scholarly journals Resonant Wave Interactions in the Presence of a Diurnally Varying Heat Source

2009 ◽  
Vol 66 (10) ◽  
pp. 3165-3183 ◽  
Author(s):  
Carlos F. M. Raupp ◽  
Pedro L. Silva Dias
Keyword(s):  
Heat Source ◽  
Gravity Waves ◽  
The Other ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Frequency Wave ◽  
Resonant Interactions ◽  
Energy Exchanges ◽  
Resonant Triads ◽  
Stationary Component

Abstract Resonant interactions among equatorial waves in the presence of a diurnally varying heat source are studied in the context of the diabatic version of the equatorial β-plane primitive equations for a motionless, hydrostatic, horizontally homogeneous and stably stratified background atmosphere. The heat source is assumed to be periodic in time and of small amplitude [i.e., O(ɛ)] and is prescribed to roughly represent the typical heating associated with deep convection in the tropical atmosphere. In this context, using the asymptotic method of multiple time scales, the free linear Rossby, Kelvin, mixed Rossby–gravity, and inertio-gravity waves, as well as their vertical structures, are obtained as leading-order solutions. These waves are shown to interact resonantly in a triad configuration at the O(ɛ) approximation, and the dynamics of these interactions have been studied in the presence of the forcing. It is shown that for the planetary-scale wave resonant triads composed of two first baroclinic equatorially trapped waves and one barotropic Rossby mode, the spectrum of the thermal forcing is such that only one of the triad components is resonant with the heat source. As a result, to illustrate the role of the diurnal forcing in these interactions in a simplified fashion, two kinds of triads have been analyzed. The first one refers to triads composed of a k = 0 first baroclinic geostrophic mode, which is resonant with the stationary component of the diurnal heat source, and two dispersive modes, namely, a mixed Rossby–gravity wave and a barotropic Rossby mode. The other class corresponds to triads composed of two first baroclinic inertio-gravity waves in which the highest-frequency wave resonates with a transient harmonic of the forcing. The integration of the asymptotic reduced equations for these selected resonant triads shows that the stationary component of the diurnal heat source acts as an “accelerator” for the energy exchanges between the two dispersive waves through the excitation of the catalyst geostrophic mode. On the other hand, since in the second class of triads the mode that resonates with the forcing is the most energetically active member because of the energy constraints imposed by the triad dynamics, the results show that the convective forcing in this case is responsible for a longer time scale modulation in the resonant interactions, generating a period doubling in the energy exchanges. The results suggest that the diurnal variation of tropical convection might play an important role in generating low-frequency fluctuations in the atmospheric circulation through resonant nonlinear interactions.

scholarly journals Resonant Wave Interactions in the Equatorial Waveguide

2008 ◽  
Vol 65 (11) ◽  
pp. 3398-3418 ◽  
Author(s):  
Carlos F. M. Raupp ◽  
Pedro L. Silva Dias ◽  
Esteban G. Tabak ◽  
Paul Milewski
Keyword(s):  
Time Scales ◽  
Gravity Waves ◽  
Resonance Condition ◽  
Low Frequency ◽  
Vertical Direction ◽  
Present Theory ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Resonant Triads ◽  
Initial Mode

Abstract Weakly nonlinear interactions among equatorial waves have been explored in this paper using the adiabatic version of the equatorial β-plane primitive equations in isobaric coordinates. Assuming rigid lid vertical boundary conditions, the conditions imposed at the surface and at the top of the troposphere were expanded in a Taylor series around two isobaric surfaces in an approach similar to that used in the theory of surface–gravity waves in deep water and capillary–gravity waves. By adopting the asymptotic method of multiple time scales, the equatorial Rossby, mixed Rossby–gravity, inertio-gravity, and Kelvin waves, as well as their vertical structures, were obtained as leading-order solutions. These waves were shown to interact resonantly in a triad configuration at the O(ɛ) approximation. The resonant triads whose wave components satisfy a resonance condition for their vertical structures were found to have the most significant interactions, although this condition is not excluding, unlike the resonant conditions for the zonal wavenumbers and meridional modes. Thus, the analysis has focused on such resonant triads. In general, it was found that for these resonant triads satisfying the resonance condition in the vertical direction, the wave with the highest absolute frequency always acts as an energy source (or sink) for the remaining triad components, as usually occurs in several other physical problems in fluid dynamics. In addition, the zonally symmetric geostrophic modes act as catalyst modes for the energy exchanges between two dispersive waves in a resonant triad. The integration of the reduced asymptotic equations for a single resonant triad shows that, for the initial mode amplitudes characterizing realistic magnitudes of atmospheric flow perturbations, the modes in general exchange energy on low-frequency (intraseasonal and/or even longer) time scales, with the interaction period being dependent upon the initial mode amplitudes. Potential future applications of the present theory to the real atmosphere with the inclusion of diabatic forcing, dissipation, and a more realistic background state are also discussed.

