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Mankin Mak

Abstract

It is shown using a quasigeostrophic multilevel channel model that the stabilization of a zonal baroclinic flow by an unstable wave would be essentially baroclinic if the meridional domain is narrow. In contrast, an unstable baroclinic wave in a sufficiently wide domain would first propagate meridionally away from its source while intensifying and would then equilibrate/decay barotropically. The equilibration in this case occurs mostly by inducing a strong horizontal zonal shear and also partly by reducing the zonal baroclinicity. Since a strong impact of the lateral boundaries is generally a model artifact, barotropic equilibration is suggested to be more important in the atmosphere.

The corresponding increase in the meridonal scale of the wave field associated with the meridional propagation of the unstable wave in a wide domain is self-limiting by the beta effect. This result can be understood in terms of a well-known aspect of geostrophic turbulence. When the model width is only comparable to the zonal scale of the unstable wave, reflection of the waves by the lateral boundaries would naturally prohibit the cascading process and would result in baroclinic stabilization.

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Mankin Mak

Abstract

Incipient marine cyclogenesis is investigated as an instability process of a mean baroclinic state with a vertically nonuniform static stability under the influence of a self-induced surface sensible heat flux in the context of a quasigeostrophic model framework. The analytic solution of such a model is first presented. The surface sensible heat flux induces strongly unstable short waves in the meso-α range and an e-folding time of the order of one day under supposedly relevant parameter conditions. Those modes have a shallow vertical structure near the surface with a pronounced westward tilt with height. The latter facilitates a release of enough potential energy from the basic state to overcompensate the destruction of potential energy by the surface heat exchange itself. The diabatic destabilization by surface sensible heat flux is therefore an alternative mechanism for initiating small marine cyclones without upper-level forcing.

A potential vorticity interpretation of this instability process is also given. A supplementary numerical analysis confirms that the meso-α unstable waves are robust because they exist when various combinations of low-level static stability and heating profiles are used. The dependence upon the heating profile is somewhat stronger, capable of inducing an additional set of unstable modes between the meso-α and synoptic-scale ranges when it increases substantially with height near the surface.

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Mankin Mak

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Mankin Mak

Abstract

A better physical understanding of the instability of a zonally varying basic flow may be gained by invoking the concept of wave-packet resonance, which complements the notions of absolute and convective instability. To highlight the nature of such instability, a generic barotropic jet that has essentially only two closed contours in its basic vorticity gradient field is analyzed. Apart from the structure of the jet itself, the domain-averaged zonal flow component and the beta effect are two determining factors that control the form of wave-packet resonance. These factors influence the propagation characteristics of an unstable disturbance. When their influences counterbalance one another, the instability is attributable to stationary wave-packet resonance; otherwise it is due to propagating wave-packet resonance. This model setting illustrates that a local mode may have a finite group velocity and the self-reseeding of a disturbance does not necessarily require recycling through the streamwise boundaries. The detailed properties of the unstable modes are examined in terms of their structure, propagating characteristics, and local energetics.

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Mankin Mak

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This paper reports a barotropic instability analysis of nonhydrostatic columnar disturbances in a layer of homogeneous fluid over a flat bottom surface. The extended form of Hamilton's principle of least action is used to obtain the canonical form of Green–Naghdi equations for this model. The basic state has a monotonic shear flow and a variable depth. For values of the parameters supposedly relevant to an environment of nonsupercell tornadoes (NST), the nonhydrostatic effect is found to have significant impacts. It is capable of sufficiently slowing down some short gravity waves so that they resonantly interact with vorticity waves of the same wavelengths in the shear zone to form strongly unstable gravity–vorticity hybrid modes. Their instability properties are by and large compatible with the observed counterparts of NST, such as growth rate, phase speed, length scale, aspect ratio, structure, and energetics. Those results are robust for a reasonable range of each key parameter. Apart from a number of caveats, it is reasonable to suggest that nonhydrostatic barotropic instability is applicable to NST genesis.

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Mankin Mak

Abstract

It is shown that a vertical asymmetry in the friction qualitatively influences the equilibration of nonlinear quasi-geostrophic unstable baroclinic waves. Specifically, the sense of this asymmetry is a crucial factor that dictates whether the equilibrated state is generally a steady multiple wave state or a vacillation. The former is generally the preferred form of an equilibrated state for the case of having a larger friction in the lower layer than in the upper layer. In contrast, vacillation is a preferred form for the case of an opposite asymmetry in the friction. The limit cycle has a weaker time mean component. A zonal barotropic jet is additionally induced by the finite amplitude waves.

