Diagnosing diabatic effects on the available energy of stratified flows in inertial and non-inertial frames

2018 ◽  
Vol 861 ◽  
pp. 608-642 ◽  
Author(s):  
Alberto Scotti ◽  
Pierre-Yves Passaggia
Keyword(s):  
Potential Vorticity ◽  
Ground State ◽  
Initial Distribution ◽  
Point Of View ◽  
Stratified Flows ◽  
Hamiltonian Density ◽  
Available Energy ◽  
Inertial Frames ◽  
Gauge Fixing ◽  
Diabatic Processes

The concept of available energy in a stratified fluid is revisited from the point of view of non-canonical Hamiltonian systems. We show that the concept of available energy arises when we minimize the energy subject to the constraints associated with the existence of Lagrangian invariants. The non-canonical structure implies that there exists a class of dynamically equivalent Hamiltonians, related by a local (in phase space) gauge symmetry. A local diagnostic energy can be defined via the Hamiltonian density chosen imposing a specific gauge-fixing condition on the class of dynamically similar Hamiltonians. The gauge-fixing condition that we introduce selects a specific local diagnostic energy which is well suited to study the effect of diabatic processes on the evolution of the available energy. Non-inertial effects, which are notoriously elusive to capture within an energetic framework, are naturally included via conservation of potential vorticity. We apply the framework to stratified flows in inertial and non-inertial frames. For stratified Boussinesq flows, when the initial distribution of potential vorticity is even around the origin, our framework recovers the available potential energy introduced by Holliday & McIntyre (J. Fluid Mech., vol. 107, 1981, pp. 221–225), and as such, depends only on the mass distribution of the flow. In rotating flows, the isopycnals of the ground state are generally not flat, and the ground state may have kinetic energy. We finally demonstrate that flows in non-inertial frames characterized by a low Rossby number ($Ro$), the local diagnostic energy has, to lowest order in $Ro$, a universal character.

Ground state molecular parameters of phosphine, PH3, from the simultaneous analysis of the high-resolution infrared, microwave and submillimeterwave spectra

1985 ◽  
Vol 50 (11) ◽  
pp. 2480-2492 ◽  
Author(s):  
Soňa Přádná ◽  
Dušan Papoušek ◽  
Jyrki Kauppinen ◽  
Sergei P. Belov ◽  
Andrei F. Krupnov ◽  
...  
Keyword(s):  
Fourier Transform ◽  
High Resolution ◽  
Ground State ◽  
Unitary Transformation ◽  
Point Of View ◽  
Acoustic Detection ◽  
Molecular Parameters ◽  
Microwave Spectrometer ◽  
Fourier Transform Spectra ◽  
First Time

Fourier transform spectra of the ν2 band of PH3 have been remeasured with 0.0045 cm-1 resolution. Ground state combination differences from these data have been fitted simultaneously with the microwave and submillimeterwave data to determine the ground state spectroscopical parameters of PH3 including the parameters of the Δk = ± 3n interactions. The correlation between the latter parameters has been discussed from the point of view of the existence of two equivalent effective rotational operators which are related by a unitary transformation. The ΔJ = 0, +1, ΔK = 0 (A1 ↔ A2, E ↔ E) rotational transitions in the ν2 and ν4 states have been measured for the first time by using a microwave spectrometer and a radiofrequency spectrometer with acoustic detection.

scholarly journals Lorentz Boosts and Wigner Rotations: Self-Adjoint Complexified Quaternions

Physics ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 352-366
Author(s):  
Thomas Berry ◽  
Matt Visser
Keyword(s):  
Point Of View ◽  
Sufficient Condition ◽  
Use Of Self ◽  
Necessary And Sufficient Condition ◽  
Wigner Rotation ◽  
Inertial Frames ◽  
Explicit Formulae ◽  
Specific Implementation ◽  
Necessary And Sufficient ◽  
Lorentz Boosts