Nonlinear Kelvin–Helmholtz instability in hydromagnetics

1979 ◽  
Vol 22 (1) ◽  
pp. 27-39 ◽  
Author(s):  
H. Nagano
Keyword(s):  
Growth Rate ◽  
Time Scales ◽  
Linear Instability ◽  
The Other ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Helmholtz Instability ◽  
Wavenumber Domain ◽  
The Difference

Nonlinear Kelvin–Helmholtz instability for an incompressible plasma under the influence of gravity is investigated theoretically, using the method of multiple time-scales. The effect of nonlinearity is to reduce the growth rate for the linear instability and to narrow the unstable wavenumber domain. There are two cases, in one of which the effect is strong and in the other slight. The difference between these cases is studied.

Resonant interactions between topographic planetary waves in a continuously stratified fluid

1978 ◽  
Vol 84 (4) ◽  
pp. 769-793 ◽  
Author(s):  
Lawrence A. Mysak
Keyword(s):  
Low Frequency ◽  
Phase Speed ◽  
Stratified Fluid ◽  
Planetary Waves ◽  
Buoyancy Frequency ◽  
Frequency Wave ◽  
Resonant Interactions ◽  
Frequency Correction ◽  
Resonant Triads ◽  
The Waves

The resonant interactions between topographic planetary waves in a continuously stratified fluid are investigated theoretically. The interacting waves form a resonant triad and travel along a channel with a uniformly sloping bottom. The basic state stratification in the channel is characterized by a constant buoyancy frequency. The existence of solutions to the quadratic resonance conditions is established graphically. Each wave by itself is a bottom-intensified oscillation of the type discovered by Rhines (1970) except for the addition of a small positive frequency correction. This correction must be included to satisfy higher-order terms in the bottom boundary condition. For strong stratification (r2[Gt ]L2, wherer= internal deformation radius andL= channel width), the waves are strongly bottom-trapped and this frequency correction is negligible. For weak stratification (r2[Lt ]L2) the waves are barotropic and the frequency correction isO(δ), where δ = fractional change in depth across the channel. In many oceanic contexts, δ lies in the range 0·1-0·4 and therefore this correction can produce a significant change in the phase speed. The amplitudes of the waves in the triad obey the classical gyroscopic equations usually encountered in quadratic resonance problems. In particular, the amplitudes evolve on the slow time scale\[ t=O(1/f_0\delta^2), \]which for our scaling assumptions is alsoO(1/f0Ro), whereRois the Rossby number.The results are applied to the Norwegian continental slope region. It is shown that, in this vicinity, there may exist resonant triads consisting of two short, high-frequency waves (periods around 3-4 days) and one long, low-frequency wave (period around 9 days).

SOME REMARKS ON THE MULTIPLE TIME SCALES OF DIFFUSION IN MINERALS AND MELTS

2018 ◽  
Author(s):  
Yan Liang ◽  
◽  
Daniele J. Cherniak ◽  
Chenguang Sun
Keyword(s):  
Time Scales ◽  
Multiple Time Scales ◽  
Multiple Time

scholarly journals Odor response adaptation in Drosophila—a continuous individualization process

2021 ◽  
Vol 383 (1) ◽  
pp. 143-148
Author(s):  
Shadi Jafari ◽  
Mattias Alenius
Keyword(s):  
Sensory Neurons ◽  
Olfactory System ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Olfactory Perception ◽  
Adaptation Mechanisms ◽  
Metabolic States ◽  
The Central Nervous System ◽  
Olfactory Adaptation ◽  
Central Adaptation

AbstractOlfactory perception is very individualized in humans and also in Drosophila. The process that individualize olfaction is adaptation that across multiple time scales and mechanisms shape perception and olfactory-guided behaviors. Olfactory adaptation occurs both in the central nervous system and in the periphery. Central adaptation occurs at the level of the circuits that process olfactory inputs from the periphery where it can integrate inputs from other senses, metabolic states, and stress. We will here focus on the periphery and how the fast, slow, and persistent (lifelong) adaptation mechanisms in the olfactory sensory neurons individualize the Drosophila olfactory system.

