Necessary conditions for the instability of quasigeostrophic waves induced by trace shortwave radiative absorbers (original) (raw)
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Models for Stratiform Instability and Convectively Coupled Waves
Journal of the Atmospheric Sciences, 2001
A simplified intermediate model for analyzing and parameterizing convectively coupled tropical waves is introduced here. This model has two baroclinic modes of vertical structure: a direct heating mode and a stratiform mode. The key essential parameter in these models is the area fraction occupied by deep convection, c. The unstable convectively coupled waves that emerge from perturbation of a radiative convective equilibrium are discussed in detail through linearized stability analysis. Without any mean flow, for an overall cooling rate of 1 K day Ϫ1 as the area fraction parameter increases from c ϭ 0.0010 to c ϭ 0.0014 the waves pass from a regime with stable moist convective damping to a regime of ''stratiform'' instability with convectively coupled waves propagating at speeds of roughly 15 m s Ϫ1 ; instabilities for a band of wavelengths in the supercluster regime, O(1000)-O(2000) km; and a vertical structure with a ''wave tilt'' where the temperature structure in the upper troposphere lags behind that in the lower troposphere. Thus, these convectively coupled waves in the model reproduce several key features of convectively coupled waves in the troposphere processed from recent observational data by Wheeler and Kiladis. As the parameter c is increased further to values such as c ϭ 0.01, the band of unstable waves increases and spreads toward a mesoscale wavelength of O(100) km while the same wave structure and quantitative features mentioned above are retained for O(1000) km. A detailed analysis of the temporal development of instability of these convectively coupled waves is presented here. In the first stage of instability, a high convective available potential energy (CAPE) region generates deep convection and a front-to-rear ascending flow with enhanced vertical shear in a stratiform wake region. Thus, these intermediate models may be useful prototypes for studying the parameterization of upscale convective momentum transport due to organized convection. In the second stage of instability, detailed analysis of the CAPE budget establishes that the effects of the second baroclinic mode in the stratiform wake produce new CAPE, which regenerates the first half of the wave cycle. Finally, since these convectively coupled stratiform waves do not require a barotropic mean flow, a barotropic mean flow, which alters the surface fluxes, is added to study its effect on their stability. These effects of a barotropic mean flow are secondary; an easterly mean flow enhances instability of the eastward-propagating convectively coupled waves and diminishes the instability of the westward-propagating waves through a wind-induced surface heat exchange mechanism.
2000
A simplified intermediate model for analyzing and parameterizing convectively coupled tropical waves is introduced here. This model has two baroclinic modes of vertical structure: a direct heating mode and a stratiform mode. The key essential parameter in these models is the area fraction occupied by deep convection, sc. The unstable convectively coupled waves that emerge from perturbation of a radiative convective equilibrium are discussed in detail through linearized stability analysis. Without any mean flow, for an overall cooling rate of 1 K day21 as the area fraction parameter increases from sc 5 0.0010 to sc 5 0.0014 the waves pass from a regime with stable moist convective damping to a regime of ‘‘stratiform’ ’ instability with convectively coupled waves propagating at speeds of roughly 15 m s21; instabilities for a band of wavelengths in the supercluster regime, O(1000)–O(2000) km; and a vertical structure with a ‘‘wave tilt’ ’ where the temperature structure in the upper tr...
The role of forcing in the local stability of stationary long waves. Part 1. Linear dynamics
Journal of Fluid Mechanics, 2007
The local linear stability of forced, stationary long waves produced by topography or potential vorticity (PV) sources is examined using a quasigeostrophic barotropic model. A multiple scale analysis yields coupled equations for the background stationary wave and lowfrequency (LF) disturbance field. Forcing structures for which the LF dynamics are Hamiltonian are shown to yield conservation laws that provide necessary conditions for instability and a constraint on the LF structures that can develop. Explicit knowledge of the forcings that produce the stationary waves is shown to be crucial to predicting a unique LF field. Various topographies or external PV sources can be chosen to produce stationary waves that differ by asymptotically small amounts, yet the LF instabilities that develop can have fundamentally different structures and growth rates. If the stationary wave field is forced solely by topography, LF oscillatory modes always emerge. In contrast, if the stationary wave field is forced solely by PV, two LF structures are possible: oscillatory modes or non-oscillatory envelope modes. The development of the envelope modes within the context of a linear LF theory is novel.
Coupled Kelvin-Wave and Mirage-Wave Instabilities In Semigeostrophic Dynamics
Journal of Physical …, 1998
A weak instability mode, associated with phase-locked counterpropagating coastal Kelvin waves in horizontal anticyclonic shear, is found in the semigeostrophic (SG) equations for stratified flow in a channel. This SG instability mode approximates a similar mode found in the Euler equations in the limit in which particle-trajectory slopes are much smaller than f /N, where f is the Coriolis frequency and N Ͼ f the buoyancy frequency. Though weak under normal parameter conditions, this instability mode is of theoretical interest because its existence accounts for the failure of an Arnol'd-type stability theorem for the SG equations. In the opposite limit, in which the particle motion is purely vertical, the Euler equations allow only buoyancy oscillations with no horizontal coupling. The SG equations, on the other hand, allow a physically spurious coastal ''mirage wave,'' so called because its velocity field vanishes despite a nonvanishing disturbance pressure field. Counterpropagating pairs of these waves can phase-lock to form a spurious ''mirage-wave instability.'' Closer examination shows that the mirage wave arises from failure of the SG approximations to be self-consistent for trajectory slopes տ f /N.
