scholarly journals The Influence of Stratification on the Instabilities in an Idealized Two-Layer Ocean Model

2014 ◽  
Vol 44 (10) ◽  
pp. 2718-2738 ◽  
Author(s):  
R. L. Irwin ◽  
F. J. Poulin
Keyword(s):  
Stability Analysis ◽  
Linear Stability Analysis ◽  
Nonlinear Evolution ◽  
Ocean Model ◽  
Vertical Shear ◽  
General Context ◽  
Layer Model ◽  
Different Types ◽  
Two Layer Model ◽  
Rotating Shallow Water

Abstract This work investigates the instability of a two-layer Bickley jet in the context of the rotating shallow water (RSW) model. This provides a general context in which the instability of oceanographic jets with simple stratification can be investigated. The three objectives of this work are as follows: First, the study investigates the morphology of unstable modes that can occur in this two-layer model. This is done by performing a linear stability analysis to investigate different types of flows both with and without vertical shear. Second, the authors study how the growth rates of the unstable modes are affected by changes in the stratification. Third, this study looks at the nonlinear evolution of some of these instabilities to determine how easy it is for nonprimary instabilities to develop. This is motivated by the fact that in the literature there have been many investigations that have found a multitude of unstable modes in this model, and it is not evident as to how easily they can be generated in oceanographic flows.

Baroclinic instability of quasi-geostrophic flows localized in a thin layer

1995 ◽  
Vol 288 ◽  
pp. 175-199 ◽  
Author(s):  
E. S. Benilov
Keyword(s):  
Baroclinic Instability ◽  
Vertical Shear ◽  
Layer Model ◽  
Effective Time ◽  
Sufficient Stability ◽  
Geostrophic Flows ◽  
Characteristic Spatial Scale ◽  
Northern Pacific ◽  
Two Layer Model ◽  
Layer I

This paper examines the baroclinic instability of a quasi-geostrophic flow with vertical shear in a continuously stratified fluid. The flow and density stratification are both localized in a thin upper layer. (i) Disturbances whose wavelength is much smaller than the deformation radius (based on the depth of the upper layer) are demonstrated to satisfy an ‘equivalent two-layer model’ with properly chosen parameters. (ii) For disturbances whose wavelength is of the order of, or greater than, the deformation radius we derive a sufficient stability criterion. The above analysis is applied to the subtropical and subarctic frontal currents in the Northern Pacific. The effective time of growth of disturbances (i) is found to be 16–22 days, the characteristic spatial scale is 130–150 km.

NEW CHARACTERISERS OF BIFURCATIONS FROM KINK SOLUTIONS IN A COUPLED SINE CIRCLE MAP LATTICE

2001 ◽  
Vol 11 (09) ◽  
pp. 2501-2508 ◽  
Author(s):  
GAURI R. PRADHAN ◽  
NEELIMA GUPTE
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Spatial Period ◽  
Circle Map ◽  
Stability Matrix ◽  
Different Types ◽  
The Stability ◽  
Bifurcation Behavior ◽  
Solution Changes

Kink solutions in coupled sine circle map lattices demonstrate interesting bifurcation behavior. These are illustrated by the study of spatial period two kink solutions for this system. Different types of spatiotemporal solutions such as temporally frozen kinks, spatiotemporally synchronized solutions and kink induced temporally intermittent solutions appear in different regions of parameter space for this system and bifurcations are seen from one type of solution to another. The upper boundaries of the regions where the kinks are stable can be picked up by linear stability analysis. However, the eigenvalues of the stability matrix do not cross the unit circle along the lower stability boundaries, although the nature of the solution changes. Thus linear stability analysis is not sufficient to identify these lower boundaries. Hence we have proposed new characterisers which are capable of identifying such boundaries. Our identifiers successfully pick up the lower boundaries missed by linear stability analysis as well as the upper boundaries. Our characterisers could be of utility in other situations as well.

What controls probability distribution of local wave activity in the midlatitudes?

2021 ◽  
Author(s):  
Noboru Nakamura ◽  
Claire Valva
Keyword(s):  
Probability Distributions ◽  
Wave Activity ◽  
Skewed Distribution ◽  
Vertical Shear ◽  
Wave Flow ◽  
Transient Eddy ◽  
Layer Model ◽  
Speed Increase ◽  
Local Wave ◽  
Two Layer Model

<p>We examine probability distributions of <em>local wave activity</em> (LWA), a measure of the jet stream's meander, and factors that control them.  The observed column-mean LWA distributions exhibit significant seasonal, interhemispheric, and regional variations but are always positively skewed in the extratropics, and their tail often involves disruptions of the jet stream.  A previously derived 1D traffic flow model driven by observed spectra of transient eddy forcing qualitatively reproduces the shape of the observed LWA distribution.  It is shown that the skewed distribution emerges from nonlinearity in the zonal advection of LWA even though the eddy forcing is symmetrically distributed.  A slower jet and stronger transient and stationary eddy forcings, when introduced independently, all broaden the LWA distribution and increase the probability of spontaneous jet disruption.  Quasigeostrophic two-layer model also simulates skewed LWA distributions in the upper layer.  However, in the two-layer model both transient eddy forcing and the jet speed increase with an increasing shear (meridional temperature gradient), and their opposing influence leaves the frequency of jet disruptions insensitive to the vertical shear.  When the model's nonlinearity in the zonal flux of potential vorticity is artificially suppressed, it hinders wave-flow interaction and virtually eliminates reversal of the upper-layer zonal wind.  The study underscores the importance of nonlinearity in the zonal transmission of Rossby waves to the frequency of jet disruptions and associated weather anomalies. </p>

scholarly journals Instability of Lenticular Vortices: Results from Laboratory Experiments, Linear Stability Analysis and Numerical Simulations

Fluids ◽  
2021 ◽  
Vol 6 (11) ◽  
pp. 380
Author(s):  
Noé Lahaye ◽  
Alexandre Paci ◽  
Stefan G. Llewellyn Smith
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Laboratory Experiments ◽  
Lower Layer ◽  
Water Model ◽  
Layer Potential ◽  
Rotating Shallow Water ◽  
Layer Flow

The instability of surface lenticular vortices is investigated using a comprehensive suite of laboratory experiments combined with numerical linear stability analysis as well as nonlinear numerical simulations in a two-layer Rotating Shallow Water model. The development of instabilities is discussed and compared between the different methods. The linear stability analysis allows for a clear description of the origin of the instability observed in both the laboratory experiments and numerical simulations. While global qualitative agreement is found, some discrepancies are observed and discussed. Our study highlights that the sensitivity of the instability outcome is related to the initial condition and the lower-layer flow. The inhibition or even suppression of some unstable modes may be explained in terms of the lower-layer potential vorticity profile.

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