A proof and applications of the expansion theorem for the Rossby normal modes in a closed rectangular basin

1987 ◽  
Vol 43 (4) ◽  
pp. 237-243 ◽  
Author(s):  
Akira Masuda
Keyword(s):  
Normal Modes ◽  
Expansion Theorem ◽  
Rectangular Basin

scholarly journals Conditional nonlinear optimal perturbations of the double-gyre ocean circulation

2008 ◽  
Vol 15 (5) ◽  
pp. 727-734 ◽  
Author(s):  
A. D. Terwisscha van Scheltinga ◽  
H. A. Dijkstra
Keyword(s):  
Time Evolution ◽  
Ocean Circulation ◽  
Initial Perturbation ◽  
Normal Modes ◽  
Finite Amplitude ◽  
Dissipation Function ◽  
Stable States ◽  
Optimal Perturbation ◽  
Rectangular Basin ◽  
Double Gyre

Abstract. In this paper, we study the development of finite amplitude perturbations on linearly stable steady barotropic double-gyre flows in a rectangular basin using the concept of Conditional Nonlinear Optimal Perturbation (CNOP). The CNOPs depend on a time scale of evolution te and an initial perturbation threshold δ. Under symmetric wind forcing, a perfect pitchfork perturbation occurs in the model. The CNOPs are determined for all linearly stable states and the time evolution of the CNOPs is studied. It is found that the patterns of the CNOPs are similar to those of the non-normal modes for small te and approach those of the normal modes for larger te. With slightly asymmetric winds, an imperfect pitchfork occurs in the model. Indications are found that the time evolution of the CNOPs is related to the value of the dissipation function of the underlying steady state.

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

2000 ◽  
Vol 42 ◽  
pp. 1482
Author(s):  
Mozheng Wei ◽  
Jorgen S. Frederiksen ◽  
Steve Kepert
Keyword(s):  
Finite Time ◽  
Normal Modes ◽  
Error Growth

Gravitational Waves

2018 ◽  
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).

Triatomic molecules

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.

Wave propagation dynamics in a fractional Zener model with stochastic excitation

2020 ◽  
Vol 23 (6) ◽  
pp. 1570-1604
Author(s):  
Teodor Atanacković ◽  
Stevan Pilipović ◽  
Dora Seleši
Keyword(s):  
Wave Propagation ◽  
Constitutive Equation ◽  
Equations Of Motion ◽  
Weak Form ◽  
Stochastic Excitation ◽  
Expansion Theorem ◽  
Zener Model ◽  
Dissipation Inequality ◽  
Regularity Properties ◽  
Fractional Zener Model

Abstract Equations of motion for a Zener model describing a viscoelastic rod are investigated and conditions ensuring the existence, uniqueness and regularity properties of solutions are obtained. Restrictions on the coefficients in the constitutive equation are determined by a weak form of the dissipation inequality. Various stochastic processes related to the Karhunen-Loéve expansion theorem are presented as a model for random perturbances. Results show that displacement disturbances propagate with an infinite speed. Some corrections of already published results for a non-stochastic model are also provided.

Wave chaos in terms of normal modes

1999 ◽  
Vol 59 (2) ◽  
pp. 1656-1668 ◽  
Author(s):  
A. L. Virovlyansky ◽  
G. M. Zaslavsky
Keyword(s):  
Normal Modes ◽  
Wave Chaos
Sign in / Sign up

Export Citation Format

Share Document