16,360 research outputs found
Hydrodynamic Flows on Curved Surfaces: Spectral Numerical Methods for Radial Manifold Shapes
We formulate hydrodynamic equations and spectrally accurate numerical methods
for investigating the role of geometry in flows within two-dimensional fluid
interfaces. To achieve numerical approximations having high precision and level
of symmetry for radial manifold shapes, we develop spectral Galerkin methods
based on hyperinterpolation with Lebedev quadratures for -projection to
spherical harmonics. We demonstrate our methods by investigating hydrodynamic
responses as the surface geometry is varied. Relative to the case of a sphere,
we find significant changes can occur in the observed hydrodynamic flow
responses as exhibited by quantitative and topological transitions in the
structure of the flow. We present numerical results based on the
Rayleigh-Dissipation principle to gain further insights into these flow
responses. We investigate the roles played by the geometry especially
concerning the positive and negative Gaussian curvature of the interface. We
provide general approaches for taking geometric effects into account for
investigations of hydrodynamic phenomena within curved fluid interfaces.Comment: 14 figure
Geodesic Transport Barriers in Jupiter's Atmosphere: A Video-Based Analysis
Jupiter's zonal jets and Great Red Spot are well known from still images. Yet
the planet's atmosphere is highly unsteady, which suggests that the actual
material transport barriers delineating its main features should be
time-dependent. Rare video footages of Jupiter's clouds provide an opportunity
to verify this expectation from optically reconstructed velocity fields.
Available videos, however, provide short-time and temporally aperiodic velocity
fields that defy classical dynamical systems analyses focused on asymptotic
features. To this end, we use here the recent theory of geodesic transport
barriers to uncover finite-time mixing barriers in the wind field extracted
from a video captured by NASA's Cassini space mission. More broadly, the
approach described here provides a systematic and frame-invariant way to
extract dynamic coherent structures from time-resolved remote observations of
unsteady continua
Transport in Transitory, Three-Dimensional, Liouville Flows
We derive an action-flux formula to compute the volumes of lobes quantifying
transport between past- and future-invariant Lagrangian coherent structures of
n-dimensional, transitory, globally Liouville flows. A transitory system is one
that is nonautonomous only on a compact time interval. This method requires
relatively little Lagrangian information about the codimension-one surfaces
bounding the lobes, relying only on the generalized actions of loops on the
lobe boundaries. These are easily computed since the vector fields are
autonomous before and after the time-dependent transition. Two examples in
three-dimensions are studied: a transitory ABC flow and a model of a
microdroplet moving through a microfluidic channel mixer. In both cases the
action-flux computations of transport are compared to those obtained using
Monte Carlo methods.Comment: 30 pages, 16 figures, 1 table, submitted to SIAM J. Appl. Dyn. Sy
Oscillatory migration of accreting protoplanets driven by a 3D distortion of the gas flow
Context. The dynamics of a low-mass protoplanet accreting solids is
influenced by the heating torque, which was found to suppress inward migration
in protoplanetary disks with constant opacities.
Aims. We investigate the differences of the heating torque between disks with
constant and temperature-dependent opacities.
Methods. Interactions of a super-Earth-sized protoplanet with the gas disk
are explored using 3D radiation hydrodynamic simulations.
Results. Accretion heating of the protoplanet creates a hot underdense region
in the surrounding gas, leading to misalignment of the local density and
pressure gradients. As a result, the 3D gas flow is perturbed and some of the
streamlines form a retrograde spiral rising above the protoplanet. In the
constant-opacity disk, the perturbed flow reaches a steady state and the
underdense gas responsible for the heating torque remains distributed in
accordance with previous studies. If the opacity is non-uniform, however, the
differences in the disk structure can lead to more vigorous streamline
distortion and eventually to a flow instability. The underdense gas develops a
one-sided asymmetry which circulates around the protoplanet in a retrograde
fashion. The heating torque thus strongly oscillates in time and does not on
average counteract inward migration.
Conclusions. The torque variations make the radial drift of the protoplanet
oscillatory, consisting of short intervals of alternating rapid inward and
outward migration. We speculate that transitions between the positive and
oscillatory heating torque may occur in specific disk regions susceptible to
vertical convection, resulting in the convergent migration of multiple
planetary embryos.Comment: Accepted for publication in A&A, 19 pages, 18 figure
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