The degree of irregularity in the vacillation increases with the frictional asymmetry. An equilibrated state of chaos prevails over a wide range of parametric conditions. The corresponding return map suggests that the chaos is not a Lorenzian strange attractor. Its property has been examined in terms of the Lyapunov characteristic number.

The energetics diagnosis confirms that the sense of the asymmetry in the friction controls the sense of the frictionally induced secondary circulation. This underlines the character of the influence of the frictional asymmetry. The findings of this analysis may have a bearing on the effects on the dynamics of a large-scale flow, due to the breaking of subgrid scale gravity waves, found in the recent high resolution, GCM/NWP models.

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Mankin Mak

Abstract

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Mankin Mak

Abstract

The influences of wave-wave and wave-zonal flow interactions an the baroclinic instability in a basic quasi-geostrophic two-layer model are investigated. A minimum spectral resolution is used. The evolution of the system obtained with (without) the wave-wave interaction is referred to as the general (special) equilibration.

The special equilibration leads to a steady single wave state. This wave, similar to Pedlosky's finding, has a longer zonal wavelength than that of the most unstable wave according to the linear theory under representative dissipative conditions. In contrast, the general equilibration leads to one of four distinctly different equilibrated states, depending upon the baroclinic forcing and the dissipation parameters. It can be a steady single-wave state, or a steady multiple-wave state, or a triad-limit-cycle or an incoherently fluctuating state. A regime diagram is given to delineate the bifurcations that give rise to such equilibrated states as a function of the forcing and damping parameters.

The triad-limit-cycle is a robust response, prevalent under a wide range of parametric conditions. The most favorable conditions for its existence are intermediate forcing and damping. Its vacillation period is of the order of tens of days under realizable parametric conditions. Furthermore, it modulates considerably higher frequency fluctuations with periods of several days. A diagnosis of the energetics reveals that while such a limit cycle arises from the wave-wave interaction, the embedded higher frequency fluctuations are mainly associated with the wave-zonal flow interaction. It also reveals that the general equilibration tends to barotropize the flow in agreement with basic findings of Rhine and Salmon for geostrophic turbulence.

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Mankin Mak

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This study investigates the effect of condensational heating on the formation of a monsoonal mid-tropospheric cyclone (MTC) by applying the heating parameterization of Mak (1982) to the dynamic model of Brode and Mak (1978) except that the beta-effect is also included. It is found that the observed basic baroclinic flow with turning provides a dynamic framework conducive for a MTC-like disturbance to interact with the embedded moist convection. The joint processes give rice to an unstable disturbance that has a large but finite growth rate and an intermediate length scale. The theoretical e-folding time is of the order of one day under a wide range of parametric heating conditions. The key structural features of the observed MTC are reproduced in the most unstable model disturbance. The main influence of the beta-effect is on the phase speed of the model disturbance. In the presence of condensational heating, the beta-effect only has a secondary influence on the growth rate. The moist processes and the unique baroclinic processes associated with a turning baroclinic flow are therefore both indispensible in the genesis of MTC. To understand whether or not the instability results might be strongly controlled by the low-level basic shears, the results computed with or without the latter am compared. It is found that such low-level shears have only a stabilizing influence and therefore do not play an essential role in the instability process.

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Mankin Mak

Abstract

The instability of quasi-geostrophic internal modes in a moist model atmosphere with the presence of a purely barotropic basic flow is investigated. The author's formulation for a self-induced condensational heating (Mak) is adopted in a prototype model that has a hyperbolic-tangent barotropic basic flow. It is shown that a cooperative interaction can occur between the quasi-geostrophic internal modes and the implicitly embedded convection. Such an internal mode, instead of the external mode, becomes the dominant unstable mode even when the heating is only moderately strong. While the generalized Rayleigh condition of shear instability (Kuo) is a necessary condition for having an unstable external mode, it is not so for having an unstable internal mode under the influence of condensational heating. Depending upon the heating intensity, the required shear for such instability can be greatly, reduced. As the heating is increased, the short-wave cutoff is significantly reduced, but the length scale of the most unstable mode is only asymptotically shortened toward an intermediate scale. The phase speed remains essentially controlled by the steering influence of the basic flow. When a heating profile with larger values in the lower troposphere than in the upper troposphere is used, there would be a larger maximum growth rate and a shorter preferred wavelength. The results concerning the structural and energetic properties of the most unstable wave are also presented.

An application of this model is made with a basic flow of an easterly jet that has a Gaussian distribution. The results suggest that the moist dynamical mechanism under consideration would provide a more general explanation of the formation of the African easterly waves.

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