319 research outputs found
The multi-scale dust formation in substellar atmospheres
Substellar atmospheres are observed to be irregularly variable for which the
formation of dust clouds is the most promising candidate explanation. The
atmospheric gas is convectively unstable and, last but not least, colliding
convective cells are seen as cause for a turbulent fluid field. Since dust
formation depends on the local properties of the fluid, turbulence influences
the dust formation process and may even allow the dust formation in an
initially dust-hostile gas. A regime-wise investigation of dust forming
substellar atmospheric situations reveals that the largest scales are
determined by the interplay between gravitational settling and convective
replenishment which results in a dust-stratified atmosphere. The regime of
small scales is determined by the interaction of turbulent fluctuations.
Resulting lane-like and curled dust distributions combine to larger and larger
structures. We compile necessary criteria for a subgrid model in the frame of
large scale simulations as result of our study on small scale turbulence in
dust forming gases.Comment: 22 Pages, 5 Figures, to appear in "Analysis and Numerics of
Conservation Laws", ed. G. Warnecke (Springer-Verlag
CRC 1114 - Report Membrane Deformation by N-BAR Proteins: Extraction of membrane geometry and protein diffusion characteristics from MD simulations
We describe simulations of Proteins and artificial pseudo-molecules
interacting and shaping lipid bilayer membranes. We extract protein diffusion
Parameters, membrane deformation profiles and the elastic properties of the
used membrane models in preparation of calculations based on a large scale
continuum model
On singular limits arising in the scale analysis of stratified fluid flows
We study the low Mach low Freude numbers limit in the compressible
Navier-Stokes equations and the transport equation for evolution of an entropy
variable -- the potential temperature . We consider the case of
well-prepared initial data on "flat" tours and Reynolds number tending to
infinity, and the case of ill-prepared data on an infinite slab. In both cases,
we show that the weak solutions to the primitive system converge to the
solution to the anelastic Navier-Stokes system and the transport equation for
the second order variation of Comment: 25 page
Intensification of tilted atmospheric vortices by asymmetric diabatic heating
P\"aschke et al. (JFM, 701, 137--170 (2012)) studied the nonlinear dynamics
of strongly tilted vortices subject to asymmetric diabatic heating by
asymptotic methods. They found, i.a., that an azimuthal Fourier mode 1 heating
pattern can intensify or attenuate such a vortex depending on the relative
orientation of tilt and heating asymmetries. The theory originally addressed
the gradient wind regime which, asymptotically speaking, corresponds to vortex
Rossby numbers of order O(1) in the limit. Formally, this restricts the
appicability of the theory to rather weak vortices in the near equatorial
region. It is shown below that said theory is, in contrast, uniformly valid for
vanishing Coriolis parameter and thus applicable to vortices up to hurricane
strength. The paper's main contribution is a series of three-dimensional
numerical simulations which fully support the analytical predictions.Comment: 22 pages, 11 figure
Balanced data assimilation for highly-oscillatory mechanical systems
Data assimilation algorithms are used to estimate the states of a dynamical
system using partial and noisy observations. The ensemble Kalman filter has
become a popular data assimilation scheme due to its simplicity and robustness
for a wide range of application areas. Nevertheless, the ensemble Kalman filter
also has limitations due to its inherent Gaussian and linearity assumptions.
These limitations can manifest themselves in dynamically inconsistent state
estimates. We investigate this issue in this paper for highly oscillatory
Hamiltonian systems with a dynamical behavior which satisfies certain balance
relations. We first demonstrate that the standard ensemble Kalman filter can
lead to estimates which do not satisfy those balance relations, ultimately
leading to filter divergence. We also propose two remedies for this phenomenon
in terms of blended time-stepping schemes and ensemble-based penalty methods.
The effect of these modifications to the standard ensemble Kalman filter are
discussed and demonstrated numerically for two model scenarios. First, we
consider balanced motion for highly oscillatory Hamiltonian systems and,
second, we investigate thermally embedded highly oscillatory Hamiltonian
systems. The first scenario is relevant for applications from meteorology while
the second scenario is relevant for applications of data assimilation to
molecular dynamics
Global well-posedness for passively transported nonlinear moisture dynamics with phase changes
We study a moisture model for warm clouds that has been used by Klein and
Majda as a basis for multiscale asymptotic expansions for deep convective
phenomena. These moisture balance equations correspond to a bulk microphysics
closure in the spirit of Kessler and of Grabowski and Smolarkiewicz, in which
water is present in the gaseous state as water vapor and in the liquid phase as
cloud water and rain water. It thereby contains closures for the phase changes
condensation and evaporation, as well as the processes of autoconversion of
cloud water into rainwater and the collection of cloud water by the falling
rain droplets. Phase changes are associated with enormous amounts of latent
heat and therefore provide a strong coupling to the thermodynamic equation.
In this work we assume the velocity field to be given and prove rigorously
the global existence and uniqueness of uniformly bounded solutions of the
moisture model with viscosity, diffusion and heat conduction. To guarantee
local well-posedness we first need to establish local existence results for
linear parabolic equations, subject to the Robin boundary conditions on the
cylindric type of domains under consideration. We then derive a priori
estimates, for proving the maximum principle, using the Stampacchia method, as
well as the iterative method by Alikakos to obtain uniform boundedness. The
evaporation term is of power law type, with an exponent in general less or
equal to one and therefore making the proof of uniqueness more challenging.
However, these difficulties can be circumvented by introducing new unknowns,
which satisfy the required cancellation and monotonicity properties in the
source terms
- …