A Spectral Filtering Procedure for Eddy-Resolving Simulations with a Spectral Element Ocean Model

Julia G. Levin, Mohamed Iskandarani, Dale B. Haidvogel

Research output: Contribution to journalArticle

36 Citations (Scopus)

Abstract

The numerical simulation of turbulent oceanic flows is susceptible to the appearance of instabilities associated with the misrepresentation of nonlinear interactions among small-scale motions. Specialized filters and differencing schemes have been successfully used in the past to suppress the growth of these instabilities in finite-difference ocean models. Here, we introduce a new filtering procedure designed to control the growth of nonlinear instabilities in the spectral element solution of nonlinear oceanic flows. The new procedure involves two separate steps. First, a spectral filter is applied to the vorticity and divergence fields to damp oscillations in high-gradient regions and to restore spectral accuracy away from them. Second, the associated velocity field is computed from a set of Poisson equations, and its boundary conditions and interelement continuity are restored. This two-step strategy avoids the loss ofC 0continuity and the weakening of Dirichlet boundary conditions that can result when the filter is directly applied to the velocity field. The behavior of the filter is investigated numerically on the canonical problem of the double-gyre wind-driven circulation in a rectangular basin using a spectral element shallow water model. The parameters of the simulation are chosen to produce mesoscale eddies. The filter is able to stabilize the simulation even at coarse resolution and to recover the "correct" statistical behavior with as few as two grid points per Rossby deformation radius. Finally, a simulation of the wind-driven circulation in the North Atlantic Ocean is performed to illustrate the effectiveness of the filter in realistic settings.

Original languageEnglish (US)
Pages (from-to)130-154
Number of pages25
JournalJournal of Computational Physics
Volume137
Issue number1
DOIs
StatePublished - Oct 1997
Externally publishedYes

Fingerprint

ocean models
vortices
filters
Boundary conditions
simulation
Poisson equation
Vorticity
Turbulent flow
velocity distribution
boundary conditions
Atlantic Ocean
Computer simulation
shallow water
continuity
vorticity
Water
divergence
grids
gradients
oscillations

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy(all)

Cite this

A Spectral Filtering Procedure for Eddy-Resolving Simulations with a Spectral Element Ocean Model. / Levin, Julia G.; Iskandarani, Mohamed; Haidvogel, Dale B.

In: Journal of Computational Physics, Vol. 137, No. 1, 10.1997, p. 130-154.

Research output: Contribution to journalArticle

@article{7aadc8483c93475489da9da818f20bbf,
title = "A Spectral Filtering Procedure for Eddy-Resolving Simulations with a Spectral Element Ocean Model",
abstract = "The numerical simulation of turbulent oceanic flows is susceptible to the appearance of instabilities associated with the misrepresentation of nonlinear interactions among small-scale motions. Specialized filters and differencing schemes have been successfully used in the past to suppress the growth of these instabilities in finite-difference ocean models. Here, we introduce a new filtering procedure designed to control the growth of nonlinear instabilities in the spectral element solution of nonlinear oceanic flows. The new procedure involves two separate steps. First, a spectral filter is applied to the vorticity and divergence fields to damp oscillations in high-gradient regions and to restore spectral accuracy away from them. Second, the associated velocity field is computed from a set of Poisson equations, and its boundary conditions and interelement continuity are restored. This two-step strategy avoids the loss ofC 0continuity and the weakening of Dirichlet boundary conditions that can result when the filter is directly applied to the velocity field. The behavior of the filter is investigated numerically on the canonical problem of the double-gyre wind-driven circulation in a rectangular basin using a spectral element shallow water model. The parameters of the simulation are chosen to produce mesoscale eddies. The filter is able to stabilize the simulation even at coarse resolution and to recover the {"}correct{"} statistical behavior with as few as two grid points per Rossby deformation radius. Finally, a simulation of the wind-driven circulation in the North Atlantic Ocean is performed to illustrate the effectiveness of the filter in realistic settings.",
author = "Levin, {Julia G.} and Mohamed Iskandarani and Haidvogel, {Dale B.}",
year = "1997",
month = "10",
doi = "10.1006/jcph.1997.5797",
language = "English (US)",
volume = "137",
pages = "130--154",
journal = "Journal of Computational Physics",
issn = "0021-9991",
publisher = "Academic Press Inc.",
number = "1",

}

TY - JOUR

T1 - A Spectral Filtering Procedure for Eddy-Resolving Simulations with a Spectral Element Ocean Model

AU - Levin, Julia G.

AU - Iskandarani, Mohamed

AU - Haidvogel, Dale B.

PY - 1997/10

Y1 - 1997/10

N2 - The numerical simulation of turbulent oceanic flows is susceptible to the appearance of instabilities associated with the misrepresentation of nonlinear interactions among small-scale motions. Specialized filters and differencing schemes have been successfully used in the past to suppress the growth of these instabilities in finite-difference ocean models. Here, we introduce a new filtering procedure designed to control the growth of nonlinear instabilities in the spectral element solution of nonlinear oceanic flows. The new procedure involves two separate steps. First, a spectral filter is applied to the vorticity and divergence fields to damp oscillations in high-gradient regions and to restore spectral accuracy away from them. Second, the associated velocity field is computed from a set of Poisson equations, and its boundary conditions and interelement continuity are restored. This two-step strategy avoids the loss ofC 0continuity and the weakening of Dirichlet boundary conditions that can result when the filter is directly applied to the velocity field. The behavior of the filter is investigated numerically on the canonical problem of the double-gyre wind-driven circulation in a rectangular basin using a spectral element shallow water model. The parameters of the simulation are chosen to produce mesoscale eddies. The filter is able to stabilize the simulation even at coarse resolution and to recover the "correct" statistical behavior with as few as two grid points per Rossby deformation radius. Finally, a simulation of the wind-driven circulation in the North Atlantic Ocean is performed to illustrate the effectiveness of the filter in realistic settings.

AB - The numerical simulation of turbulent oceanic flows is susceptible to the appearance of instabilities associated with the misrepresentation of nonlinear interactions among small-scale motions. Specialized filters and differencing schemes have been successfully used in the past to suppress the growth of these instabilities in finite-difference ocean models. Here, we introduce a new filtering procedure designed to control the growth of nonlinear instabilities in the spectral element solution of nonlinear oceanic flows. The new procedure involves two separate steps. First, a spectral filter is applied to the vorticity and divergence fields to damp oscillations in high-gradient regions and to restore spectral accuracy away from them. Second, the associated velocity field is computed from a set of Poisson equations, and its boundary conditions and interelement continuity are restored. This two-step strategy avoids the loss ofC 0continuity and the weakening of Dirichlet boundary conditions that can result when the filter is directly applied to the velocity field. The behavior of the filter is investigated numerically on the canonical problem of the double-gyre wind-driven circulation in a rectangular basin using a spectral element shallow water model. The parameters of the simulation are chosen to produce mesoscale eddies. The filter is able to stabilize the simulation even at coarse resolution and to recover the "correct" statistical behavior with as few as two grid points per Rossby deformation radius. Finally, a simulation of the wind-driven circulation in the North Atlantic Ocean is performed to illustrate the effectiveness of the filter in realistic settings.

UR - http://www.scopus.com/inward/record.url?scp=0001198024&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001198024&partnerID=8YFLogxK

U2 - 10.1006/jcph.1997.5797

DO - 10.1006/jcph.1997.5797

M3 - Article

AN - SCOPUS:0001198024

VL - 137

SP - 130

EP - 154

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 1

ER -