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Cited by 9 publications
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References 13 publications
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“…The phase speed is also generally affected through the application of explicit diffusion, although to the best of the author's knowledge there are no studies that consider this effect. Some preliminary evidence suggests that diffusion, if added in an time‐split manner, may improve the phase speed of numerical methods. As noted by Rančic et al (2008) and Thuburn (2011), proper simulation of the nonlinear energy and enstrophy cascade is essential to any long‐term integration of the equations of motion. This cascade does not appear in the linear analysis, but it is an important consideration when selecting a numerical method for scientific operation.…”
Section: Methodsmentioning
confidence: 99%
“…The phase speed is also generally affected through the application of explicit diffusion, although to the best of the author's knowledge there are no studies that consider this effect. Some preliminary evidence suggests that diffusion, if added in an time‐split manner, may improve the phase speed of numerical methods. As noted by Rančic et al (2008) and Thuburn (2011), proper simulation of the nonlinear energy and enstrophy cascade is essential to any long‐term integration of the equations of motion. This cascade does not appear in the linear analysis, but it is an important consideration when selecting a numerical method for scientific operation.…”
Section: Methodsmentioning
confidence: 99%
“…Since acoustic waves can be considered insignificant for atmospheric applications due to their low energy, one is tempted to discard numerical errors in the dispersion and dissipation of acoustic waves. However, there is an argument (Thuburn, 2012) that correct representation of even energetically weak waves in atmosphere is crucial for restoration of hydrostatic balance. Among other 2nd order schemes, M2a, M2b and M2c, it is hard to declare a clear winner.…”
Section: Analysing the M2 Schemesmentioning
confidence: 99%
“…We consider the spherical hydrostatic primitive equations under the shallow-atmosphere approximation (Kasahara 1974;Thuburn 2011) and with continuous stratification represented by a generalized vertical coordinate. In their adiabatic, frictionless form, the governing equations read…”
Section: Formulationmentioning
confidence: 99%