scholarly journals Are We Doing ‘Systems’ Research? An Assessment of Methods for Climate Change Adaptation to Hydrohazards in a Complex World

2019 ◽  
Vol 11 (4) ◽  
pp. 1163 ◽  
Author(s):  
Melissa Bedinger ◽  
Lindsay Beevers ◽  
Lila Collet ◽  
Annie Visser
Keyword(s):  
Climate Change ◽  
Human Nature ◽  
Climate Change Adaptation ◽  
Time Scales ◽  
Spatial Scales ◽  
Local Context ◽  
Multiple Time Scales ◽  
Future Research ◽  
Multiple Time ◽  
Systems Research

Climate change is a product of the Anthropocene, and the human–nature system in which we live. Effective climate change adaptation requires that we acknowledge this complexity. Theoretical literature on sustainability transitions has highlighted this and called for deeper acknowledgment of systems complexity in our research practices. Are we heeding these calls for ‘systems’ research? We used hydrohazards (floods and droughts) as an example research area to explore this question. We first distilled existing challenges for complex human–nature systems into six central concepts: Uncertainty, multiple spatial scales, multiple time scales, multimethod approaches, human–nature dimensions, and interactions. We then performed a systematic assessment of 737 articles to examine patterns in what methods are used and how these cover the complexity concepts. In general, results showed that many papers do not reference any of the complexity concepts, and no existing approach addresses all six. We used the detailed results to guide advancement from theoretical calls for action to specific next steps. Future research priorities include the development of methods for consideration of multiple hazards; for the study of interactions, particularly in linking the short- to medium-term time scales; to reduce data-intensivity; and to better integrate bottom–up and top–down approaches in a way that connects local context with higher-level decision-making. Overall this paper serves to build a shared conceptualisation of human–nature system complexity, map current practice, and navigate a complexity-smart trajectory for future research.

scholarly journals A multistate model incorporating estimation of excess hazards and multiple time scales

2021 ◽  
Vol 40 (9) ◽  
pp. 2139-2154
Author(s):  
Caroline E. Weibull ◽  
Paul C. Lambert ◽  
Sandra Eloranta ◽  
Therese M. L. Andersson ◽  
Paul W. Dickman ◽  
...  
Keyword(s):  
Time Scales ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Multistate Model

scholarly journals Structural Disorder and Collective Behavior of Two-Dimensional Magnetic Nanostructures

Nanomaterials ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 1392
Author(s):  
David Gallina ◽  
G. M. Pastor
Keyword(s):  
Interaction Energy ◽  
Time Evolution ◽  
Magnetic Nanostructures ◽  
Thermal Quenching ◽  
Structural Disorder ◽  
Square Lattice ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Two Dimensional ◽  
Energy Landscapes

Structural disorder has been shown to be responsible for profound changes of the interaction-energy landscapes and collective dynamics of two-dimensional (2D) magnetic nanostructures. Weakly-disordered 2D ensembles have a few particularly stable magnetic configurations with large basins of attraction from which the higher-energy metastable configurations are separated by only small downward barriers. In contrast, strongly-disordered ensembles have rough energy landscapes with a large number of low-energy local minima separated by relatively large energy barriers. Consequently, the former show good-structure-seeker behavior with an unhindered relaxation dynamics that is funnelled towards the global minimum, whereas the latter show a time evolution involving multiple time scales and trapping which is reminiscent of glasses. Although these general trends have been clearly established, a detailed assessment of the extent of these effects in specific nanostructure realizations remains elusive. The present study quantifies the disorder-induced changes in the interaction-energy landscape of two-dimensional dipole-coupled magnetic nanoparticles as a function of the magnetic configuration of the ensembles. Representative examples of weakly-disordered square-lattice arrangements, showing good structure-seeker behavior, and of strongly-disordered arrangements, showing spin-glass-like behavior, are considered. The topology of the kinetic networks of metastable magnetic configurations is analyzed. The consequences of disorder on the morphology of the interaction-energy landscapes are revealed by contrasting the corresponding disconnectivity graphs. The correlations between the characteristics of the energy landscapes and the Markovian dynamics of the various magnetic nanostructures are quantified by calculating the field-free relaxation time evolution after either magnetic saturation or thermal quenching and by comparing them with the corresponding averages over a large number of structural arrangements. Common trends and system-specific features are identified and discussed.

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