479 research outputs found
Marginally unstable Holmboe modes
Marginally unstable Holmboe modes for smooth density and velocity profiles
are studied. For a large family of flows and stratification that exhibit
Holmboe instability, we show that the modes with phase velocity equal to the
maximum or the minimum velocity of the shear are marginally unstable. This
allows us to determine the critical value of the control parameter R
(expressing the ratio of the velocity variation length scale to the density
variation length scale) that Holmboe instability appears R=2. We then examine
systems for which the parameter R is very close to this critical value. For
this case we derive an analytical expression for the dispersion relation of the
complex phase speed c(k) in the unstable region. The growth rate and the width
of the region of unstable wave numbers has a very strong (exponential)
dependence on the deviation of R from the critical value. Two specific examples
are examined and the implications of the results are discussed.Comment: Submitted to Physics of Fluid
Stratified shear flow instabilities at large Richardson numbers
Numerical simulations of stratified shear flow instabilities are performed in
two dimensions in the Boussinesq limit. The density variation length scale is
chosen to be four times smaller than the velocity variation length scale so
that Holmboe or Kelvin-Helmholtz unstable modes are present depending on the
choice of the global Richardson number Ri. Three different values of Ri were
examined Ri =0.2, 2, 20. The flows for the three examined values are all
unstable due to different modes namely: the Kelvin-Helmholtz mode for Ri=0.2,
the first Holmboe mode for Ri=2, and the second Holmboe mode for Ri=20 that has
been discovered recently and it is the first time that it is examined in the
non-linear stage. It is found that the amplitude of the velocity perturbation
of the second Holmboe mode at the non-linear stage is smaller but comparable to
first Holmboe mode. The increase of the potential energy however due to the
second Holmboe modes is greater than that of the first mode. The
Kelvin-Helmholtz mode is larger by two orders of magnitude in kinetic energy
than the Holmboe modes and about ten times larger in potential energy than the
Holmboe modes. The results in this paper suggest that although mixing is
suppressed at large Richardson numbers it is not negligible, and turbulent
mixing processes in strongly stratified environments can not be excluded.Comment: Submitted to Physics of Fluid
Shell to shell energy transfer in MHD, Part I: steady state turbulence
We investigate the transfer of energy from large scales to small scales in
fully developed forced three-dimensional MHD-turbulence by analyzing the
results of direct numerical simulations in the absence of an externally imposed
uniform magnetic field. Our results show that the transfer of kinetic energy
from the large scales to kinetic energy at smaller scales, and the transfer of
magnetic energy from the large scales to magnetic energy at smaller scales, are
local, as is also found in the case of neutral fluids, and in a way that is
compatible with Kolmogorov (1941) theory of turbulence. However, the transfer
of energy from the velocity field to the magnetic field is a highly non-local
process in Fourier space. Energy from the velocity field at large scales can be
transfered directly into small scale magnetic fields without the participation
of intermediate scales. Some implications of our results to MHD turbulence
modeling are also discussed.Comment: Submitted to PR
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
Non-local interactions in hydrodynamic turbulence at high Reynolds numbers: the slow emergence of scaling laws
We analyze the data stemming from a forced incompressible hydrodynamic
simulation on a grid of 2048^3 regularly spaced points, with a Taylor Reynolds
number of Re~1300. The forcing is given by the Taylor-Green flow, which shares
similarities with the flow in several laboratory experiments, and the
computation is run for ten turnover times in the turbulent steady state. At
this Reynolds number the anisotropic large scale flow pattern, the inertial
range, the bottleneck, and the dissipative range are clearly visible, thus
providing a good test case for the study of turbulence as it appears in nature.
Triadic interactions, the locality of energy fluxes, and structure functions of
the velocity increments are computed. A comparison with runs at lower Reynolds
numbers is performed, and shows the emergence of scaling laws for the relative
amplitude of local and non-local interactions in spectral space. The scalings
of the Kolmogorov constant, and of skewness and flatness of velocity
increments, performed as well and are consistent with previous experimental
results. Furthermore, the accumulation of energy in the small-scales associated
with the bottleneck seems to occur on a span of wavenumbers that is independent
of the Reynolds number, possibly ruling out an inertial range explanation for
it. Finally, intermittency exponents seem to depart from standard models at
high Re, leaving the interpretation of intermittency an open problem.Comment: 8 pages, 8 figure
Non-existence of stationary two-black-hole configurations: The degenerate case
In a preceding paper we examined the question whether the spin-spin repulsion
and the gravitational attraction of two aligned sub-extremal black holes can
balance each other. Based on the solution of a boundary value problem for two
separate (Killing-) horizons and a novel black hole criterion we were able to
prove the non-existence of the equilibrium configuration in question. In this
paper we extend the non-existence proof to extremal black holes.Comment: 18 pages, 2 figure
Submarine pockmarks area localization using in-situ radio-tracing technique in Eckernförde bay, Germany
Large scale flow effects, energy transfer, and self-similarity on turbulence
The effect of large scales on the statistics and dynamics of turbulent
fluctuations is studied using data from high resolution direct numerical
simulations. Three different kinds of forcing, and spatial resolutions ranging
from 256^3 to 1024^3, are being used. The study is carried out by investigating
the nonlinear triadic interactions in Fourier space, transfer functions,
structure functions, and probability density functions. Our results show that
the large scale flow plays an important role in the development and the
statistical properties of the small scale turbulence. The role of helicity is
also investigated. We discuss the link between these findings and
intermittency, deviations from universality, and possible origins of the
bottleneck effect. Finally, we briefly describe the consequences of our results
for the subgrid modeling of turbulent flows
Critical exponents in zero dimensions
In the vicinity of the onset of an instability, we investigate the effect of
colored multiplicative noise on the scaling of the moments of the unstable mode
amplitude. We introduce a family of zero dimensional models for which we can
calculate the exact value of the critical exponents for all the
moments. The results are obtained through asymptotic expansions that use the
distance to onset as a small parameter. The examined family displays a variety
of behaviors of the critical exponents that includes anomalous exponents:
exponents that differ from the deterministic (mean-field) prediction, and
multiscaling: non-linear dependence of the exponents on the order of the
moment
Scale interactions and scaling laws in rotating flows at moderate Rossby numbers and large Reynolds numbers
The effect of rotation is considered to become important when the Rossby
number is sufficiently small, as is the case in many geophysical and
astrophysical flows. Here we present direct numerical simulations to study the
effect of rotation in flows with moderate Rossby numbers (down to Ro~0.1) but
at Reynolds numbers large enough to observe the beginning of a turbulent
scaling at scales smaller than the energy injection scale. We use coherent
forcing at intermediate scales, leaving enough room in the spectral space for
an inverse cascade of energy to also develop. We analyze the spectral behavior
of the simulations, the shell-to-shell energy transfer, scaling laws, and
intermittency, as well as the geometry of the structures in the flow. At late
times, the direct transfer of energy at small scales is mediated by
interactions with the largest scale in the system, the energy containing eddies
with k_perp~1, where "perp" refers to wavevectors perpendicular the axis of
rotation. The transfer between modes with wavevector parallel to the rotation
is strongly quenched. The inverse cascade of energy at scales larger than the
energy injection scale is non-local, and energy is transferred directly from
small scales to the largest available scale. Also, as time evolves and the
energy piles up at the large scales, the intermittency of the direct cascade of
energy is preserved while corrections due to intermittency are found to be the
same (within error bars) as in homogeneous turbulence.Comment: 12 pages, 16 figure
- …