402,355 research outputs found
SPH simulations of turbulence in fixed and rotating boxes in two dimensions with no-slip boundaries
In this paper we study decaying turbulence in fixed and rotating boxes in two
dimen- sions using the particle method SPH. The boundaries are specified by
boundary force particles, and the turbulence is initiated by a set of gaussian
vortices. In the case of fixed boxes we recover the results of Clercx and his
colleagues obtained using both a high accuracy spectral method and experiments.
Our results for fixed boxes are also in close agreement with those of Monaghan1
and Robinson and Monaghan2 obtained using SPH. A feature of decaying turbulence
in no-slip, square, fixed boundaries is that the angular momentum of the fluid
varies with time because of the reaction on the fluid of the viscous stresses
on the boundary. We find that when the box is allowed to rotate freely, so that
the total angular momentum of box and fluid is constant, the change in the
angular momentum of the fluid is a factor ~ 500 smaller than is the case for
the fixed box, and the final vorticity distribution is different. We also
simulate the behaviour of the turbulence when the box is forced to rotate with
small and large Rossby number, and the turbulence is initiated by gaussian
vortices as before. If the rotation of the box is maintained after the
turbulence is initiated we find that in the rotating frame the decay of kinetic
energy, enstrophy and the vortex structure is insensitive to the angular
velocity of the box. On the other hand, If the box is allowed to rotate freely
after the turbulence is initiated, the evolved vortex structure is completely
different
Initial Conditions for Models of Dynamical Systems
The long-time behaviour of many dynamical systems may be effectively
predicted by a low-dimensional model that describes the evolution of a reduced
set of variables. We consider the question of how to equip such a
low-dimensional model with appropriate initial conditions, so that it
faithfully reproduces the long-term behaviour of the original high-dimensional
dynamical system. Our method involves putting the dynamical system into normal
form, which not only generates the low-dimensional model, but also provides the
correct initial conditions for the model. We illustrate the method with several
examples.
Keywords: normal form, isochrons, initialisation, centre manifoldComment: 24 pages in standard LaTeX, 66K, no figure
Magnetohydrodynamic activity inside a sphere
We present a computational method to solve the magnetohydrodynamic equations
in spherical geometry. The technique is fully nonlinear and wholly spectral,
and uses an expansion basis that is adapted to the geometry:
Chandrasekhar-Kendall vector eigenfunctions of the curl. The resulting lower
spatial resolution is somewhat offset by being able to build all the boundary
conditions into each of the orthogonal expansion functions and by the
disappearance of any difficulties caused by singularities at the center of the
sphere. The results reported here are for mechanically and magnetically
isolated spheres, although different boundary conditions could be studied by
adapting the same method. The intent is to be able to study the nonlinear
dynamical evolution of those aspects that are peculiar to the spherical
geometry at only moderate Reynolds numbers. The code is parallelized, and will
preserve to high accuracy the ideal magnetohydrodynamic (MHD) invariants of the
system (global energy, magnetic helicity, cross helicity). Examples of results
for selective decay and mechanically-driven dynamo simulations are discussed.
