### Abstract

Recent studies indicate that altimetric observations of the ocean's mesoscale eddy field reflect the combined influence of surface buoyancy and interior potential vorticity anomalies. The former have a surface-trapped structure, while the latter are often well represented by the barotropic and first baroclinic modes. To assess the relative importance of each contribution to the signal, it is useful to project the observed field onto a set of modes that separates their influence in a natural way. However, the surface-trapped dynamics are not well represented by standard baroclinic modes; moreover, they are dependent on horizontal scale. Here the authors derive a modal decomposition that results from the simultaneous diagonalization of the energy and a generalization of potential enstrophy that includes contributions from the surface buoyancy fields. This approach yields a family of orthonormal bases that depend on two parameters; the standard baroclinic modes are recovered in a limiting case, while other choices provide modes that represent surface and interior dynamics in an efficient way. For constant stratification, these modes consist of symmetric and antisymmetric exponential modes that capture the surface dynamics and a series of oscillating modes that represent the interior dynamics. Motivated by the ocean, where shears are concentrated near the upper surface, the authors consider the special case of a quiescent lower surface. In this case, the interior modes are independent of wavenumber, and there is a single exponential surface mode that replaces the barotropic mode. The use and effectiveness of these modes is demonstrated by projecting the energy in a set of simulations of baroclinic turbulence.

Original language | English (US) |
---|---|

Pages (from-to) | 548-562 |

Number of pages | 15 |

Journal | Journal of Physical Oceanography |

Volume | 43 |

Issue number | 3 |

DOIs | |

State | Published - May 2013 |

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### ASJC Scopus subject areas

- Oceanography

### Cite this

*Journal of Physical Oceanography*,

*43*(3), 548-562. https://doi.org/10.1175/JPO-D-12-0107.1

**A Surface-aware projection basis for quasigeostrophic flow.** / Shafer Smith, K.; Vanneste, Jacques.

Research output: Contribution to journal › Article

*Journal of Physical Oceanography*, vol. 43, no. 3, pp. 548-562. https://doi.org/10.1175/JPO-D-12-0107.1

}

TY - JOUR

T1 - A Surface-aware projection basis for quasigeostrophic flow

AU - Shafer Smith, K.

AU - Vanneste, Jacques

PY - 2013/5

Y1 - 2013/5

N2 - Recent studies indicate that altimetric observations of the ocean's mesoscale eddy field reflect the combined influence of surface buoyancy and interior potential vorticity anomalies. The former have a surface-trapped structure, while the latter are often well represented by the barotropic and first baroclinic modes. To assess the relative importance of each contribution to the signal, it is useful to project the observed field onto a set of modes that separates their influence in a natural way. However, the surface-trapped dynamics are not well represented by standard baroclinic modes; moreover, they are dependent on horizontal scale. Here the authors derive a modal decomposition that results from the simultaneous diagonalization of the energy and a generalization of potential enstrophy that includes contributions from the surface buoyancy fields. This approach yields a family of orthonormal bases that depend on two parameters; the standard baroclinic modes are recovered in a limiting case, while other choices provide modes that represent surface and interior dynamics in an efficient way. For constant stratification, these modes consist of symmetric and antisymmetric exponential modes that capture the surface dynamics and a series of oscillating modes that represent the interior dynamics. Motivated by the ocean, where shears are concentrated near the upper surface, the authors consider the special case of a quiescent lower surface. In this case, the interior modes are independent of wavenumber, and there is a single exponential surface mode that replaces the barotropic mode. The use and effectiveness of these modes is demonstrated by projecting the energy in a set of simulations of baroclinic turbulence.

AB - Recent studies indicate that altimetric observations of the ocean's mesoscale eddy field reflect the combined influence of surface buoyancy and interior potential vorticity anomalies. The former have a surface-trapped structure, while the latter are often well represented by the barotropic and first baroclinic modes. To assess the relative importance of each contribution to the signal, it is useful to project the observed field onto a set of modes that separates their influence in a natural way. However, the surface-trapped dynamics are not well represented by standard baroclinic modes; moreover, they are dependent on horizontal scale. Here the authors derive a modal decomposition that results from the simultaneous diagonalization of the energy and a generalization of potential enstrophy that includes contributions from the surface buoyancy fields. This approach yields a family of orthonormal bases that depend on two parameters; the standard baroclinic modes are recovered in a limiting case, while other choices provide modes that represent surface and interior dynamics in an efficient way. For constant stratification, these modes consist of symmetric and antisymmetric exponential modes that capture the surface dynamics and a series of oscillating modes that represent the interior dynamics. Motivated by the ocean, where shears are concentrated near the upper surface, the authors consider the special case of a quiescent lower surface. In this case, the interior modes are independent of wavenumber, and there is a single exponential surface mode that replaces the barotropic mode. The use and effectiveness of these modes is demonstrated by projecting the energy in a set of simulations of baroclinic turbulence.

UR - http://www.scopus.com/inward/record.url?scp=84878941883&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84878941883&partnerID=8YFLogxK

U2 - 10.1175/JPO-D-12-0107.1

DO - 10.1175/JPO-D-12-0107.1

M3 - Article

VL - 43

SP - 548

EP - 562

JO - Journal of Physical Oceanography

JF - Journal of Physical Oceanography

SN - 0022-3670

IS - 3

ER -