In this paper, Lorentz boosts and Wigner rotations are considered from a (complexified) quaternionic point of view. It is demonstrated that, for a suitably defined self-adjoint complex quaternionic 4-velocity, pure Lorentz boosts can be phrased in terms of the quaternion square root of the relative 4-velocity connecting the two inertial frames. Straightforward computations then lead to quite explicit and relatively simple algebraic formulae for the composition of 4-velocities and the Wigner angle. The Wigner rotation is subsequently related to the generic non-associativity of the composition of three 4-velocities, and a necessary and sufficient condition is developed for the associativity to hold. Finally, the authors relate the composition of 4-velocities to a specific implementation of the Baker–Campbell–Hausdorff theorem. As compared to ordinary 4×4 Lorentz transformations, the use of self-adjoint complexified quaternions leads, from a computational view, to storage savings and more rapid computations, and from a pedagogical view to to relatively simple and explicit formulae.

scholarly journals Potential Vorticity Diagnostics to Quantify Effects of Latent Heating in Extratropical Cyclones. Part I: Methodology

2017 ◽  
Vol 74 (11) ◽  
pp. 3567-3590 ◽  
Author(s):  
Dominik Büeler ◽  
Stephan Pfahl
Keyword(s):  
Potential Vorticity ◽  
Weather Prediction ◽  
Baroclinic Instability ◽  
Numerical Weather Prediction Model ◽  
Cloud Formation ◽  
Extratropical Cyclones ◽  
Latent Heating ◽  
Strongly Coupled ◽  
Cyclone Intensity ◽  
Diabatic Processes

Abstract Extratropical cyclones develop because of baroclinic instability, but their intensification is often substantially amplified by diabatic processes, most importantly, latent heating (LH) through cloud formation. Although this amplification is well understood for individual cyclones, there is still need for a systematic and quantitative investigation of how LH affects cyclone intensification in different, particularly warmer and moister, climates. For this purpose, the authors introduce a simple diagnostic to quantify the contribution of LH to cyclone intensification within the potential vorticity (PV) framework. The two leading terms in the PV tendency equation, diabatic PV modification and vertical advection, are used to derive a diagnostic equation to explicitly calculate the fraction of a cyclone’s positive lower-tropospheric PV anomaly caused by LH. The strength of this anomaly is strongly coupled to cyclone intensity and the associated impacts in terms of surface weather. To evaluate the performance of the diagnostic, sensitivity simulations of 12 Northern Hemisphere cyclones with artificially modified LH are carried out with a numerical weather prediction model. Based on these simulations, it is demonstrated that the PV diagnostic captures the mean sensitivity of the cyclones’ PV structure to LH as well as parts of the strong case-to-case variability. The simple and versatile PV diagnostic will be the basis for future climatological studies of LH effects on cyclone intensification.

HAMILTONIAN THEORY OF THE RELATIVISTIC STRING

1990 ◽  
Vol 02 (03) ◽  
pp. 355-398 ◽  
Author(s):  
G.P. Pron’ko
Keyword(s):  
String Theory ◽  
Spectral Problem ◽  
Dimensional Space ◽  
Space Time ◽  
Point Of View ◽  
Relativistic String ◽  
Hamiltonian Theory ◽  
Gauge Fixing ◽  
Dimensional Space Time ◽  
Invariant Gauge

The relativistic string theory is considered from the Hamiltonian point of view. It is proposed to formulate the dynamics of string in d-dimensional space-time with the help of the auxiliary spectral problem. This approach gives the possibility to construct a completely new set of variables of string relevant for Lorentz-invariant gauge fixing. The notion of smooth string is introduced for which the successive relativistic invariant quantization could be done explicitly for the d=4 case.

The Twin Paradox

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
High Speed ◽  
Point Of View ◽  
Introductory Physics ◽  
Twin Paradox ◽  
Classic Problem ◽  
Galilean Relativity ◽  
Inertial Frames ◽  
Cognitive Overload ◽  
Spacetime Diagram ◽  
Thinking Tools

To prepare for the high‐speed world where Galilean relativity breaks down, we now practice the skill of thinking in different frames. Practicing this in our familiar lowspeed world will help us avoid cognitive overload when we enter the more counterintuitive high‐speed world. We examine two problems that illustrate the process of thinking in different frames. Te frst is a brain‐teaser that suddenly becomes easier in a particular frame; the second is a classic problem from introductory physics that we can solve in a new way using symmetry and frame-based thinking tools alone. Along the way, we will learn how to use the spacetime diagram, a major tool that will appear throughout this book. Te chapter concludes with another look at accelerated vs. inertial frames, from the spacetime diagram point of view.