Instability of Topographically Forced Rossby Waves in a Two-layer Model
Journal of the Meteorological Society of Japan, 1987
Stability properties of topographically forced baroclinic Rossby waves and zonal flows are investigated by the use of a two-layer, quasi-geostrophic*-channel model. Two kinds of instabilities are found when the vertical shear of the zonal flow exceeds the minimum critical shear for the conventional baroclinic instability of the zonal flow: One is the topographic instability which is identical with that examined by Charney and DeVore (1979) and Mukougawa and Hirota (1986a) in the barotropic model. This instability appears in the near-resonant flow. The other is the baroclinic instability composed of synoptic disturbances with a horizontal modulation by effects of the forced wave. This is found to correspond to the storm-track type instability of free baroclinic Rossby waves investigated by Frederiksen (1978, 1982). Examination of various effects of these unstable modes on the basic flow reveals that the role of the synoptic disturbances on the transition of the weather regime is not so important as suggested by Reinhold and Pierrehumbert (1982). Alternatively, other unstable modes, such as those due to the topographic instability, are expected to cause the regime transition because their effects on the basic flow are completely different from those of the baroclinic instability.
Journal of Fluid Mechanics, 1995
There exists a well-developed body of theory based on quasi-geostrophic (QG) dynamics that is central to our present understanding of large-scale atmospheric and oceanic dynamics. An important question is the extent to which this body of theory may generalize to more accurate dynamical models. As a first step in this process, we here generalize a set of theoretical results, concerning the evolution of disturbances to prescribed basic states, to semi-geostrophic (SG) dynamics. SG dynamics, like QG dynamics, is a Hamiltonian balanced model whose evolution is described by the material conservation of potential vorticity, together with an invertibility principle relating the potential vorticity to the advecting fields. SG dynamics has features that make it a good prototype for balanced models that are more accurate than QG dynamics.In the first part of this two-part study, we derive a pseudomomentum invariant for the SG equations, and use it to obtain: (i) linear and nonlinear generaliz...
Journal of Fluid Mechanics, 2010
Proudman resonance amplifies the oceanic forced wave beneath moving atmospheric pressure disturbances. The amplification varies with water depth; consequently, the forced wave beneath a disturbance crossing topography radiates transient free waves. Transients are shown to magnify the effects of Proudman resonance for disturbances crossing the coast or shelf at particular angles. A Snell like reflection law gives rise to a type of resonance for relatively slow moving disturbances crossing a coast in an otherwise flat-bottomed ocean. This occurs for translation speeds less than the shallow water wave speed for disturbances approaching the coast at a critical angle given by the inverse sine of the Froude number of the disturbance. A disturbance crossing the shelf at particular angles can also excite seiche modes of the shelf via generation of a transient at the continental slope. Beyond a typically small angle of incidence, transients generated by a disturbance crossing the continental slope and coast will be trapped on the shelf by internal reflection. The refraction law for a fast-moving forced wave crossing an ocean ridge at greater than a small angle of incidence also results in trapped free-wave transients with tsunami-like periods propagating along the ridge. The subcritical resonance, excitation of shelf modes and trapping of the transients may have implications for storm surges and the generation of destructive meteotsunami.
Journal of the Atmospheric Sciences, 2008
The equatorial atmospheric variability shows a spectrum of significant peaks in the wavenumberfrequency domain. These peaks have been identified with the equatorially trapped wave modes of rotating shallow water wave theory. This paper addresses the observation that the various wave types (e.g., Kelvin, Rossby, etc.) and wavenumbers show differing signal strength relative to a red background. It is hypothesized that this may be due to variations in the linear stability of the atmosphere in response to the various wave types depending on both the specific wave type and the wavenumber. A simple model of the convectively coupled waves on the equatorial beta plane is constructed to identify processes that contribute to this dependence. The linear instability spectrum of the resulting coupled system is evaluated by eigenvalue analysis. This analysis shows unstable waves with phase speeds, growth rates, and structures (vertical and horizontal) that are broadly consistent with the results from observations. The linear system, with an idealized single intertropical convergence zone (ITCZ) as a mean state, shows peak unstable Kelvin waves around zonal wavenumber 7 with peak growth rates of ϳ0.08 day Ϫ1 (e-folding time of ϳ13 days). The system also shows unstable mixed Rossby-gravity (MRG) and inertio-gravity waves with significant growth in the zonal wavenumber range from Ϫ15 (negative indicates westward phase speed) to ϩ10 (positive indicates eastward phase speed). The peak MRG n ϭ 0 eastward inertio-gravity wave (EIG) growth rate is around one-third that of the Kelvin wave and occurs at zonal wavenumber 3. The Rossby waves in this system are stable, and the Madden-Julian oscillation is not observed. Within this model, it is shown that in addition to the effect of the ITCZ configuration, the differing instabilities of the different wave modes are also related to their different efficiency in converting input energy into divergent flow. This energy conversion efficiency difference is suggested as an additional factor that helps to shape the observed wave spectrum.