scholarly journals Interactions between Rotation and Pulsation

2004 ◽  
Vol 215 ◽  
pp. 404-413
Author(s):  
Rich Townsend
Keyword(s):  
Angular Momentum ◽  
Coriolis Force ◽  
Rossby Waves ◽  
Narrow Band ◽  
Rotating Stars ◽  
Stellar Rotation ◽  
Coriolis Forces ◽  
Wave Dynamics ◽  
Propagating Waves ◽  
Physical Principles

In this contribution, I will examine the interaction between stellar rotation and pulsation. I begin with a brief review of the non-rotating case, emphasizing the character of pulsations as azimuthally-propagating waves. I then go on to discuss how these waves are modified under the influence of the centrifugal and Coriolis forces. Through simple arguments, I outline the conditions under which each force can become significant in determining the wave dynamics. Particular attention is paid to the Coriolis force, since it is responsible for the formation of a waveguide, which confines the pulsation to a narrow band centered on the stellar equator. Using the example of a prograde sectoral pulsation mode, I explain the basic physical principles underlying this trapping.The Coriolis force is also responsible for the existence of Rossby waves, which are not found in non-rotating stars. I demonstrate how these waves may be understood in terms of a conservation law for angular momentum, and review their most important characteristics. I then examine how rotation modifies the frequencies of pulsation, and explain how observations of such modifications can provide information regarding a star's rotation rate. To conclude, I focus on the converse of the pulsation-rotation interaction: how the transport of angular momentum by pulsation might be important in determining the evolution of a star's rotation profile.

scholarly journals Instability of coupled gravity-inertial-Rossby waves on a β-plane in solar system atmospheres

2009 ◽  
Vol 27 (11) ◽  
pp. 4221-4227 ◽  
Author(s):  
J. F. McKenzie
Keyword(s):  
Rossby Waves ◽  
Narrow Band ◽  
Boussinesq Approximation ◽  
The Other ◽  
The Earth ◽  
Propagating Waves ◽  
Inertial Wave ◽  
The One ◽  
Fifth Order ◽  
Critical Latitude

Abstract. This paper provides an analysis of the combined theory of gravity-inertial-Rossby waves on a β-plane in the Boussinesq approximation. The wave equation for the system is fifth order in space and time and demonstrates how gravity-inertial waves on the one hand are coupled to Rossby waves on the other through the combined effects of β, the stratification characterized by the Väisälä-Brunt frequency N, the Coriolis frequency f at a given latitude, and vertical propagation which permits buoyancy modes to interact with westward propagating Rossby waves. The corresponding dispersion equation shows that the frequency of a westward propagating gravity-inertial wave is reduced by the coupling, whereas the frequency of a Rossby wave is increased. If the coupling is sufficiently strong these two modes coalesce giving rise to an instability. The instability condition translates into a curve of critical latitude Θc versus effective equatorial rotational Mach number M, with the region below this curve exhibiting instability. "Supersonic" fast rotators are unstable in a narrow band of latitudes around the equator. For example Θc~12° for Jupiter. On the other hand slow "subsonic" rotators (e.g. Mercury, Venus and the Sun's Corona) are unstable at all latitudes except very close to the poles where the β effect vanishes. "Transonic" rotators, such as the Earth and Mars, exhibit instability within latitudes of 34° and 39°, respectively, around the Equator. Similar results pertain to Oceans. In the case of an Earth's Ocean of depth 4km say, purely westward propagating waves are unstable up to 26° about the Equator. The nonlinear evolution of this instability which feeds off rotational energy and gravitational buoyancy may play an important role in atmospheric dynamics.

scholarly journals Testing models of rotating stars

2010 ◽  
Vol 6 (S272) ◽  
pp. 73-78
Author(s):  
Adrian T. Potter ◽  
Christopher A. Tout
Keyword(s):  
Angular Momentum ◽  
Stellar Evolution ◽  
Momentum Transport ◽  
Rotating Stars ◽  
Stellar Rotation ◽  
Rapid Rotation ◽  
Angular Momentum Transport ◽  
Free Parameters ◽  
Stellar Models ◽  
The Many

