Wave-mean flow interaction, forced triads, and recharge-discharge Processes as noncanonical Hamiltonian Systems

2020 ◽  
Author(s):  
Richard Blender ◽  
Joscha Fregin
Keyword(s):  
Phase Space ◽  
Three Dimensional ◽  
Interaction Model ◽  
Nonlinear Oscillators ◽  
Atmospheric Dynamics ◽  
Wave Number ◽  
Mean Flow ◽  
Forced Wave ◽  
Flow Interaction ◽  
Dimensional Phase Space

<p>We consider recharge-discharge processes in a forced wave-mean flow interaction model and in a forced Rossby wave triad. Such processes are common in atmospheric dynamics and are typically modelled by nonlinear oscillators, for example for mid-latitude storms by Ambaum and Novak (2013) and for convective cycles by Yano and Plant (2012). A similar behaviour can be seen in the simulation of a forced wave number triad by Lynch (2009). Here we construct noncanonical Hamiltonian and Nambu representations in three-dimensional phase space for available and prescribed conservation laws during the recharge and discharge regimes. Divergence in phase space is modelled by a pre-factor. The approach allows the design of conservative and forced dynamical systems.</p>

scholarly journals Dynamical properties and extremes of Northern Hemisphere climate fields over the past 60 years

2017 ◽  
Vol 24 (4) ◽  
pp. 713-725 ◽  
Author(s):  
Davide Faranda ◽  
Gabriele Messori ◽  
M. Carmen Alvarez-Castro ◽  
Pascal Yiou
Keyword(s):  
Phase Space ◽  
Sea Level ◽  
Northern Hemisphere ◽  
Atmospheric Dynamics ◽  
Complex Nature ◽  
Human Welfare ◽  
Sea Level Pressure ◽  
Level Pressure ◽  
Dimensional Phase Space ◽  
Dynamical Properties

Abstract. Atmospheric dynamics are described by a set of partial differential equations yielding an infinite-dimensional phase space. However, the actual trajectories followed by the system appear to be constrained to a finite-dimensional phase space, i.e. a strange attractor. The dynamical properties of this attractor are difficult to determine due to the complex nature of atmospheric motions. A first step to simplify the problem is to focus on observables which affect – or are linked to phenomena which affect – human welfare and activities, such as sea-level pressure, 2 m temperature, and precipitation frequency. We make use of recent advances in dynamical systems theory to estimate two instantaneous dynamical properties of the above fields for the Northern Hemisphere: local dimension and persistence. We then use these metrics to characterize the seasonality of the different fields and their interplay. We further analyse the large-scale anomaly patterns corresponding to phase-space extremes – namely time steps at which the fields display extremes in their instantaneous dynamical properties. The analysis is based on the NCEP/NCAR reanalysis data, over the period 1948–2013. The results show that (i) despite the high dimensionality of atmospheric dynamics, the Northern Hemisphere sea-level pressure and temperature fields can on average be described by roughly 20 degrees of freedom; (ii) the precipitation field has a higher dimensionality; and (iii) the seasonal forcing modulates the variability of the dynamical indicators and affects the occurrence of phase-space extremes. We further identify a number of robust correlations between the dynamical properties of the different variables.

Superconductivity and the existence of Nambu's three-dimensional phase space mechanics

1984 ◽  
Vol 104 (2) ◽  
pp. 106-108 ◽  
Author(s):  
Reinaldo Angulo ◽  
Simón Codriansky ◽  
Carlos A. Gonzalez-Bernardo ◽  
Andrés J. Kalnay ◽  
Freddy Perez-M ◽  
...  
Keyword(s):  
Phase Space ◽  
Three Dimensional ◽  
Dimensional Phase Space ◽  
Space Mechanics

scholarly journals Constraining cluster masses from the stacked phase space distribution at large radii

