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understood to fall outside the stationary wave theory itself. In this study we focus on the so-called “stationary wave nonlinearity,” also known as “stationary nonlinearity” or “nonlinear self-interaction,” which arises primarily through advective terms in the equations of motion and becomes more important for larger-amplitude stationary waves (e.g., Ting et al. 2001 , and references therein). For example, in quasigeostrophic (QG) dynamics, stationary wave nonlinearity involves the flux of stationary
understood to fall outside the stationary wave theory itself. In this study we focus on the so-called “stationary wave nonlinearity,” also known as “stationary nonlinearity” or “nonlinear self-interaction,” which arises primarily through advective terms in the equations of motion and becomes more important for larger-amplitude stationary waves (e.g., Ting et al. 2001 , and references therein). For example, in quasigeostrophic (QG) dynamics, stationary wave nonlinearity involves the flux of stationary
1. Introduction and motivation We are interested here in the nonlinear dynamics of planetary waves in fairly realistic, high-dimensional atmospheric models. A promising way of better understanding the dynamics is to investigate the properties of state-averaged trajectories in a low-dimensional subspace of the full model’s phase space. The mean (i.e., state-averaged) phase-space tendencies describe long-term preferred motion in the observed or simulated atmosphere and can possibly be related to
1. Introduction and motivation We are interested here in the nonlinear dynamics of planetary waves in fairly realistic, high-dimensional atmospheric models. A promising way of better understanding the dynamics is to investigate the properties of state-averaged trajectories in a low-dimensional subspace of the full model’s phase space. The mean (i.e., state-averaged) phase-space tendencies describe long-term preferred motion in the observed or simulated atmosphere and can possibly be related to
equivalently consider constant potential temperature at the boundaries with δ sheets of potential vorticity just inside the boundaries, given by The discrete operator Γ nm effectively includes an approximation of the δ sheets that is accurate to O ( Nδz / f )—see appendix of Smith (2007) —so surface temperature dynamics at horizontal scales smaller than O ( Nδz / f ) are not captured. 3. The structure of nonlinear Eady turbulence Here we consider the nonlinear Eady problem ( Eady 1949 ): f
equivalently consider constant potential temperature at the boundaries with δ sheets of potential vorticity just inside the boundaries, given by The discrete operator Γ nm effectively includes an approximation of the δ sheets that is accurate to O ( Nδz / f )—see appendix of Smith (2007) —so surface temperature dynamics at horizontal scales smaller than O ( Nδz / f ) are not captured. 3. The structure of nonlinear Eady turbulence Here we consider the nonlinear Eady problem ( Eady 1949 ): f
; Takayabu 1991 ; Plu and Arbogast 2005 ) exhibit a quasi-systematic poleward (equatorward) shift of surface cyclones (anticyclones). Takayabu (1991) stressed the fact that the interaction with an upper disturbance is predominant in the mechanisms leading to the poleward displacement. It should be noted that Rivière (2008) studied the effects of jet crossing by synoptic-scale eddies in a barotropic framework and underlined the key role played by nonlinear dynamics. There is therefore a clear need to
; Takayabu 1991 ; Plu and Arbogast 2005 ) exhibit a quasi-systematic poleward (equatorward) shift of surface cyclones (anticyclones). Takayabu (1991) stressed the fact that the interaction with an upper disturbance is predominant in the mechanisms leading to the poleward displacement. It should be noted that Rivière (2008) studied the effects of jet crossing by synoptic-scale eddies in a barotropic framework and underlined the key role played by nonlinear dynamics. There is therefore a clear need to
difficult, if not impossible, to investigate, turn out to be straightforward in their framework. In this study, we present an application of their multiscale energy and vorticity analysis (MS-EVA) and the MS-EVA-based theory of hydrodynamic stability, which are fully nonlinear and capable of handling oceanic and atmospheric processes intermittent in space and time. 1 Toward the end of this study, one will see that underlying a seemingly chaotic circulation, the dynamics are not that complicated. That
difficult, if not impossible, to investigate, turn out to be straightforward in their framework. In this study, we present an application of their multiscale energy and vorticity analysis (MS-EVA) and the MS-EVA-based theory of hydrodynamic stability, which are fully nonlinear and capable of handling oceanic and atmospheric processes intermittent in space and time. 1 Toward the end of this study, one will see that underlying a seemingly chaotic circulation, the dynamics are not that complicated. That