AbstractThe effects of rapid rotation on stellar evolution can be profound but we are only now starting to gather the data necessary to adequately determine the validity of the many proposed models of rotating stars. Some aspects of stellar rotation, particularly the treatment of angular momentum transport within convective zones, still remain very poorly explored. Distinguishing between different models is made difficult by the typically large number of free parameters in models compared with the amount of available data. This also makes it difficult to determine whether increasing the complexity of a model actually results in a better reflection of reality. We present a new code to straightforwardly compare different rotating stellar models using otherwise identical input physics. We use it to compare several models with different treatments for the transport of angular momentum within convective zones.

scholarly journals The Rotation of Low-Mass Pre-Main-Sequence Stars

2004 ◽  
Vol 215 ◽  
pp. 113-122 ◽  
Author(s):  
Robert D. Mathieu
Keyword(s):  
Angular Momentum ◽  
Main Sequence ◽  
Rotation Period ◽  
Rotating Stars ◽  
Stellar Rotation ◽  
Main Sequence Stars ◽  
Star Forming ◽  
Rotation Periods ◽  
Order Of Magnitude ◽  
Critical Velocities

Major photometric monitoring campaigns of star-forming regions in the past decade have provided rich rotation period distributions of pre-main-sequence stars. The rotation periods span more than an order of magnitude in period, with most falling between 1 and 10 days. Thus the broad rotation period distributions found in 100 Myr clusters are already established by an age of 1 Myr. The most rapidly rotating stars are within a factor of 2-3 of their critical velocities; if angular momentum is conserved as they evolve to the ZAMS, these stars may come to exceed their critical velocities. Extensive efforts have been made to find connections between stellar rotation and the presence of protostellar disks; at best only a weak correlation has been found in the largest samples. Magnetic disk-locking is a theoretically attractive mechanism for angular momentum evolution of young stars, but the links between theoretical predictions and observational evidence remain ambiguous. Detailed observational and theoretical studies of the magnetospheric environments will provide better insight into the processes of pre-main-sequence stellar angular momentum evolution.

scholarly journals Forced Nonradial Oscillations in Early-Type Rotating Stars

2000 ◽  
Vol 176 ◽  
pp. 376-376
Author(s):  
M. G. Witte ◽  
G. J. Savonije
Keyword(s):  
Gravitational Force ◽  
Rotation Speed ◽  
Internal Damping ◽  
Rotating Stars ◽  
Stellar Rotation ◽  
Stellar Spectrum ◽  
Coriolis Forces ◽  
Nonradial Oscillation ◽  
External Driving ◽  
Nonradial Oscillations

A method of calculating nonradial oscillations in rotating stars is presented. Using this method, we are able to calculate the spectrum of g-, f- and p-mode eigenfunctions of a star for different stellar rotation speeds, and also the spectrum of rotational r modes. Stability of the modes as a function of stellar rotation speed can be investigated. By regarding the response of a star which undergoes periodic deformations due to the gravitational force of an orbiting companion as a forced nonradial oscillation, the problem of determining the eigenfrequencies of the star becomes one of finding resonances with the forcing potential. Expanding the potential of the orbiting (point mass) companion in terms of the usual spherical functions, the response of the star to each tidal term , with l and m fixed, can be calculated separately. By varying the forcing frequency σ we are then able to calculate the stellar spectrum. To calculate the response of the star we numerically solve the fully non-adiabatic, but linearised hydrodynamical equations for the star, in which the Coriolis forces due to stellar rotation are fully taken into account. To this end we utilise an implicit 2D finite difference scheme which solves the equations on an (r, ϑ) grid. A calculated solution describes the steady state in which the power σT due to the external driving force is in equilibrium with the internal damping. For results and more references see Witte & Savonije (1999).

scholarly journals Inertial Forces Acting on a Propeller of Aircraft

2018 ◽  
Vol 7 (1) ◽  
pp. 1-13
Author(s):  
R. Usubamatov ◽  
T. Zhumaev
Keyword(s):  
Angular Momentum ◽  
Mathematical Models ◽  
Inertial Forces ◽  
Aerospace Vehicles ◽  
Coriolis Forces ◽  
Rotating Blades ◽  
Variable Resistance ◽  
Combined Action ◽  
The Masses ◽  
Physical Principles