2019 ◽  
Vol 489 (1) ◽  
pp. 1344-1356
Author(s):  
Akinari Hamabata ◽  
Masamune Oguri ◽  
Takahiro Nishimichi
Keyword(s):  
Phase Space ◽  
Three Dimensional ◽  
Space Distribution ◽  
Line Of Sight ◽  
Mass Dependence ◽  
Mass Measurements ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
Transverse Distance ◽  
Hubble Flow

Abstract Velocity dispersions have been employed as a method to measure masses of clusters. To complement this conventional method, we explore the possibility of constraining cluster masses from the stacked phase space distribution of galaxies at larger radii, where infall velocities are expected to have a sensitivity to cluster masses. First, we construct a two-component model of the three-dimensional phase space distribution of haloes surrounding clusters up to 50 $\, h^{-1}$ Mpc from cluster centres based on N-body simulations. We confirm that the three-dimensional phase space distribution shows a clear cluster mass dependence up to the largest scale examined. We then calculate the probability distribution function of pairwise line-of-sight velocities between clusters and haloes by projecting the three-dimensional phase space distribution along the line of sight with the effect of the Hubble flow. We find that this projected phase space distribution, which can directly be compared with observations, shows a complex mass dependence due to the interplay between infall velocities and the Hubble flow. Using this model, we estimate the accuracy of dynamical mass measurements from the projected phase space distribution at the transverse distance from cluster centres larger than $2\, h^{-1}$ Mpc. We estimate that, by using 1.5 × 105 spectroscopic galaxies, we can constrain the mean cluster masses with an accuracy of 14.5 per cent if we fully take account of the systematic error coming from the inaccuracy of our model. This can be improved down to 5.7 per cent by improving the accuracy of the model.

scholarly journals Time evolution of companies towards a stable scaling curve obtained from flow diagrams in three-dimensional phase space

2019 ◽  
Vol 21 (4) ◽  
pp. 043038
Author(s):  
Yuh Kobayashi ◽  
Hideki Takayasu ◽  
Shlomo Havlin ◽  
Misako Takayasu
Keyword(s):  
Phase Space ◽  
Time Evolution ◽  
Three Dimensional ◽  
Dimensional Phase Space ◽  
Flow Diagrams

scholarly journals CANONICAL TRANSFORMATIONS IN THREE-DIMENSIONAL PHASE-SPACE

2009 ◽  
Vol 24 (25n26) ◽  
pp. 4769-4788 ◽  
Author(s):  
TEKİN DERELİ ◽  
ADNAN TEĞMEN ◽  
TUĞRUL HAKİOĞLU
Keyword(s):  
Phase Space ◽  
Canonical Transformation ◽  
Generating Functions ◽  
General Framework ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Canonical Transformations ◽  
Dimensional Phase Space ◽  
Nambu Bracket ◽  
Definition Of

Canonical transformation in a three-dimensional phase-space endowed with Nambu bracket is discussed in a general framework. Definition of the canonical transformations is constructed based on canonoid transformations. It is shown that generating functions, transformed Hamilton functions and the transformation itself for given generating functions can be determined by solving Pfaffian differential equations corresponding to that quantities. Types of the generating functions are introduced and all of them are listed. Infinitesimal canonical transformations are also discussed. Finally, we show that the decomposition of canonical transformations is also possible in three-dimensional phase space as in the usual two-dimensional one.

scholarly journals Features of pulsed synchronization of an autooscillatory system with a three-dimensional phase space

2006 ◽  
Vol 32 (4) ◽  
pp. 343-346 ◽  
Author(s):  
A. P. Kuznetsov ◽  
N. V. Stankevich ◽  
L. V. Tyuryukina
Keyword(s):  
Phase Space ◽  
Three Dimensional ◽  
Dimensional Phase Space

THE 2-D SEXTIC HAMILTONIAN OSCILLATOR

2013 ◽  
Vol 23 (06) ◽  
pp. 1330019
Author(s):  
F. J. MOLERO ◽  
J. C. VAN DER MEER ◽  
S. FERRER ◽  
F. J. CÉSPEDES
Keyword(s):  
Phase Space ◽  
Elliptic Functions ◽  
Singular Values ◽  
Nonlinear Oscillators ◽  
Momentum Mapping ◽  
Dimensional Model ◽  
Integrable Hamiltonian Systems ◽  
One Dimensional ◽  
Dimensional Phase Space ◽  
The One

