Nonlinear Aspects of Symmetric Instability

Thorpe, Ashley; Rotunno, Richard

doi:10.1175/1520-0469(1989)046<1285:naosi>2.0.co;2

Cited by 64 publications

(53 citation statements)

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“…Figure 1 illustrates a thought experiment, describing a hypothetical series of events, which would allow M adjustment and CSI to occur consecutively. This hypothetical life-cycle is described graphically using a series of sketches, most of which are inspired by the numerical simulations of Holt and Thorpe (1991), Fischer and Lalaurette (1995a,b) and Thorpe and Rotunno (1989). Striving for clarity, these sketches try to capture the important features of their numerical simulations by subjectively smoothing their results and by removing some of the confusing noise.…”

Section: A Hypothesis Linking Line Convection M Adjustment and Csimentioning

confidence: 99%

“…When viscosity is taken into account, the updraughts are still narrow, but they now have a finite width. Consequently regions of negative EPV can actually be stable to viscous CSI depending on their geometry (Thorpe and Rotunno 1989). Assuming that the whole of the negative-EPV region created by the M adjustment is saturated, and that, as the region grows, the geometry is now such that it is unstable to viscous CSI, then only a triggering mechanism is needed for the CSI to be released.…”

Section: (A) Initial Conditions and Line Convectionmentioning

confidence: 99%

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Formation and release of symmetric instability following Delta‐M adjustment

Morcrette

Browning

2006

Quart J Royal Meteoro Soc

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SUMMARYConditional Symmetric Instability (CSI) and Delta-M adjustment have both been suggested as possible mechanisms to explain the slantwise circulations that lead to two-dimensional precipitation bands near midlatitude cold fronts. Previous work has shown how the initial state required for CSI to occur is similar to the state produced as a result of Delta-M adjustment. An idealized dry numerical model is used to test the hypothesis that slantwise circulations can occur due to the release of symmetric instability formed by the Delta-M adjustment process. The numerical simulation shows the coexistence of two pairs of slantwise circulations: one due directly to Delta-M adjustment, and the other which occurs in a region of symmetric instability which was formed by the Delta-M adjustment process. The simulated circulation is qualitatively similar to some high-resolution Doppler radar observations of vertically stacked slantwise circulations. It is argued that a combined Delta-M/CSI mechanism may also be responsible for the creation of multiple slantwise circulations in the moist atmosphere.

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Section: A Hypothesis Linking Line Convection M Adjustment and Csimentioning

confidence: 99%

Section: (A) Initial Conditions and Line Convectionmentioning

confidence: 99%

Formation and release of symmetric instability following Delta‐M adjustment

Morcrette

Browning

2006

Quart J Royal Meteoro Soc

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“…ear regime. Thorpe and Rotunno (1989) put forward the hypothesis that nonlinear equilibration is characterised by a sort of inverse cascading of energy and the progressive emergence of larger scale circulations. Time-integration with the spectral model makes it possible to follow directly the timeevolution of the energy associated to each x-harmonic: evidence is that there is no inverse cascading of energy from smaller to higher scales.…”

Section: Nonlinear Systemmentioning

confidence: 49%

“…This behaviour seems to be in contrast with the previously proposed idea (see Miller, 1984) that the dominance of one kind of circulation on the other may be determined by Prandtl number being different from one. In fact, in the present case (as, for example, in Rotunno, 1989 andJones andThorpe, 1992, where the momentum diffusion coefficient is equal to the heat diffusion coefficient) the predominant selection of the anticlockwise circulations is evident. We did not test the structural stability of this result since it was outside the scope of our work.…”

Section: Nonlinear Systemmentioning

confidence: 95%

Baroclinic instability of a symmetric, rotating, stratified flow: a study of the nonlinear stabilisation mechanisms in the presence of viscosity

Mantovani

Speranza

2002

Nonlin. Processes Geophys.

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Abstract. This paper presents the analysis of symmetric circulations of a rotating baroclinic flow, forced by a steady thermal wind and dissipated by Laplacian friction. The analysis is performed with numerical time-integration. Symmetric flows, vertically bound by horizontal walls and subject to either periodic or vertical wall lateral boundary conditions, are investigated in the region of parameter-space where unstable small amplitude modes evolve into stable stationary nonlinear solutions. The distribution of solutions in parameter-space is analysed up to the threshold of chaotic behaviour and the physical nature of the nonlinear interaction operating on the finite amplitude unstable modes is investigated. In particular, analysis of time-dependent energyconversions allows understanding of the physical mechanisms operating from the initial phase of linear instability to the finite amplitude stable state. Vertical shear of the basic flow is shown to play a direct role in injecting energy into symmetric flow since the stage of linear growth. Dissipation proves essential not only in limiting the energy of linearly unstable modes, but also in selecting their dominant spacescales in the finite amplitude stage.

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“…Numerical simulations of the finite-amplitude evolution of SI in idealized environment were performed among others by Thorpe and Rotunno (1989) and Persson and Warner (1995).…”

Section: Introductionmentioning

confidence: 99%

Numerical study of slantwise circulations in a strongly sheared prefrontal environment

Fantini¹,

Malguzzi²,

Buzzi³

2011

Quart J Royal Meteoro Soc

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The simultaneous presence of convective, symmetric and inertial instability in a prefrontal region of strong vertical wind shear was simulated with the nonhydrostatic model MOLOCH. Model diagnostics of absolute vorticity, pseudoangular momentum, saturated equivalent potential temperature and vorticity reveal a sequence of events that includes ' M-adjustment', followed by slanted ascent in symmetrically unstable regions, becoming saturated in the later stages. An idealized experiment without orography was performed to isolate the presence and role of instabilities characterizing the development. The diagnosed circulation is reminiscent of a wavenumber-two normal mode of dry symmetric instability, while moist symmetric instability is confined to a very limited region, despite the appearance of wider areas of negative moist potential vorticity. The evaluation of moist thermodynamic quantities which give proper account of condensate loading is suggested as a possible resolution of this apparent inconsistency.

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Nonlinear Aspects of Symmetric Instability

Cited by 64 publications

References 0 publications

Formation and release of symmetric instability following Delta‐M adjustment

Formation and release of symmetric instability following Delta‐M adjustment

Baroclinic instability of a symmetric, rotating, stratified flow: a study of the nonlinear stabilisation mechanisms in the presence of viscosity

Numerical study of slantwise circulations in a strongly sheared prefrontal environment

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