EQUIVALENCE OF THE LAGRANGIAN AND HAMILTONIAN BRST CHARGES FOR THE BOSONIC STRING IN THE HARMONIC AND CONFORMAL GAUGES

1988 ◽  
Vol 03 (05) ◽  
pp. 1081-1101 ◽  
Author(s):  
V. DEL DUCA ◽  
L. MAGNEA ◽  
P. VAN NIEUWENHUIZEN
Keyword(s):  
Phase Space ◽  
Equations Of Motion ◽  
Hamiltonian Formulation ◽  
Point Of View ◽  
Bosonic String ◽  
Lagrangian Formalism ◽  
Brst Charge ◽  
Gauge Fixing ◽  
Conformal Gauge ◽  
Brst Invariance

We consider the BRST formalism for the bosonic string in arbitrary gauges, both from the Hamiltonian and from the Lagrangian point of view. In the Hamiltonian formulation we construct the BRST charge Q(H) following the Batalin-Fradkin-Fradkina-Vilkovisky (BFFV) formalism in phase space. In the Lagrangian formalism, we use the Noether procedure to construct the BRST charge Q(L) in configuration space. We then discuss how to go from configuration to phase space and demonstrate that the dependence of Q(L) on the gauge fixing disappears and that both charges become equal. We work through two gauges in detail: the conformal gauge and the de Donder (harmonic) gauge. In the conformal gauge one must use equations of motion, and a simple canonical transformation is found which exhibits the equivalence. In the de Donder gauge, nontrivial canonical transformations are needed. Our results overlap with work by Beaulieu, Siegel and Zwiebach on the de Donder gauge, but since we only require BRST invariance and not anti-BRST invariance, we need simpler field redefinitions; moreover, we stay off-shell.

A variational derivation of the geostrophic momentum approximation

2014 ◽  
Vol 751 ◽  
Author(s):  
Marcel Oliver
Keyword(s):  
Shallow Water ◽  
Potential Vorticity ◽  
Point Of View ◽  
Order Operator ◽  
Coriolis Parameter ◽  
First Order ◽  
Slow Part ◽  
Momentum Approximation ◽  
Balanced Dynamics ◽  
Spatially Varying

AbstractThis paper demonstrates that the shallow water semigeostrophic equations arise from a degenerate second-order Hamilton principle of very special structure. The associated Euler–Lagrange operator factors into a fast and a slow first-order operator; restricting to the slow part yields the geostrophic momentum approximation as balanced dynamics. While semigeostrophic theory has been considered variationally before, this structure appears to be new. It leads to a straightforward derivation of the geostrophic momentum approximation and its associated potential vorticity law. Our observations further affirm, from a different point of view, the known difficulty in generalizing the semigeostrophic equations to the case of a spatially varying Coriolis parameter.

scholarly journals The Game of Poker Chips, Dominoes and Survival

2021 ◽  
Vol 8 (14) ◽  
pp. 91-104
Author(s):  
Larry Goldstein
Keyword(s):  
Team Building ◽  
Management Training ◽  
Initial Distribution ◽  
Point Of View ◽  
Discrete Mathematics ◽  
Entire Group ◽  
Group Survival ◽  
Group Members ◽  
High Level ◽  
Training Exercises

Abstract The Game of Poker Chips, Dominoes and Survival fosters team building and high level cooperation in large groups, and is a tool applied in management training exercises. Each player, initially given two colored poker chips, is allowed to make exchanges with the game coordinator according to two rules, and must secure a domino before time is called in order to ‘survive’. Though the rules are simple, it is not evident by their form that the survival of the entire group requires that they cooperate at a high level. From the point of view of the game coordinator, the di culty of the game for the group can be controlled not only by the time limit, but also by the initial distribution of chips, in a way we make precise by a time complexity type argument. That analysis also provides insight into good strategies for group survival, those taking the least amount of time. In addition, coordinators may also want to be aware of when the game is ‘solvable’, that is, when their initial distribution of chips permits the survival of all group members if given su cient time to make exchanges. It turns out that the game is solvable if and only if the initial distribution contains seven chips that have one of two particular color distributions. In addition to being a lively game to play in management training or classroom settings, the analysis of the game after play can make for an engaging exercise in any discrete mathematics course to give a basic introduction to elements of game theory, logical reasoning, number theory and the computation of algorithmic complexities.

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