In the dynamo cases, spontaneous flips of the dipole orientation are observed.Comment: 15 pages, 19 figures. Improved figures, in press in Physics of Fluid
On the resilience of helical magnetic fields to turbulent diffusion and the astrophysical implications
The extent to which large scale magnetic fields are susceptible to turbulent
diffusion is important for interpreting the need for in situ large scale
dynamos in astrophysics and for observationally inferring field strengths
compared to kinetic energy. By solving coupled equations for magnetic energy
and magnetic helicity in a system initiated with isotropic turbulence and an
arbitrarily helical large scale field, we quantify the decay rate of the latter
for a bounded or periodic system. The energy associated with the non-helical
magnetic field rapidly decays by turbulent diffusion, but the decay rate of the
helical component depends on whether the ratio of its magnetic energy to the
turbulent kinetic energy exceeds a critical value given by M_{1,c}
=(k_1/k_2)^2, where k_1 and k_2 are the wave numbers of the large and forcing
scales. Turbulently diffusing helical fields to small scales while conserving
magnetic helicity requires a rapid increase in total magnetic energy. As such,
only when the helical fields are sub-critical can they so diffuse. When
super-critical, the large scale helical field decays slowly, at a rate
determined by microphysical dissipation even when macroscopic turbulence is
present. Amplification of small scale magnetic helicity abates the turbulent
diffusion. Two implications are that: (1) Standard arguments supporting the
need for in situ large scale dynamos based on the otherwise rapid turbulent
diffusion of large scale fields require re-thinking since only the non-helical
field is so diffused in a closed system. Boundary terms could however provide
potential pathways for rapid change of the large scale helical field. (2) Since
M_{1,c} <<1 for k_1 << k_2, the presence of long-lived ordered large scale
helical fields, as in extragalactic jets, does not guarantee that the magnetic
field dominates the kinetic energy.Comment: published in MNRAS (in this replacement, the missing .bbl file has
been added
Nonlinear structural vibrations by the linear acceleration method
Numerical integration method for calculating dynamic response of nonlinear elastic structure
Experiments and analyses of upstream-advancing solitary waves generated by moving disturbances
In this joint theoretical, numerical and experimental study, we investigate the phenomenon of forced generation of nonlinear waves by disturbances moving steadily with a transcritical velocity through a layer of shallow water. The plane motion considered here is modelled by the generalized Boussinesq equations and the forced Korteweg-de Vries (fKdV) equation, both of which admit two types of forcing agencies in the form of an external surface pressure and a bottom topography. Numerical results are obtained using both theoretical models for the two types of forcings. These results illustrate that within a transcritical speed range, a succession of solitary waves are generated, periodically and indefinitely, to form a procession advancing upstream of the disturbance, while a train of weakly nonlinear and weakly dispersive waves develops downstream of an ever elongating stretch of a uniformly depressed water surface immediately behind the disturbance. This is a beautiful
example showing that the response of a dynamic system to steady forcing need not asymptotically tend to a steady state, but can be conspicuously periodic, after an impulsive start, when the system is being forced at resonance.
A series of laboratory experiments was conducted with a cambered bottom topography impulsively started from rest to a constant transcritical velocity U, the corresponding depth Froude number F = U/(gh[sub]0)^1/2 (g being the gravitational constant and h[sub]0 the original uniform water depth) being nearly the critical value of unity. For the two types of forcing, the generalized Boussinesq model indicates that the surface pressure can be more effective in generating the precursor solitary waves than the submerged topography of the same normalized spatial distribution. However, according to the fKdV model, these two types of forcing are entirely equivalent. Besides these and some other rather refined differences, a broad agreement is found between theory and experiment, both in respect of the amplitudes and phases of the waves generated, when the speed is nearly critical (0.9 F > 0.2, finally disappear at F ~= 0.2. In the other direction, as the Froude number is increased beyond F ~= 1.2, the precursor soliton phenomenon was found also to evanesce as no finite-amplitude solitary waves can outrun, nor can any two-dimensional waves continue to follow, the rapidly moving disturbance. In this supercritical range and for asymptotically large times, all the effects remain only
local to the disturbance. Thus, the criterion of the fascinating phenomenon of the generation of precursor solitons is ascertained
Coupling between corotation and Lindblad resonances in the elliptic planar three-body problem
We investigate the dynamics of two satellites with masses and
orbiting a massive central planet in a common plane, near a first
order mean motion resonance +1: ( integer). We consider only the
resonant terms of first order in eccentricity in the disturbing potential of
the satellites, plus the secular terms causing the orbital apsidal precessions.
We obtain a two-degree of freedom system, associated with the two critical
resonant angles and , where and are the mean
longitude and longitude of periapsis of , respectively, and where the
primed quantities apply to . We consider the special case where (restricted problem). The symmetry between the two angles
and is then broken, leading to two different kinds of resonances,
classically referred to as Corotation Eccentric resonance (CER) and Lindblad
Eccentric Resonance (LER), respectively. We write the four reduced equations of
motion near the CER and LER, that form what we call the CoraLin model. This
model depends upon only two dimensionless parameters that control the dynamics
of the system: the distance between the CER and LER, and a forcing
parameter that includes both the mass and the orbital eccentricity
of the disturbing satellite. Three regimes are found: for the system is
integrable, for of order unity, it exhibits prominent chaotic regions,
while for large compared to 2, the behavior of the system is regular and
can be qualitatively described using simple adiabatic invariant arguments. We
apply this model to three recently discovered small Saturnian satellites
dynamically linked to Mimas through first order mean motion resonances :
Aegaeon, Methone and Anthe
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