211 research outputs found
Evidence for Bolgiano-Obukhov scaling in rotating stratified turbulence using high-resolution direct numerical simulations
We report results on rotating stratified turbulence in the absence of
forcing, with large-scale isotropic initial conditions, using direct numerical
simulations computed on grids of up to 4096^3 points. The Reynolds and Froude
numbers are respectively equal to Re=5.4 x 10^4 and Fr=0.0242. The ratio of the
Brunt-V\"ais\"al\"a to the inertial wave frequency, N/f, is taken to be equal
to 4.95, a choice appropriate to model the dynamics of the southern abyssal
ocean at mid latitudes. This gives a global buoyancy Reynolds number
R_B=ReFr^2=32, a value sufficient for some isotropy to be recovered in the
small scales beyond the Ozmidov scale, but still moderate enough that the
intermediate scales where waves are prevalent are well resolved. We concentrate
on the large-scale dynamics, for which we find a spectrum compatible with the
Bolgiano-Obukhov scaling, and confirm that the Froude number based on a typical
vertical length scale is of order unity, with strong gradients in the vertical.
Two characteristic scales emerge from this computation, and are identified from
sharp variations in the spectral distribution of either total energy or
helicity. A spectral break is also observed at a scale at which the partition
of energy between the kinetic and potential modes changes abruptly, and beyond
which a Kolmogorov-like spectrum recovers. Large slanted layers are ubiquitous
in the flow in the velocity and temperature fields, with local overturning
events indicated by small Richardson numbers, and a small large-scale
enhancement of energy directly attributable to the effect of rotation is also
observed.Comment: 19 pages, 9 figures (including compound figures
Analytic approach to solve a degenerate parabolic PDE for the Heston Model
We present an analytic approach to solve a degenerate parabolic problem associated to the Heston model, which is widely used in mathematical finance to derive the price of an European option on an risky asset with stochastic volatility. We give a variational formulation, involving weighted Sobolev spaces, of the second order degenerate elliptic operator of the parabolic PDE. We use this approach to prove, under appropriate assumptions on some involved unknown parameters, the existence and uniqueness of weak solutions to the parabolic problem on unbounded subdomains of the half-plane
Numerical solutions of the three-dimensional magnetohydrodynamic alpha-model
We present direct numerical simulations and alpha-model simulations of four
familiar three-dimensional magnetohydrodynamic (MHD) turbulence effects:
selective decay, dynamic alignment, inverse cascade of magnetic helicity, and
the helical dynamo effect. The MHD alpha-model is shown to capture the
long-wavelength spectra in all these problems, allowing for a significant
reduction of computer time and memory at the same kinetic and magnetic Reynolds
numbers. In the helical dynamo, not only does the alpha-model correctly
reproduce the growth rate of magnetic energy during the kinematic regime, but
it also captures the nonlinear saturation level and the late generation of a
large scale magnetic field by the helical turbulence.Comment: 12 pages, 19 figure
Helicity cascades in rotating turbulence
The effect of helicity (velocity-vorticity correlations) is studied in direct
numerical simulations of rotating turbulence down to Rossby numbers of 0.02.
The results suggest that the presence of net helicity plays an important role
in the dynamics of the flow. In particular, at small Rossby number, the energy
cascades to large scales, as expected, but helicity then can dominate the
cascade to small scales. A phenomenological interpretation in terms of a direct
cascade of helicity slowed down by wave-eddy interactions leads to the
prediction of new inertial indices for the small-scale energy and helicity
spectra.Comment: 7 pages, 8 figure
The imprint of large-scale flows on turbulence
We investigate the locality of interactions in hydrodynamic turbulence using
data from a direct numerical simulation on a grid of 1024^3 points; the flow is
forced with the Taylor-Green vortex. An inertial range for the energy is
obtained in which the flux is constant and the spectrum follows an approximate
Kolmogorov law. Nonlinear triadic interactions are dominated by their non-local
components, involving widely separated scales. The resulting nonlinear transfer
itself is local at each scale but the step in the energy cascade is independent
of that scale and directly related to the integral scale of the flow.
Interactions with large scales represent 20% of the total energy flux. Possible
explanations for the deviation from self-similar models, the link between these
findings and intermittency, and their consequences for modeling of turbulent
flows are briefly discussed
Dynamo action at low magnetic Prandtl numbers: mean flow vs. fully turbulent motion
We compute numerically the threshold for dynamo action in Taylor-Green
swirling flows. Kinematic calculations, for which the flow field is fixed to
its time averaged profile, are compared to dynamical runs for which both the
Navier-Stokes and the induction equations are jointly solved. The kinematic
instability is found to have two branches, for all explored Reynolds numbers.
The dynamical dynamo threshold follows these branches: at low Reynolds number
it lies within the low branch while at high kinetic Reynolds number it is close
to the high branch.Comment: 4 pages, 4 figure
Universality of the Small-Scale Dynamo Mechanism
We quantify possible differences between turbulent dynamo action in the Sun
and the dynamo action studied in idealized simulations. For this purpose we
compare Fourier-space shell-to-shell energy transfer rates of three
incrementally more complex dynamo simulations: an incompressible, periodic
simulation driven by random flow, a simulation of Boussinesq convection, and a
simulation of fully compressible convection that includes physics relevant to
the near-surface layers of the Sun. For each of the simulations studied, we
find that the dynamo mechanism is universal in the kinematic regime because
energy is transferred from the turbulent flow to the magnetic field from
wavenumbers in the inertial range of the energy spectrum. The addition of
physical effects relevant to the solar near-surface layers, including
stratification, compressibility, partial ionization, and radiative energy
transport, does not appear to affect the nature of the dynamo mechanism. The
role of inertial-range shear stresses in magnetic field amplification is
independent from outer-scale circumstances, including forcing and
stratification. Although the shell-to-shell energy transfer functions have
similar properties to those seen in mean-flow driven dynamos in each simulation
studied, the saturated states of these simulations are not universal because
the flow at the driving wavenumbers is a significant source of energy for the
magnetic field.Comment: 16 pages, 9 figures, accepted for publication in Ap
Novel Reconstruction Errors for Saliency Detection in Hyperspectral Images
When hyperspectral images are analyzed, a big amount of data, representing the reflectance at hundreds of wavelengths, needs to be processed. Hence, dimensionality reduction techniques are used to discard unnecessary information. In order to detect the so called “saliency”, i.e., the relevant pixels, we propose a bottom-up approach based on three main ingredients: sparse non negative matrix factorization (SNMF), spatial and spectral functions to measure the reconstruction error between the input image and the reconstructed one and a final clustering technique. We introduce novel error functions and show some useful mathematical properties. The method is validated on hyperspectral images and compared with state-of-the-art different approaches
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