Some effects of horizontal discretization on linear baroclinic and symmetric instabilities. (May 2018)

• Record Type: Journal Article
• Authors: Barham, William; Bachman, Scott; Grooms, Ian
• Is Part Of: Ocean modelling. Volume 125(2018)
• Page Start: 106
• Page End: 116
• Publication Date: 2018-05
• Subjects: Baroclinic instability -- Symmetric instability -- Discretization; Oceanography -- Periodicals; Océanographie -- Périodiques; Oceanography; Periodicals; 551.46
• DOI: 10.1016/j.ocemod.2018.03.004
• Languages: English
• ISSNs: 1463-5003

Abstract

Highlights: B Grid represents linear baroclinic instability better than C Grid. C Grid represents linear symmetric instability better than B Grid. There is a spurious small-scale baroclinic instability on the C Grid. Fourth order tracer advection improves (but does not remove) the spurious instability. Abstract: The effects of horizontal discretization on linear baroclinic and symmetric instabilities are investigated by analyzing the behavior of the hydrostatic Eady problem in ocean models on the B and C grids. On the C grid a spurious baroclinic instability appears at small wavelengths. This instability does not disappear as the grid scale decreases; instead, it simply moves to smaller horizontal scales. The peak growth rate of the spurious instability is independent of the grid scale as the latter decreases. It is equal to c f / Ri where Ri is the balanced Richardson number, f is the Coriolis parameter, and c is a nondimensional constant that depends on the Richardson number. As the Richardson number increases c increases towards an upper bound of approximately 1/2; for large Richardson numbers the spurious instability is faster than the Eady instability. To suppress the spurious instability it is recommended to use fourth-order centered tracer advection along with biharmonic viscosity and diffusion with coefficients ( Δ x ) 4 f / ( 32 Ri ) or larger where Δx is the grid scale. On the B grid, the growth rates of baroclinic and symmetric instabilities are too small, and converge upwards towards the correct values as the grid scale decreases; no spurious instabilities are observed. In B grid models at eddy-permitting resolution, the reduced growth rate of baroclinic instability may contribute to partially-resolved eddies being too weak. On the C grid the growth rate of symmetric instability is better (larger) than on the B grid, and converges upwards towards the correct value as the grid scale decreases.