1. Introduction The driving forces and dominant functional form of planetary wave dynamics is an important topic in recent literature. Depending on the school of thought, planetary wave dynamics are either dominated by deterministic linear dynamics that are driven by additive white noise ( Penland and Sardeshmukh 1995 ; Newman et al. 1997 ; Branstator and Haupt 1998 ; Branstator and Frederiksen 2003 ) or are intrinsically nonlinear. The latter view is motivated by studies of highly truncated
1. Introduction The driving forces and dominant functional form of planetary wave dynamics is an important topic in recent literature. Depending on the school of thought, planetary wave dynamics are either dominated by deterministic linear dynamics that are driven by additive white noise ( Penland and Sardeshmukh 1995 ; Newman et al. 1997 ; Branstator and Haupt 1998 ; Branstator and Frederiksen 2003 ) or are intrinsically nonlinear. The latter view is motivated by studies of highly truncated
present paper revisits in detail the theoretical importance of resolved nonlinear dry dynamics for MJO-like phenomena. In particular, here the hypothesis is tested that episodic MJO-like structures propagate eastward as a result of nonlinear Rossby wave dynamics in a background flow preconditioned with lateral coupling to the extratropics. In the equatorial troposphere a correlation between eastward-propagating signals and extratropical wave activity appears to be in agreement with observations and
present paper revisits in detail the theoretical importance of resolved nonlinear dry dynamics for MJO-like phenomena. In particular, here the hypothesis is tested that episodic MJO-like structures propagate eastward as a result of nonlinear Rossby wave dynamics in a background flow preconditioned with lateral coupling to the extratropics. In the equatorial troposphere a correlation between eastward-propagating signals and extratropical wave activity appears to be in agreement with observations and
Alexander 2003 ). Numerical studies of the nonlinear breaking process, which is the focus of this paper, have traditionally resorted to some kind of large-eddy simulation (LES) with a flux-gradient type turbulence parameterization ( Winters and D’Asaro 1994 ; Andreassen et al. 1994 ; Fritts et al. 1994 ; Isler et al. 1994 ; Lelong and Dunkerton 1998a , b ). Direct numerical simulations (DNS) with their least ambiguous results on the corresponding turbulence dynamics have only recently become
Alexander 2003 ). Numerical studies of the nonlinear breaking process, which is the focus of this paper, have traditionally resorted to some kind of large-eddy simulation (LES) with a flux-gradient type turbulence parameterization ( Winters and D’Asaro 1994 ; Andreassen et al. 1994 ; Fritts et al. 1994 ; Isler et al. 1994 ; Lelong and Dunkerton 1998a , b ). Direct numerical simulations (DNS) with their least ambiguous results on the corresponding turbulence dynamics have only recently become
assimilation systems to improve upon the errors of each method. The oceanic and atmospheric systems have multiple scales of dynamics interacting nonlinearly in time and space. For instance, the atmospheric system varies on time scales from climate to weather. The weather is fast varying, nonlinear, and chaotic and is known as an initial-value problem, whereas the climate is slowly varying and is known as a boundary value problem ( Lorenz 1991 ). Ocean physics also involves multiple processes on multiple
assimilation systems to improve upon the errors of each method. The oceanic and atmospheric systems have multiple scales of dynamics interacting nonlinearly in time and space. For instance, the atmospheric system varies on time scales from climate to weather. The weather is fast varying, nonlinear, and chaotic and is known as an initial-value problem, whereas the climate is slowly varying and is known as a boundary value problem ( Lorenz 1991 ). Ocean physics also involves multiple processes on multiple
1. Introduction a. Background Nonlinearities in the internal dynamics of the atmosphere have the potential to influence the behavior of planetary waves in key respects. For example they can produce highly predictable states, and they can affect the way planetary waves react to external forcing ( Palmer 1999) . Although effects of nonlinearity are obvious in highly truncated models, as for example in the formation of multiple equilibria in Charney and DeVore’s (1979) model of planetary waves
1. Introduction a. Background Nonlinearities in the internal dynamics of the atmosphere have the potential to influence the behavior of planetary waves in key respects. For example they can produce highly predictable states, and they can affect the way planetary waves react to external forcing ( Palmer 1999) . Although effects of nonlinearity are obvious in highly truncated models, as for example in the formation of multiple equilibria in Charney and DeVore’s (1979) model of planetary waves