Background:Aerospace vehicles use propellers with the different design that possess gyroscopic properties. Recent investigations in the area of gyroscope theory have demonstrated that the gyroscope properties are based on the action of the centrifugal, common inertial, and Coriolis forces of the distributed mass elements of the spinning rotor, as well as the change in the angular momentum.Objective:The combined action of the interrelated inertial forces on the propellers presents the interests for the design of the blades. The objective of the manuscript is the derivation of mathematical models for the inertial torques acting on the spinning propellers that enable computing the stresses of the blades and increasing their reliability.Method:The inertial torques generated by the masses of the rotating blades acting on the propellers are represented by mathematical models in L. Euler’s form.Results:The inertial torques are generated by the several inertial forces of the propeller’s blades and hub and manifested the fluctuation of the variable resistance and precession torques acting around different axes of the propeller. Derived mathematical models for the inertial torques are new and should be used for the computing forces and stresses acting on the propellers of the aircraft.Conclusion:The mathematical models for the torques acting on the propellers consider the several inertial forces of the rotating masses that manifest their gyroscope properties. Derived mathematical models for inertial torques enable for computing the stresses of the aircraft propellers and clearly demonstrate the physical principles and origin of the acting inertial forces.

scholarly journals Nuclear burning in collapsar accretion discs

2020 ◽  
Vol 499 (3) ◽  
pp. 4097-4113 ◽  
Author(s):  
Yossef Zenati ◽  
Daniel M Siegel ◽  
Brian D Metzger ◽  
Hagai B Perets
Keyword(s):  
Angular Momentum ◽  
Gamma Ray ◽  
Nuclear Reactions ◽  
Reaction Network ◽  
Accretion Discs ◽  
Late Time ◽  
Rotating Stars ◽  
Stellar Envelope ◽  
Nuclear Burning ◽  
R Process

ABSTRACT The core collapse of massive, rapidly-rotating stars are thought to be the progenitors of long-duration gamma-ray bursts (GRB) and their associated hyperenergetic supernovae (SNe). At early times after the collapse, relatively low angular momentum material from the infalling stellar envelope will circularize into an accretion disc located just outside the black hole horizon, resulting in high accretion rates necessary to power a GRB jet. Temperatures in the disc mid-plane at these small radii are sufficiently high to dissociate nuclei, while outflows from the disc can be neutron-rich and may synthesize r-process nuclei. However, at later times, and for high progenitor angular momentum, the outer layers of the stellar envelope can circularize at larger radii ≳ 107 cm, where nuclear reactions can take place in the disc mid-plane (e.g. 4He + 16O → 20Ne + γ). Here we explore the effects of nuclear burning on collapsar accretion discs and their outflows by means of hydrodynamical α-viscosity torus simulations coupled to a 19-isotope nuclear reaction network, which are designed to mimic the late infall epochs in collapsar evolution when the viscous time of the torus has become comparable to the envelope fall-back time. Our results address several key questions, such as the conditions for quiescent burning and accretion versus detonation and the generation of 56Ni in disc outflows, which we show could contribute significantly to powering GRB SNe. Being located in the slowest, innermost layers of the ejecta, the latter could provide the radioactive heating source necessary to make the spectral signatures of r-process elements visible in late-time GRB-SNe spectra.

scholarly journals Rossby Waves in Astrophysics

2021 ◽  
Vol 217 (1) ◽  
Author(s):  
T. V. Zaqarashvili ◽  
M. Albekioni ◽  
J. L. Ballester ◽  
Y. Bekki ◽  
L. Biancofiore ◽  
...  
Keyword(s):  
Large Scale ◽  
Rossby Waves ◽  
Magnetic Activity ◽  
Future Research ◽  
Rotating Stars ◽  
Spatial And Temporal Scales ◽  
Physical Role ◽  
Astrophysical Objects ◽  
Exoplanetary Atmospheres ◽  
Rapidly Rotating Stars

AbstractRossby waves are a pervasive feature of the large-scale motions of the Earth’s atmosphere and oceans. These waves (also known as planetary waves and r-modes) also play an important role in the large-scale dynamics of different astrophysical objects such as the solar atmosphere and interior, astrophysical discs, rapidly rotating stars, planetary and exoplanetary atmospheres. This paper provides a review of theoretical and observational aspects of Rossby waves on different spatial and temporal scales in various astrophysical settings. The physical role played by Rossby-type waves and associated instabilities is discussed in the context of solar and stellar magnetic activity, angular momentum transport in astrophysical discs, planet formation, and other astrophysical processes. Possible directions of future research in theoretical and observational aspects of astrophysical Rossby waves are outlined.

scholarly journals The concept of creating thrust based on angular momentum change

