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Stochastic Reductions for Inertial Fluid-Structure Interactions Subject to Thermal Fluctuations
We present analysis for the reduction of an inertial description of
fluid-structure interactions subject to thermal fluctuations. We show how the
viscous coupling between the immersed structures and the fluid can be
simplified in the regime where this coupling becomes increasingly strong. Many
descriptions in fluid mechanics and in the formulation of computational methods
account for fluid-structure interactions through viscous drag terms to transfer
momentum from the fluid to immersed structures. In the inertial regime, this
coupling often introduces a prohibitively small time-scale into the temporal
dynamics of the fluid-structure system. This is further exacerbated in the
presence of thermal fluctuations. We discuss here a systematic reduction
technique for the full inertial equations to obtain a simplified description
where this coupling term is eliminated. This approach also accounts for the
effective stochastic equations for the fluid-structure dynamics. The analysis
is based on use of the Infinitesmal Generator of the SPDEs and a singular
perturbation analysis of the Backward Kolomogorov PDEs. We also discuss the
physical motivations and interpretation of the obtained reduced description of
the fluid-structure system. Working paper currently under revision. Please
report any comments or issues to [email protected]
Systematic Stochastic Reduction of Inertial Fluid-Structure Interactions subject to Thermal Fluctuations
We present analysis for the reduction of an inertial description of
fluid-structure interactions subject to thermal fluctuations. We show how the
viscous coupling between the immersed structures and the fluid can be
simplified in the regime where this coupling becomes increasingly strong. Many
descriptions in fluid mechanics and in the formulation of computational methods
account for fluid-structure interactions through viscous drag terms to transfer
momentum from the fluid to immersed structures. In the inertial regime, this
coupling often introduces a prohibitively small time-scale into the temporal
dynamics of the fluid-structure system. This is further exacerbated in the
presence of thermal fluctuations. We discuss here a systematic reduction
technique for the full inertial equations to obtain a simplified description
where this coupling term is eliminated. This approach also accounts for the
effective stochastic equations for the fluid-structure dynamics. The analysis
is based on use of the Infinitesmal Generator of the SPDEs and a singular
perturbation analysis of the Backward Kolomogorov PDEs. We also discuss the
physical motivations and interpretation of the obtained reduced description of
the fluid-structure system. Working paper currently under revision. Please
report any comments or issues to [email protected]: 19 pages, 1 figure. arXiv admin note: substantial text overlap with
arXiv:1009.564
Spinodal decomposition of off-critical quenches with a viscous phase using dissipative particle dynamics in two and three spatial dimensions
We investigate the domain growth and phase separation of
hydrodynamically-correct binary immiscible fluids of differing viscosity as a
function of minority phase concentration in both two and three spatial
dimensions using dissipative particle dynamics. We also examine the behavior of
equal-viscosity fluids and compare our results to similar lattice-gas
simulations in two dimensions.Comment: 34 pages (11 figures); accepted for publication in Phys. Rev.
Quasi-Two-Dimensional Dynamics of Plasmas and Fluids
In the lowest order of approximation quasi-twa-dimensional dynamics of planetary atmospheres and of plasmas in a magnetic field can be described by a common convective vortex equation, the Charney and Hasegawa-Mirna (CHM) equation. In contrast to the two-dimensional Navier-Stokes equation, the CHM equation admits "shielded vortex solutions" in a homogeneous limit and linear waves ("Rossby waves" in the planetary atmosphere and "drift waves" in plasmas) in the presence of inhomogeneity. Because of these properties, the nonlinear dynamics described by the CHM equation provide rich solutions which involve turbulent, coherent and wave behaviors. Bringing in non ideal effects such as resistivity makes the plasma equation significantly different from the atmospheric equation with such new effects as instability of the drift wave driven by the resistivity and density gradient. The model equation deviates from the CHM equation and becomes coupled with Maxwell equations. This article reviews the linear and nonlinear dynamics of the quasi-two-dimensional aspect of plasmas and planetary atmosphere starting from the introduction of the ideal model equation (CHM equation) and extending into the most recent progress in plasma turbulence.U. S. Department of Energy DE-FG05-80ET-53088Ministry of Education, Science and Culture of JapanFusion Research Cente
Aeronautical Engineering: A continuing bibliography, supplement 120
This bibliography contains abstracts for 297 reports, articles, and other documents introduced into the NASA scientific and technical information system in February 1980
Towards a solution of the closure problem for convective atmospheric boundary-layer turbulence
We consider the closure problem for turbulence in the dry convective atmospheric boundary
layer (CBL). Transport in the CBL is carried by small scale eddies near the surface and large
plumes in the well mixed middle part up to the inversion that separates the CBL from the
stably stratified air above. An analytically tractable model based on a multivariate Delta-PDF
approach is developed. It is an extension of the model of Gryanik and Hartmann [1] (GH02)
that additionally includes a term for background turbulence. Thus an exact solution is derived
and all higher order moments (HOMs) are explained by second order moments, correlation
coefficients and the skewness. The solution provides a proof of the extended universality
hypothesis of GH02 which is the refinement of the Millionshchikov hypothesis (quasi-
normality of FOM). This refined hypothesis states that CBL turbulence can be considered as
result of a linear interpolation between the Gaussian and the very skewed turbulence regimes.
Although the extended universality hypothesis was confirmed by results of field
measurements, LES and DNS simulations (see e.g. [2-4]), several questions remained
unexplained. These are now answered by the new model including the reasons of the
universality of the functional form of the HOMs, the significant scatter of the values of the
coefficients and the source of the magic of the linear interpolation. Finally, the closures
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predicted by the model are tested against measurements and LES data. Some of the other
issues of CBL turbulence, e.g. familiar kurtosis-skewness relationships and relation of area
coverage parameters of plumes (so called filling factors) with HOM will be discussed also
Matrix generalizations of some dynamic field theories
We introduce matrix generalizations of the Navier--Stokes (NS) equation for
fluid flow, and the Kardar--Parisi--Zhang (KPZ) equation for interface growth.
The underlying field, velocity for the NS equation, or the height in the case
of KPZ, is promoted to a matrix that transforms as the adjoint representation
of . Perturbative expansions simplify in the limit,
dominated by planar graphs. We provide the results of a one--loop analysis, but
have not succeeded in finding the full solution of the theory in this limit.Comment: 9 pages, Hard copy figures available from: [email protected]
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