Kelvin Wave Instability: Critical Latitudes and Exponentially Small Effects

2017 ◽  
pp. 297-309
Author(s):  
John P. Boyd
Keyword(s):  
Kelvin Wave ◽  
Wave Instability ◽  
Exponentially Small

The strange instability of the equatorial Kelvin wave

2020 ◽  
Author(s):  
Stephen Griffiths
Keyword(s):  
Growth Rate ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Numerical Verification ◽  
Kelvin Wave ◽  
Perturbation Expansions ◽  
Wave Instability ◽  
Regular Perturbation ◽  
Confluent Hypergeometric Functions ◽  
Linear Equations Of Motion

<p>The Kelvin wave is perhaps the most important of the equatorially trapped waves in the terrestrial atmosphere and ocean, and plays a role in various phenomena such as tropical convection and El Nino. Theoretically, it can be understood from the linear dynamics of a stratified fluid on an equatorial β-plane, which, with simple assumptions about the disturbance structure, leads to wavelike solutions propagating along the equator, with exponential decay in latitude. However, when the simplest possible background flow is added (with uniform latitudinal shear), the Kelvin wave (but not the other equatorial waves) becomes unstable. This happens in an extremely unusual way: there is instability for arbitrarily small nondimensional shear <em>λ</em>, and the growth rate is proportional to exp(-1/λ^2) as λ → 0. This in contrast to most hydrodynamic instabilities, in which the growth rate typically scales as a positive power of λ-λ<sub>c</sub> as the control parameter λ passes through a critical value λ<sub>c</sub>.</p><p>This Kelvin wave instability has been established numerically by Natarov and Boyd, who also speculated as to the underlying mathematical cause by analysing a quantum harmonic oscillator perturbed by a potential with a remote pole. Here we show how the growth rate and full spatial structure of the Kelvin wave instability may be derived using matched asymptotic expansions applied to the (linear) equations of motion. This involves an adventure with confluent hypergeometric functions in the exponentially-decaying tails of the Kelvin waves, and a trick to reveal the exponentially small growth rate from a formulation that only uses regular perturbation expansions. Numerical verification of the analysis is also interesting and challenging, since special high-precision solutions of the governing ordinary differential equations are required even when the nondimensional shear is not that small (circa 0.5). </p>

Tuning Avtogenerator with Exponentially Small Band

2012 ◽  
Vol 1 (3) ◽  
pp. 68-76
Author(s):  
S. V. Boritko ◽  
◽  
V. I. Pustovoit ◽  
V. A. Suvorov ◽  
◽  
...  
Keyword(s):  
Small Band ◽  
Exponentially Small

TEMPERATURE VARIABILITY AT SENUNU BAY, WEST SUMBAWA

2013 ◽  
Vol 5 (2) ◽  
Author(s):  
Syamsul Hidayat ◽  
Mulia Purba ◽  
Jorina Waworuntu
Keyword(s):  
Layer Thickness ◽  
Mixed Layer ◽  
Cross Correlation ◽  
Sea Surface ◽  
Thermocline Depth ◽  
Kelvin Wave ◽  
The West ◽  
Sea Bottom ◽  
Annual Period ◽  
Regional Processes

The purposes of this study were to determine the variability of temperature and its relation to regional processes in the Senunu Bay. The result showed clear vertical stratifications i.e., mixed layer thickness about 39-119 m with isotherm of 27°C, thermocline layer thickness about 83-204 m with isotherm of 14–26°C, and  the deeper layer from the thermocline lower limit to the sea bottom with isotherm <13°C. Temperature and the thickness of each layers varied with season in which during the Northwest Monsoon the temperature was warmer and the mixed layer was thicker than those during Southeast Monsoon. During Southeast Monsoon, the thermocline layer rose  about 24 m. The 2001, 2006, and 2009 (weak La Nina years),  the Indonesia Throughflow (ITF) carried warmer water, deepening thermocline depth and reducing upwelling strength.  In 2003 and 2008 thickening of mixed layer occurred in transition season  was believed  associated with the  arrival of Kelvin Wave from the west. In 2002 and 2004 (weak El Nino period,) ITF carries colder water shallowing thermocline depth and enhancing upwelling strength. In 2007 was believed to be related with positive IODM where the sea surface temperature were decreasing due to intensification of southeast wind which induced strong upwelling. The temperature spectral density of mixed layer and thermocline was influenced by annual, semi-annual, intra-annual and inter-annual period fluctuations. The cross-correlation between wind and temperature showed significant value in the annual period.  Keywords: temperature, thermocline, variability, ENSO, IODM.

Getting Rid of Fast Waves: Slow Dynamics

2018 ◽  
Author(s):  
Vladimir Zeitlin
Keyword(s):  
Rossby Waves ◽  
Baroclinic Instability ◽  
Nonlinear Effects ◽  
Kelvin Wave ◽  
Beta Plane ◽  
Equatorial Wave ◽  
Flow Over Topography ◽  
Wave Guides ◽  
Rotating Shallow Water ◽  
Fast Waves

After analysis of general properties of horizontal motion in primitive equations and introduction of principal parameters, the key notion of geostrophic equilibrium is introduced. Quasi-geostrophic reductions of one- and two-layer rotating shallow-water models are obtained by a direct filtering of fast inertia–gravity waves through a choice of the time scale of motions of interest, and by asymptotic expansions in Rossby number. Properties of quasi-geostrophic models are established. It is shown that in the beta-plane approximations the models describe Rossby waves. The first idea of the classical baroclinic instability is given, and its relation to Rossby waves is explained. Modifications of quasi-geostrophic dynamics in the presence of coastal, topographic, and equatorial wave-guides are analysed. Emission of mountain Rossby waves by a flow over topography is demonstrated. The phenomena of Kelvin wave breaking, and of soliton formation by long equatorial and topographic Rossby waves due to nonlinear effects are explained.

