scholarly journals The influence of fast waves and fluctuations on the evolution of the dynamics on the slow manifold

2014 ◽  
Vol 757 ◽  
pp. 155-178 ◽  
Author(s):  
Jared P. Whitehead ◽  
Beth A. Wingate
Keyword(s):  
Energy Transfer ◽  
Kinetic Energy ◽  
Potential Energy ◽  
Slow Manifold ◽  
Slow Potential ◽  
Rapid Rotation ◽  
Reduced Equations ◽  
Triply Periodic ◽  
Fast Waves ◽  
Slow Kinetic

AbstractThe effect of non-slow (typically fast) components of a rotating stratified Boussinesq flow on the dynamics of the slow manifold is quantified using a decomposition that isolates the part of the flow living on the slow manifold. In this system, there are three distinct asymptotic limits with corresponding reduced equations, each defining a slow manifold. All three of these distinct limits, namely rapid rotation, strong stratification, and simultaneous strong stratification and rapid rotation (quasi-geostrophy), are considered. Numerical simulations indicate that, for the geometry considered (triply periodic) and the type of forcing applied, the fluctuations act as a conduit, moving energy onto the slow manifold. This decomposition clarifies how the energy is exchanged when either the stratification or the rotation is weak. In the quasi-geostrophic limit, most of the energy transfer is between slow potential energy and slow kinetic energy, but the energetics due to the fluctuations are less clear. It is observed that the energy off the slow manifold in each case equilibrates to a quasi-steady value.

scholarly journals Rapidly rotating strange stars

2000 ◽  
Vol 177 ◽  
pp. 661-662 ◽  
Author(s):  
D. Gondek-Rosińska ◽  
P. Haensel ◽  
J. L. Zdunik ◽  
E. Gourgoulhon
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Quark Mass ◽  
Strange Quark ◽  
Gravitational Potential Energy ◽  
Rapid Rotation ◽  
Strange Stars ◽  
Absolute Value ◽  
Strange Quark Mass ◽  
Global Parameters

AbstractWe study effects of the strange quark mass,ms, and of the QCD interactions, calculated to lowest order inαc, on the rapid rotation of strange stars (SS). The influence of rotation on global parameters of SS is greater than in the case of the neutron stars (NS). We show that independently ofmsandαcthe ratio of the rotational kinetic energy to the absolute value of the gravitational potential energyT/Wfor a rotating SS is significantly higher than for an ordinary NS. This might indicate that rapidly rotating SS could be important sources of gravitational waves.

MULTI–INERT OSCILLATORY MECHANISM

2020 ◽  
Vol 2 ◽  
pp. 19-25
Author(s):  
I.P. POPOV
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Oscillation Frequency ◽  
Free Oscillation ◽  
Initial Conditions ◽  
Oscillatory System ◽  
Harmonic Oscillations ◽  
Oscillatory Systems ◽  
Oscillatory Mechanism ◽  
Mutual Conversion

A mechanical oscillatory system with homogeneous elements, namely, with n massive loads (multi– inert oscillator), is considered. The possibility of the appearance of free harmonic oscillations of loads in such a system is shown. Unlike the classical spring pendulum, the oscillations of which are due to the mutual conversion of the kinetic energy of the load into the potential energy of the spring, in a multi–inert oscillator, the oscillations are due to the mutual conversion of only the kinetic energies of the goods. In this case, the acceleration of some loads occurs due to the braking of others. A feature of the multi–inert oscillator is that its free oscillation frequency is not fixed and is determined mainly by the initial conditions. This feature can be very useful for technical applications, for example, for self–neutralization of mechanical reactive (inertial) power in oscillatory systems.

Tracker-assisted modelling: simultaneous validation of the conservation law of energy and the work-energy theorem

2021 ◽  
Vol 57 (1) ◽  
pp. 015012
Author(s):  
Unofre B Pili ◽  
Renante R Violanda
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Gravitational Potential ◽  
Conservation Law ◽  
Gravitational Potential Energy ◽  
Time Data ◽  
Home Based ◽  
Basic Physics ◽  
Free Falling ◽  
Work Done

Abstract The video of a free-falling object was analysed in Tracker in order to extract the position and time data. On the basis of these data, the velocity, gravitational potential energy, kinetic energy, and the work done by gravity were obtained. These led to a rather simultaneous validation of the conservation law of energy and the work–energy theorem. The superimposed plots of the kinetic energy, gravitational potential energy, and the total energy as respective functions of time and position demonstrate energy conservation quite well. The same results were observed from the plots of the potential energy against the kinetic energy. On the other hand, the work–energy theorem has emerged from the plot of the total work-done against the change in kinetic energy. Because of the accessibility of the setup, the current work is seen as suitable for a home-based activity, during these times of the pandemic in particular in which online learning has remained to be the format in some countries. With the guidance of a teacher, online or face-to-face, students in their junior or senior high school—as well as for those who are enrolled in basic physics in college—will be able to benefit from this work.