2021 ◽  
Author(s):  
Sergei Kupreev
Keyword(s):  
Angular Momentum ◽  
Vacuum Chamber ◽  
Loop Quantum Gravity ◽  
Low Energy ◽  
Practical Implementation ◽  
Material Body ◽  
The World ◽  
Classical And Quantum Mechanics ◽  
Physical Principles ◽  
Kinetic Moment

Abstract The change in the kinetic moment of a material body is considered regarding to classical and quantum mechanics. The possibility of creating the propulsion system in terms of energy efficiency exceeding the photon engine has been theoretically proved. The proposed new principle of motion is based on the law of conservation of angular momentum and is fully consistent with the basic fundamental laws of physics. It is proposed to use the emission/absorption of streams of low-energy particles with spin in the direction perpendicular to the movement of the material body. The practical implementation of this idea is confirmed by the presence of promising approaches to solving the problem of quantizing gravity (string theory, loop quantum gravity, etc.) recognized by the world scientific community and by the successful results of experiments conducted by the authors with the motion of bodies in a vacuum chamber. The proposed idea, the examples and experiments has given grounds for the formation of new physical concepts of the speed, mass and inertia of bodies. The obtained results can be used in experiments to search for elementary particles with low energy, to explain a number of physics phenomena and to develop transport of objects based on new physical principles.

scholarly journals Zonal Momentum Balance in the Tropical Atmospheric Circulation during the Global Monsoon Mature Months

2013 ◽  
Vol 70 (2) ◽  
pp. 583-599 ◽  
Author(s):  
Wenchang Yang ◽  
Richard Seager ◽  
Mark A. Cane
Keyword(s):  
Angular Momentum ◽  
Pressure Gradient ◽  
Atmospheric Circulation ◽  
Coriolis Force ◽  
Gradient Force ◽  
Pressure Gradient Force ◽  
Global Monsoon ◽  
Upper Troposphere ◽  
Nonlinear Advection ◽  
Zonal Momentum

Abstract In this paper, zonal momentum balances of the tropical atmospheric circulation during the global monsoon mature months (January and July) are analyzed in three dimensions based on the ECMWF Interim Re-Analysis (ERA-Interim). It is found that the dominant terms in the balance of the atmospheric boundary layer (ABL) in both months are the pressure gradient force, the Coriolis force, and friction. The nonlinear advection term plays a significant role only in the Asian summer monsoon regions within the ABL. In the upper troposphere, the pressure gradient force, the Coriolis force, and the nonlinear advection are the dominant terms. The transient eddy force and the residual force (which can be explained as convective momentum transfer over open oceans) are secondary, yet cannot be neglected near the equator. Zonal-mean equatorial upper-troposphere easterlies are maintained by the absolute angular momentum advection associated with the cross-equatorial Hadley circulation. Equatorial upper-troposphere easterlies over the Asian monsoon regions are also controlled by the absolute angular momentum advection but are mainly maintained by the pressure gradient force in January. The equivalent linear Rayleigh friction, which is widely applied in simple tropical models, is calculated and the corresponding spatial distribution of the local coefficient and damping time scale are estimated from the linear regression. It is found that the linear momentum model is in general capable of crudely describing the tropical atmospheric circulation dynamics, yet the caveat should be kept in mind that the friction coefficient is not uniformly distributed and is even negative in some regions.

A Balanced Approximation of the One-Layer Shallow-Water Equations on a Sphere

2009 ◽  
Vol 66 (6) ◽  
pp. 1735-1748 ◽  
Author(s):  
W. T. M. Verkley
Keyword(s):  
Shallow Water ◽  
Potential Vorticity ◽  
Shallow Water Equations ◽  
Rossby Waves ◽  
Coriolis Parameter ◽  
Beta Plane ◽  
Propagating Waves ◽  
Barotropic Vorticity Equation ◽  
Barotropic Vorticity ◽  
The One

Abstract A global version of the equivalent barotropic vorticity equation is derived for the one-layer shallow-water equations on a sphere. The equation has the same form as the corresponding beta plane version, but with one important difference: the stretching (Cressman) term in the expression of the potential vorticity retains its full dependence on f 2, where f is the Coriolis parameter. As a check of the resulting system, the dynamics of linear Rossby waves are considered. It is shown that these waves are rather accurate approximations of the westward-propagating waves of the second class of the original shallow-water equations. It is also concluded that for Rossby waves with short meridional wavelengths the factor f 2 in the stretching term can be replaced by the constant value f02, where f0 is the Coriolis parameter at ±45° latitude.

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