer hydrodynamic finite-depth version of the same model. Numerical experiments are performed using integrations of both an idealized double gyre and a realistic Greenland Iceland Norwegian (GIN) Sea configuration. To illustrate the need for improved boundary treatment, we present a numerical study of boundary errors. The study illustrates the fragile nature of nested boundary conditions. With even small errors, a dramatic impact is observed on the formation (or lack thereof) of the Atlantic-Norwegian Current, which is responsible for transporting North Atlantic water to the Arctic Ocean, in the GIN Sea configuration.

[1]  A. L. Perkins.  Regional Gulf-Stream Initial Conditions for the SPEM Primitive Equation Model , 1995 .

[2]  George Keith Batchelor,et al.  An Introduction to Fluid Dynamics. , 1969 .

[3]  Clifford D. Johnson,et al.  Simulations of the mesoscale circulation of the Greenland‐Iceland‐Norwegian Seas , 1995 .

[4]  Akio Arakawa,et al.  Computational Design of the Basic Dynamical Processes of the UCLA General Circulation Model , 1977 .

[5]  Da‐Lin Zhang,et al.  A two-way interactive nesting procedure with variable terrain resolution , 1986 .

[6]  Steven E. Koch,et al.  A Survey of Nested Grid Techniques and Their Potential for Use Within the MASS Weather , 1987 .

[7]  Gregory J. Tripoli,et al.  Design of a Movable Nested-Mesh Primitive Equation Model , 1979 .

[8]  Ping Chen,et al.  A nested‐grid ocean model: With application to the simulation of meanders and eddies in the Norwegian Coastal Current , 1992 .

[9]  J. Pedlosky.  Geophysical Fluid Dynamics , 1979 .

[10]  L. Trefethen.  Group velocity interpretation of the stability theory of Gustafsson, Kreiss, and Sundström , 1983 .

[11]  W. Schmitz,et al.  A limited-area model of the Gulf Stream: design, initial experiments, and model-data intercomparison , 1989 .

[12]  J. Oliger,et al.  Theoretical and practical aspects of some initial-boundary value problems in fluid dynamics , 1976 .

[13]  R. E. Young,et al.  Initialization and data assimilation experiments with a primitive equation model , 1989 .

[14]  A. Majda,et al.  Absorbing boundary conditions for the numerical simulation of waves , 1977 .

[15]  S. J. Maskell,et al.  Two-Way Interactive Nesting of Primitive Equation Ocean Models with Topography , 1995 .

[16]  Sol Hellerman,et al.  Normal Monthly Wind Stress Over the World Ocean with Error Estimates , 1983 .

[17]  H. Hurlburt,et al.  The dynamics of the loop current and shed eddies in a numerical model of the Gulf of Mexico , 1982 .

[18]  M. Meredith,et al.  Erratum: Correction to ``On the temporal variability of the transport through Drake Passage'' , 1996 .

[19]  H. Hurlburt,et al.  A Numerical Study of Loop Current Intrusions and Eddy Shedding , 1980 .

[20]  I. Orlanski.  A Simple Boundary Condition for Unbounded Hyperbolic Flows , 1976 .

[21]  J. Oliger,et al.  Adaptive grid refinement for numerical weather prediction , 1989 .

[22]  Z. Sirkes,et al.  Modeling of the Global and Pacific Oceans: On the Path to Eddy-Resolving Ocean Prediction , 1992 .

[23]  Andrew F. Bennett,et al.  Inverse Methods in Physical Oceanography: Frontmatter , 1992 .

[24]  E. Joseph Metzger,et al.  Statistical inference of weakly correlated subthermocline fields from satellite altimeter data , 1990 .

[25]  K. Miyakoda,et al.  One-Way Nested Grid Models: The Interface Conditions and the Numerical Accuracy , 1977 .

[26]  G. K. Verboom,et al.  Weakly-reflective boundary conditions for two-dimensional shallow water flow problems , 1984 .

[27]  An Adaptive Finite Difference Method for Hyperbolic Systems on One Space Dimension, Revision, , 1982 .

[28]  Ping Chen,et al.  A model simulation of circulation in the northeast Atlantic shelves and seas , 1992 .

[29]  Numerical inaccuracies across the interface of a nested grid , 1994 .

[30]  Michael A. Spall,et al.  A nested primitive equation model for oceanic applications , 1991 .

[31]  A. Perkins.  Internal Boundary Conditions and the Feedback Loop for Nested Two-Way Communication Schemes , 1993 .

[32]  Y. Ookochi.  A Computational Scheme for the Nesting Fine Mesh in the Primitive Equation Model , 1972 .