Nuclear fission

“…"sharp"? This question is of enormous conceptual importance in the theory of turbulence, since the energy dissipation rate is the central object in classical turbulence theories [1][2][3][4][5], and its behavior at high Reynolds numbers may reveal whether there are intermittency corrections to classical scaling [6,7]. Since full numerical simulations of shear flows with Reynolds numbers of the order of 10 6 or above are out of reach, and will remain so in the foreseeable future, rigorous estimates of the dissipation rate derived directly from the Navier-Stokes equations are one of the few tools left to the theorist for approaching such questions.…”

Section: Introductionmentioning

confidence: 99%

Variational bound on energy dissipation in plane Couette flow

1997

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We present numerical solutions to the extended Doering-Constantin variational principle for upper bounds on the energy dissipation rate in turbulent plane Couette flow. Using the compound matrix technique in order to reformulate this principle's spectral constraint, we derive a system of equations that is amenable to numerical treatment in the entire range from low to asymptotically high Reynolds numbers. Our variational bound exhibits a minimum at intermediate Reynolds numbers, and reproduces the Busse bound in the asymptotic regime. As a consequence of a bifurcation of the minimizing wavenumbers, there exist two length scales that determine the optimal upper bound: the effective width of the variational profile's boundary segments, and the extension of their flat interior part.

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“…The exact nature of these geostrophic adjustment processes is not known. Cahn (1945) and Obukhov (1949) suggested that the phasevelocity dispersion of gravity waves of different wavelength could account for the quick dissipation of the initial wave-packet. This does not explain, however, the net decrease of gravity wave oscillation energy in a closed system.…”

Section: Geostrophic Adjustmentmentioning

confidence: 99%

Dynamic approach to meteorological data assimilation

Morel

Talagrand

1974

Tellus A: Dynamic Meteorology and Oceanography

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The methods of four-dimensional assimilation of meteorological data ar0 discussed on the basis of theoretical considerations as well as of numerical results obtained with two different models. The fundamental role of geostrophio adjustment and of the damping of inertia-gravity waves is particularly studied. A number of general dynamic concepts are defined, which lead t o a possible understanding of the results of data assimilation experiments in terms of three parameters: the predictability of the reference flow by the model, the gravity wave damping time constant and the data acquisition rate. The equivaIence between synoptic and asynoptic data is discussed, and proved in one particular case. Finally, "intermittent" and "continuous" assimilations are compared.

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Nuclear fission

Cited by 12 publications

References 14 publications

Narrow‐Gap and Gapless Semiconductors under Uniaxial Stress. Energy Spectrum and Galvanomagnetic Phenomena

Narrow‐Gap and Gapless Semiconductors under Uniaxial Stress. Energy Spectrum and Galvanomagnetic Phenomena

Variational bound on energy dissipation in plane Couette flow

Dynamic approach to meteorological data assimilation

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