415 research outputs found
Optimal Transport, Convection, Magnetic Relaxation and Generalized Boussinesq equations
We establish a connection between Optimal Transport Theory and classical
Convection Theory for geophysical flows. Our starting point is the model
designed few years ago by Angenent, Haker and Tannenbaum to solve some Optimal
Transport problems. This model can be seen as a generalization of the
Darcy-Boussinesq equations, which is a degenerate version of the
Navier-Stokes-Boussinesq (NSB) equations. In a unified framework, we relate
different variants of the NSB equations (in particular what we call the
generalized Hydrostatic-Boussinesq equations) to various models involving
Optimal Transport (and the related Monge-Ampere equation. This includes the 2D
semi-geostrophic equations and some fully non-linear versions of the so-called
high-field limit of the Vlasov-Poisson system and of the Keller-Segel for
Chemotaxis. Finally, we show how a ``stringy'' generalization of the AHT model
can be related to the magnetic relaxation model studied by Arnold and Moffatt
to obtain stationary solutions of the Euler equations with prescribed topology
Global well-posedness for the Navier-Stokes-Boussinesq system with axisymmetric data
In this paper we prove the global well-posedness for a three-dimensional
Boussinesq system with axisymmetric initial data. This system couples the
Navier-Stokes equation with a transport-diffusion equation governing the
temperature. Our result holds uniformly with respect to the heat conductivity
coefficient which may vanish.Comment: 22 page
Second All-Union Seminar on Hydromechanics and Heat and Mass Exchange in Weightlessness, summaries of reports
Abstracts of reports are given which were presented at the Second All Union Seminar on Hydromechanics and Heat-Mass Transfer in Weightlessness. Topics include: (1) features of crystallization of semiconductor materials under conditions of microacceleration; (2) experimental results of crystallization of solid solutions of CDTE-HGTE under conditions of weightlessness; (3) impurities in crystals cultivated under conditions of weightlessness; and (4) a numerical investigation of the distribution of impurities during guided crystallization of a melt
Notes on the 1969 Summer Study Program in Geophysical Fluid Dynamics at the Woods Hole Oceanographic Institution
Originally issued as Reference No. 69-41, series later renamed WHOI-.The principal theme of this eleventh Summer Program has been
Astrophysical Fluid Dynamics. As in the past, we have explored the
region of overlap in technique and theory of our summer theme and
other aspects of Fluid Dynamics. An interesting example of this
overlap is the application of the physics of salt-finger instability,
a significant oceanographic process, to instabilities due to differential
rotation in the sun, a critical problem in stellar evolution.National Science Foundatio
Global well-posedness for the Euler-Boussinesq system with axisymmetric data
In this paper we prove the global well-posedness for the three-dimensional
Euler-Boussinesq system with axisymmetric initial data without swirl. This
system couples the Euler equation with a transport-diffusion equation governing
the temperature.Comment: 39 page
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
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