scholarly journals The role of tropical volcanic eruptions in exacerbating Indian droughts

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Suvarna Fadnavis ◽  
Rolf Müller ◽  
Tanusri Chakraborty ◽  
T. P. Sabin ◽  
Anton Laakso ◽  
...  
Keyword(s):  
El Niño ◽  
Climate Model ◽  
El Nino ◽  
Volcanic Eruptions ◽  
Summer Monsoon Rainfall ◽  
Indian Region ◽  
Volcanic Plume ◽  
Kelvin Wave ◽  
Central Pacific ◽  
Climate Model Simulations

AbstractThe Indian summer monsoon rainfall (ISMR) is vital for the livelihood of millions of people in the Indian region; droughts caused by monsoon failures often resulted in famines. Large volcanic eruptions have been linked with reductions in ISMR, but the responsible mechanisms remain unclear. Here, using 145-year (1871–2016) records of volcanic eruptions and ISMR, we show that ISMR deficits prevail for two years after moderate and large (VEI > 3) tropical volcanic eruptions; this is not the case for extra-tropical eruptions. Moreover, tropical volcanic eruptions strengthen El Niño and weaken La Niña conditions, further enhancing Indian droughts. Using climate-model simulations of the 2011 Nabro volcanic eruption, we show that eruption induced an El Niño like warming in the central Pacific for two consecutive years due to Kelvin wave dissipation triggered by the eruption. This El Niño like warming in the central Pacific led to a precipitation reduction in the Indian region. In addition, solar dimming caused by the volcanic plume in 2011 reduced Indian rainfall.

scholarly journals Kelvin/Rossby Wave Partition of Madden-Julian Oscillation Circulations

Climate ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 2
Author(s):  
Patrick Haertel
Keyword(s):  
Rossby Wave ◽  
Large Scale ◽  
Atmospheric Model ◽  
Circulation System ◽  
System Of Equations ◽  
Wave Component ◽  
Madden Julian Oscillation ◽  
Kelvin Wave ◽  
Realistic View ◽  
State Of Rest

The Madden Julian Oscillation (MJO) is a large-scale convective and circulation system that propagates slowly eastward over the equatorial Indian and Western Pacific Oceans. Multiple, conflicting theories describe its growth and propagation, most involving equatorial Kelvin and/or Rossby waves. This study partitions MJO circulations into Kelvin and Rossby wave components for three sets of data: (1) a modeled linear response to an MJO-like heating; (2) a composite MJO based on atmospheric sounding data; and (3) a composite MJO based on data from a Lagrangian atmospheric model. The first dataset has a simple dynamical interpretation, the second provides a realistic view of MJO circulations, and the third occurs in a laboratory supporting controlled experiments. In all three of the datasets, the propagation of Kelvin waves is similar, suggesting that the dynamics of Kelvin wave circulations in the MJO can be captured by a system of equations linearized about a basic state of rest. In contrast, the Rossby wave component of the observed MJO’s circulation differs substantially from that in our linear model, with Rossby gyres moving eastward along with the heating and migrating poleward relative to their linear counterparts. These results support the use of a system of equations linearized about a basic state of rest for the Kelvin wave component of MJO circulation, but they question its use for the Rossby wave component.

scholarly journals Cloud Masks Derived from the Mars Daily Global Maps and an Application to the Tropical Cloud Belt on Mars

Geosciences ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 324
Author(s):  
Huiqun Wang ◽  
Gonzalo González Abad
Keyword(s):  
Processing Technique ◽  
Oscillatory Behavior ◽  
Early Summer ◽  
Dust Storms ◽  
Transitional Period ◽  
Image Processing Technique ◽  
Kelvin Wave ◽  
Blue Channel ◽  
Zonal Wavenumber ◽  
Shift Pattern

An image processing technique is used to derive cloud masks from the color Mars Daily Global Maps (MDGMs) that are composed from the Mars Reconnaissance Orbiter (MRO) Mars Color Imager (MARCI) wide-angle image swaths. The blue channel of each MDGM is used to select cloud candidates and the blue-to-red ratio map is compared with a reference ratio map to filter out false positives. Quality control is performed manually. The derived cloud masks cover 1 Mars year from the summer of Mars year (MY) 28 to the summer of MY 29. The product has a 0.1° longitude by 0.1° latitude resolution and is available each day. This makes it possible to characterize the evolution of the tropical cloud belt from several new perspectives. The tropical cloud belt steadily builds up during northern spring and early summer, peaks near the early- to mid-summer transitional period, and rapidly declines afterward. From the perspective of cloud occurrence frequency and time mean, the cloud belt appears meandrous and zonally discontinuous, with minima in the Amazonis Planitia and Arabia Terra longitudinal sectors. A pronounced cloud branch diverges from the main cloud belt and extends from the Valles Marineris towards the Noachis and Hellas region. The cloud belt exhibits noticeable oscillatory behavior whereby cloud brightening alternates between the western and eastern hemispheres near the equator with a periodicity between 20 and 30 sols. The cloud belt oscillation occurred each Mars year around Ls = 140°, except for the Mars years when intense dust storms made disruptions. The phenomenon appears to be associated with an eastward propagating equatorial Kelvin wave with zonal wavenumber 1. This wave has a much longer wave period than the diurnal and semidiurnal Kelvin waves discussed in most of the previous studies and may be an important factor for the intra-seasonal variability of the tropical cloud belt. The convolution of clouds’ local time variation with MRO’s orbit shift pattern results in a seemingly highly regular 5-day traveling wave in Hovmöller diagrams of cloud masks.

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