Normal modes with boundary dynamics in geophysical fluids

The normal modes of a horizontally uniform, vertically sheared flow over a sloping bottom are considered in two active layers underneath a deep motionless third layer. The variations of the layer thickness are assumed to be small to analyse the sixth-order eigenvalue problem for finite-Froude-number typical for oceanic currents. The dispersion curves for the Rossby waves and the Poincaré modes of inertia–gravity waves (IGW) are investigated to identify the different types of instabilities that occur if there is a pair of wave components which have almost the same Doppler-shifted frequency related to crossover of the branches when the Froude number increases. Simple criteria for ageostrophic instabilities due to a resonance between the IGW and the Rossby wave because of the thickness gradient in either the lower or middle layer, are derived. They exactly correspond to violation of sufficient Ripa's conditions for the flow stability. In both cases the growth rate and the interval of unstable wavenumbers are shown to be proportional to the square root of the corresponding gradient of the layer thickness. These types of ageostrophic instability can coexist (and with Kelvin–Helmholtz instability). However, their role in generating unbalanced motions and mixing processes in geophysical fluids appears limited due to small growth rates and narrow intervals of the unstable wavenumbers in comparison to Kelvin–Helmholtz instability.

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Lectures on waves in geophysical fluids

Annales de Physique ◽

10.1051/anphys:0198400902030700 ◽

1984 ◽

Vol 9 (2) ◽

pp. 307-346

Author(s):

D.G. Andrews

Keyword(s):

Geophysical Fluids

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A method for computing low-frequency normal modes of large symmetric assemblies of macromolecules : Application to the disk of tobacco mosaic virus protein

Journal de Chimie Physique ◽

10.1051/jcp/1991882726 ◽

1991 ◽

Vol 88 ◽

pp. 2726-2726

Author(s):

T Simonson ◽

D Perahia

Keyword(s):

Tobacco Mosaic Virus ◽

Mosaic Virus ◽

Normal Modes ◽

Low Frequency ◽

Virus Protein

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Filtering methods for finite-time normal modes and atmospheric error growth

ANZIAM Journal ◽

10.21914/anziamj.v42i0.655 ◽

2000 ◽

Vol 42 ◽

pp. 1482

Author(s):

Mozheng Wei ◽

Jorgen S. Frederiksen ◽

Steve Kepert

Keyword(s):

Finite Time ◽

Normal Modes ◽

Error Growth

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Love Without Boundaries? How Ethnic Boundary Dynamics Shape Interethnic Partner Choice among Turkish Belgians

DiGeSt Journal of Diversity and Gender Studies ◽

10.11116/jdivegendstud.1.2.0039 ◽

2014 ◽

Vol 1 (2) ◽

pp. 39

Author(s):

Klaartje Van Kerckem ◽

Bart Van de Putte ◽

Peter Stevens

Keyword(s):

Partner Choice ◽

Ethnic Boundary ◽

Boundary Dynamics

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Gravitational Waves

10.1093/oso/9780198570899.001.0001 ◽

2018 ◽

Cited By ~ 33

Author(s):

Michele Maggiore

Keyword(s):

Black Hole ◽

Perturbation Theory ◽

Gravitational Waves ◽

Transfer Functions ◽

Normal Modes ◽

Cosmological Perturbation ◽

Tests Of General Relativity ◽

Pulsar Timing ◽

Tensor Perturbations ◽

Stochastic Backgrounds

A comprehensive and detailed account of the physics of gravitational waves and their role in astrophysics and cosmology. The part on astrophysical sources of gravitational waves includes chapters on GWs from supernovae, neutron stars (neutron star normal modes, CFS instability, r-modes), black-hole perturbation theory (Regge-Wheeler and Zerilli equations, Teukoslky equation for rotating BHs, quasi-normal modes) coalescing compact binaries (effective one-body formalism, numerical relativity), discovery of gravitational waves at the advanced LIGO interferometers (discoveries of GW150914, GW151226, tests of general relativity, astrophysical implications), supermassive black holes (supermassive black-hole binaries, EMRI, relevance for LISA and pulsar timing arrays). The part on gravitational waves and cosmology include discussions of FRW cosmology, cosmological perturbation theory (helicity decomposition, scalar and tensor perturbations, Bardeen variables, power spectra, transfer functions for scalar and tensor modes), the effects of GWs on the Cosmic Microwave Background (ISW effect, CMB polarization, E and B modes), inflation (amplification of vacuum fluctuations, quantum fields in curved space, generation of scalar and tensor perturbations, Mukhanov-Sasaki equation,reheating, preheating), stochastic backgrounds of cosmological origin (phase transitions, cosmic strings, alternatives to inflation, bounds on primordial GWs) and search of stochastic backgrounds with Pulsar Timing Arrays (PTA).

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Triatomic molecules

10.1093/oso/9780198788980.003.0004 ◽

2018 ◽

Author(s):

John H. D. Eland ◽

Raimund Feifel

Keyword(s):

Degrees Of Freedom ◽

Normal Modes ◽

Electronic States ◽

Triatomic Molecules ◽

Doubly Charged Ions ◽

Spectral Bands ◽

Valence Electrons ◽

Doubly Charged ◽

Charged Ions ◽

Double Ionisation

Double ionisation of the triatomic molecules presented in this chapter shows an added degree of complexity. Besides potentially having many more electrons, they have three vibrational degrees of freedom (three normal modes) instead of the single one in a diatomic molecule. For asymmetric and bent triatomic molecules multiple modes can be excited, so the spectral bands may be congested in all forms of electronic spectra, including double ionisation. Double photoionisation spectra of H2O, H2S, HCN, CO2, N2O, OCS, CS2, BrCN, ICN, HgCl2, NO2, and SO2 are presented with analysis to identify the electronic states of the doubly charged ions. The order of the molecules in this chapter is set first by the number of valence electrons, then by the molecular weight.

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