The 2-D sextic oscillator is studied as a family of axial symmetric parametric integrable Hamiltonian systems, presenting a bifurcation analysis of the different flows. It includes the "elliptic core" model in 1-D nonlinear oscillators, recently proposed in the literature. We make use of the energy-momentum mapping, which will give us the fundamental fibration of the four-dimensional phase space. Special attention is given to the singular values of the energy-momentum mapping connected with rectilinear and circular orbits. They are related to the saddle-center and pitchfork scenarios with the associated homoclinic and heteroclinic trajectories. We also study how the geometry of the phase space evolves during the transition from the one-dimensional to the two-dimensional model. Within an elliptic function approach, the solutions are given using Legendre elliptic integrals of the first and third kind and the corresponding Jacobi elliptic functions.

On the mean motion induced by internal gravity waves

1969 ◽  
Vol 36 (4) ◽  
pp. 785-803 ◽  
Author(s):  
Francis P. Bretherton
Keyword(s):  
Gravity Waves ◽  
Wave Energy ◽  
Wave Train ◽  
Three Dimensional ◽  
Internal Gravity Waves ◽  
Wave Number ◽  
Mean Flow ◽  
Mean Velocity ◽  
Mean Motion ◽  
The Mean

A train of internal gravity waves in a stratified liquid exerts a stress on the liquid and induces changes in the mean motion of second order in the wave amplitude. In those circumstances in which the concept of a slowly varying quasi-sinusoidal wave train is consistent, the mean velocity is almost horizontal and is determined to a first approximation irrespective of the vertical forces exerted by the waves. The sum of the mean flow kinetic energy and the wave energy is then conserved. The circulation around a horizontal circuit moving with the mean velocity is increased in the presence of waves according to a simple formula. The flow pattern is obtained around two- and three-dimensional wave packets propagating into a liquid at rest and the results are generalized for any basic state of motion in which the internal Froude number is small. Momentum can be associated with a wave packet equal to the horizontal wave-number times the wave energy divided by the intrinsic frequency.

scholarly journals Upper tropospheric energetics of standing eddies In wave number domain during contrasting Monsoon activity over India

MAUSAM ◽  
2021 ◽  
Vol 43 (4) ◽  
pp. 403-410
Author(s):  
S.S. BAWISKAR ◽  
S.M. SINGH
Keyword(s):  
Energy Source ◽  
Kinetic Energy ◽  
Interaction Analysis ◽  
Standing Waves ◽  
Wave Interaction ◽  
Wave Number ◽  
Mean Flow ◽  
S Wave ◽  
Flow Interaction ◽  
Energy Equations

The upper tropospheric energetics of the standing eddies in wave number domain during contrasting monsoon' activity over India have been investigated. Two normal monsoon years (1970. 1971) and two drought monsoon years (1972, 1979) are considered for a comparative study, Energy equations of Saltzman (1957) are used to compute wave-wave Interaction and wave to zonal mean flow Interaction. Analysis of the results show that the standing eddies in the region of tropical easterlies (5°S-24 .2°N) have larger kinetic energy than those in the region of southern hemispheric, westerlies (24.2°S-5°S). Wave to zonal mean flow interaction of all waves (waves 1-15) Indicate that the standing eddies are a source of kinetic energy to zonal mean flow ID the region of easterlies and there sink of kinetic energy to zonal mean flow in the region of westerlies. In the region of easterlies planetary standing waves (waves 1-2) are the major kinetic energy source to other standing waves and wave-wave Interaction of all waves leads to positive Imbalance of kinetic energy during normal monsoon years (1970, 1971) and negative imbalance, of kinetic, energy during drought monsoon years (1972, 19~9). In the region of westerlies the imbalance of kinetic energy IS negative during normal monsoon years and positive during drought monsoon years.

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