## Abstract

For an f-plane many-layer primitive-equation isopycnal model, three 'contour-advective semi-Lagrangian' (CASL) algorithms and a standard pseudo-spectral (PS) algorithm are compared as regards their representation of balance and imbalance during the evolution of a highly complex vortical flow with substantial activity in small horizontal and vertical scales. The three CASL algorithms employ (q, h, delta), (q, delta, gamma), and (q, gamma, Xi) as their prognostic variables, where q is the Rossby potential vorticity, h is layer thickness, 6 is horizontal divergence, gamma and Xi represent departures of vorticity from, respectively, geostrophic and Bolin-Charney balance. It is demonstrated that the CASL algorithm with (q, delta, gamma) improves on the algorithm with (q, h, delta) across nearly the whole range of applicability of the algorithms, i.e. practically up to the limit where overturning and diabatic effects may dominate. Unlike in the PS algorithm, the improvement is achieved without sacrificing the accuracy of the vortical part of the flow by excessive damping.

Original language | English |
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Pages (from-to) | 347-364 |

Number of pages | 18 |

Journal | Quarterly Journal of the Royal Meteorological Society |

Volume | 130 |

DOIs | |

Publication status | Published - Jan 2004 |

## Keywords

- balance
- gravity waves
- hybrid algorithm
- potential vorticity
- POTENTIAL-VORTICITY INVERSION
- SHALLOW-WATER EQUATIONS
- GRAVITY-WAVES
- BAROCLINIC INSTABILITY
- BALANCE