Study of the Mechanisms of Vortex Variability in the Lofoten Basin Based on the Energy Analysis

2021 ◽  
Vol 37 (3) ◽  
Author(s):  
V. S. Travkin ◽  
◽  
T. V. Belonenko ◽  
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Baroclinic Instability ◽  
Positive Trend ◽  
Barotropic Instability ◽  
Available Potential Energy ◽  
Conversion Rates ◽  
Order Of Magnitude ◽  
The Mean ◽  
Mean Kinetic Energy

Purpose. The Lofoten Basin is one of the most energetic zones of the World Ocean characterized by high activity of mesoscale eddies. The study is aimed at analyzing different components of general energy in the basin, namely the mean kinetic and vortex kinetic energy calculated using the integral of the volume of available potential and kinetic energy of the Lofoten Vortex, as well as variability of these characteristics. Methods and Results. GLORYS12V1 reanalysis data for the period 2010–2018 were used. The mean kinetic energy and the eddy kinetic one were analyzed; and as for the Lofoten Vortex, its volume available potential and kinetic energy were studied. The mesoscale activity of eddies in winter is higher than in summer. Evolution of the available potential energy and kinetic energy of the Lofoten Vortex up to the 1000 m horizon was studied. It is shown that the vortex available potential energy exceeds the kinetic one by an order of magnitude, and there is a positive trend with the coefficient 0,23⋅1015 J/year. It was found that in the Lofoten Basin, the intermediate layer from 600 to 900 m made the largest contribution to the potential energy, whereas the 0–400 m layer – to kinetic energy. The conversion rates of the mean kinetic energy into the vortex kinetic one and the mean available potential energy into the vortex available potential one (barotropic and baroclinic instability) were analyzed. It is shown that the first type of transformation dominates in summer, while the second one is characterized by its increase in winter. Conclusions. The vertical profile shows that the kinetic energy of eddies in winter is higher than in summer. The available potential energy of a vortex is by an order of magnitude greater than the kinetic energy. An increase in the available potential energy is confirmed by a significant positive trend and by a decrease in the vortex Burger number. The graphs of the barotropic instability conversion rate demonstrate the multidirectional flows in the vortex zone with the dipole structure observed in a winter period, and the tripole one – in summer. The barotropic instability highest intensity is observed in summer. The baroclinic instability is characterized by intensification of the regime in winter that is associated with weakening of stratification in this period owing to winter convection.

scholarly journals Walking in simulated reduced gravity: mechanical energy fluctuations and exchange

1999 ◽  
Vol 86 (1) ◽  
pp. 383-390 ◽  
Author(s):  
Timothy M. Griffin ◽  
Neil A. Tolani ◽  
Rodger Kram
Keyword(s):  
Kinetic Energy ◽  
Potential Energy ◽  
Gravitational Potential ◽  
Inverted Pendulum ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Metabolic Cost ◽  
Metabolic Energy ◽  
Gravitational Potential Energy ◽  
Reduced Gravity

Walking humans conserve mechanical and, presumably, metabolic energy with an inverted pendulum-like exchange of gravitational potential energy and horizontal kinetic energy. Walking in simulated reduced gravity involves a relatively high metabolic cost, suggesting that the inverted-pendulum mechanism is disrupted because of a mismatch of potential and kinetic energy. We tested this hypothesis by measuring the fluctuations and exchange of mechanical energy of the center of mass at different combinations of velocity and simulated reduced gravity. Subjects walked with smaller fluctuations in horizontal velocity in lower gravity, such that the ratio of horizontal kinetic to gravitational potential energy fluctuations remained constant over a fourfold change in gravity. The amount of exchange, or percent recovery, at 1.00 m/s was not significantly different at 1.00, 0.75, and 0.50 G (average 64.4%), although it decreased to 48% at 0.25 G. As a result, the amount of work performed on the center of mass does not explain the relatively high metabolic cost of walking in simulated reduced gravity.

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