Journal ArticleDOI
Improved bounds on linear instability of barotropic zonal flow within the shallow water equations
A.D. Clark,Isom H. Herron +1 more
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In this paper, the authors developed mathematical results to describe the location of linear instability of a parallel mean flow within the framework of the shallow water equations; growth estimates of near neutral modes (for disturbances subcritical with respect to gravity wave speed) in the cases of non-rotating and rotating shallow water.Abstract:
Here we develop mathematical results to describe the location of linear instability of a parallel mean flow within the framework of the shallow water equations; growth estimates of near neutral modes (for disturbances subcritical with respect to gravity wave speed) in the cases of non-rotating and rotating shallow water. The bottom topography is taken to be one-dimensional and the isobaths are parallel to the mean flow. In the case of a rotating fluid, the isobaths and the mean flow are assumed to be zonal. The flow is front-like: there is a monotonic increase of mean flow velocity. Our results show that for barotropic flows the location of instabilities will be a semi-ellipse region in the complex wave velocity plane, that is based on the wave-number, Froude number, and depth of the fluid layer. We also explore the instability region for the case of spatially unbounded mean velocity profiles for non-rotating shallow water.read more
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Semi-analytical solutions of shallow water waves with idealised bottom topographies
Chang-ming Liu,Antwan D. Clark +1 more
TL;DR: In this article , the authors employ the Adomian decomposition method (ADM) to develop semi-analytical formulations of these problems that preserve the direct correlation of the physical parameters while capturing the nonlinear phenomenon.
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On compressible circular Rayleigh problem of hydrodynamic stability
P Pavithra,M Subbiah +1 more
TL;DR: In this article, the authors developed general analytical results on the linear instability problem of inviscid compressible axial flows in the annular region between two coaxial cylinders to axisymmetric disturbances.
References
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Geophysical Fluid Dynamics
TL;DR: In this article, the authors propose a quasigeostrophic motion of a Stratified Fluid on a Sphere (SFL) on a sphere, which is based on an Inviscid Shallow-Water Theory.
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Long Waves and Cyclone Waves
TL;DR: In this paper, it was shown that a simple state of steady baroclinic large-scale atmospheric motion is almost invariably unstable, and that such states of motion can be represented by components of a certain simple type, some of which grow exponentially with time.
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On the stability of heterogeneous shear flows
TL;DR: In this paper, small perturbations of a parallel shear flow U(y) in an inviscid, incompressible fluid of variable density ρ 0 (y) are considered.
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The dynamics of long waves in a baroclinic westerly current
TL;DR: In this article, it was shown that the instability increases with shear, lapse rate, and latitude, and decreases with wave length, and that the westerlies of middle latitudes are a seat of constant dynamic instability.
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Note on a paper of John W. Miles
TL;DR: In this article, the theorem X established by Miles in the preceding paper is given a simpler and more general proof, and further theoretical results concerning the stability of heterogeneous shear flows are also presented, in particular a demonstration that the complex wave velocity of any unstable mode must lie in a certain semicircle.