Further non-separable exact solutions of the deep- and shallow-atmosphere equations

Staniforth, Andrew; White, A. A.

doi:10.1002/asl.349

Cited by 9 publications

(6 citation statements)

References 15 publications

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“…First, a balanced steady‐state test case for deep‐atmosphere described in Staniforth and White () and Staniforth and Wood () is carried out. The initial conditions of the steady‐state test case are axially symmetric and can be written in the form

\begin{matrix} u = u (ϕ, r), v = w = 0, \\ q = q (ϕ, r) = \ln (p (ϕ, r)), \\ T = T (ϕ, r) . \end{matrix}

…”

Section: Test Casesmentioning

confidence: 99%

A semi‐implicit deep‐atmosphere spectral dynamical kernel using a hydrostatic‐pressure coordinate

Yang

Song

et al. 2017

Quart J Royal Meteoro Soc

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Most of the present deep‐atmosphere models are based on finite‐difference schemes. This article proposes a novel deep‐atmosphere non‐hydrostatic spectral dynamical kernel with hydrostatic‐pressure based terrain‐following vertical coordinate. Contrary to finite‐difference methods, a spectral transform method is used for the horizontal discretization. The prognostic variables in our dynamical kernel are analogous to the typical ALADIN‐NH spectral model. A two time level semi‐implicit semi‐Lagrangian time‐stepping scheme is applied to enable large time steps and improve the efficiency of integration. A set of test cases are conducted to evaluate the accuracy and stability of the deep‐atmosphere dynamic kernel.

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\begin{matrix} u = u (ϕ, r), v = w = 0, \\ q = q (ϕ, r) = \ln (p (ϕ, r)), \\ T = T (ϕ, r) . \end{matrix}

…”

Section: Test Casesmentioning

confidence: 99%

A semi‐implicit deep‐atmosphere spectral dynamical kernel using a hydrostatic‐pressure coordinate

Yang

Song

et al. 2017

Quart J Royal Meteoro Soc

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“…A key element of the approach taken herein is therefore to abandon the use of the isobaric coordinate system, and instead to adopt spherical radius (and/or its equivalent, geometric height, defined by z ≡ r − a ) as vertical coordinate. It is then possible to exploit the exact shallow‐ and deep‐atmosphere class of steady axisymmetric solutions derived in Staniforth and White (2011) and Staniforth and Wood (2013) (hereafter referred to as SW11 and SW12, respectively).…”

Section: Introductionmentioning

confidence: 99%

A proposed baroclinic wave test case for deep‐ and shallow‐atmosphere dynamical cores

Ullrich

Melvin

Jablonowski

et al. 2013

Quart J Royal Meteoro Soc

101

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Idealised studies of key dynamical features of the atmosphere provide insight into the behaviour of atmospheric models. A very important, well understood, aspect of midlatitude dynamics is baroclinic instability. This can be idealised by perturbing a vertically sheared basic state in geostrophic and hydrostatic balance. An unstable wave mode then results with exponential growth (due to linear dynamics) in time until, eventually, nonlinear effects dominate and the wave breaks. A new, unified, idealised baroclinic instability test case is proposed. This improves on previous ones in three ways. First, it is suitable for both deep‐ and shallow‐atmosphere models. Second, the constant surface pressure and zero surface geopotential of the basic state makes it particularly well‐suited for models employing a pressure‐ or height‐based vertical coordinate. Third, the wave triggering mechanism selectively perturbs the rotational component of the flow; this, together with a vertical tapering, significantly improves dynamic balance.

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“…It is evident that the derivation of analytical solutions for this 3D problem is even more difficult than for the 2D case. Staniforth and White (2011) find non-separable steady and zonally symmetric solutions by inserting appropriate ansatz functions into the nonlinear Euler equations. They derive such solutions for both shallow and deep atmospheres.…”

Section: Introductionmentioning

confidence: 99%

An analytical solution for linear gravity and sound waves on the sphere as a test for compressible, non-hydrostatic numerical models

Baldauf

Reinert

Zängl

2014

Q.J.R. Meteorol. Soc.

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An analytical solution for the expansion of gravity and sound waves for the linearized form of the fully compressible, non‐hydrostatic, shallow atmosphere Euler equations on the sphere is derived. The waves are generated by a weak initial temperature and density perturbation of an isothermal atmosphere. The derived analytical solution can be used as a benchmark to assess dynamical cores of global models based on the above‐mentioned (in general nonlinear) equation system. Three different test configurations, with or without Coriolis force or additional advection, are discussed. Convergence studies of the newly developed ICOsahedral Non‐hydrostatic global model (ICON) against this solution are performed.

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Further non-separable exact solutions of the deep- and shallow-atmosphere equations

Cited by 9 publications

References 15 publications

A semi‐implicit deep‐atmosphere spectral dynamical kernel using a hydrostatic‐pressure coordinate

A semi‐implicit deep‐atmosphere spectral dynamical kernel using a hydrostatic‐pressure coordinate

A proposed baroclinic wave test case for deep‐ and shallow‐atmosphere dynamical cores

An analytical solution for linear gravity and sound waves on the sphere as a test for compressible, non-hydrostatic numerical models

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