Energy‐Dependent Boltzmann Equation in the Fast Domain

This work presents some aspects of the static energy‐dependent Boltzmann equation in plane geometry using a continuous‐energy formulation. In a first part, solutions are found for a class of synthetic separable (but nondegenerate) energy‐transfer kernels. Such kernels are representative, for instance, of neutron inelastic slowing down. In a second part, the same problem is considered with the addition of a projection kernel (typical of neutron fission); it is shown that the solutions split into space‐energy separable components and nonseparable ``slowing‐down transients.''Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69987/2/JMAPAQ-11-1-174-1.pd

Bursting Dynamics of the 3D Euler Equations in Cylindrical Domains

A class of three-dimensional initial data characterized by uniformly large vorticity is considered for the Euler equations of incompressible fluids. The fast singular oscillating limits of the Euler equations are studied for parametrically resonant cylinders. Resonances of fast swirling Beltrami waves deplete the Euler nonlinearity. The resonant Euler equations are systems of three-dimensional rigid body equations, coupled or not. Some cases of these resonant systems have homoclinic cycles, and orbits in the vicinity of these homoclinic cycles lead to bursts of the Euler solution measured in Sobolev norms of order higher than that corresponding to the enstrophy

The Cauchy problem for the Navier-Stokes equations with spatially almost periodic initial data

A unique classical solution of the Cauchy problem for the Navier-Stokes equations is considered when the initial velocity is spatially almost periodic. It is shown that the solution is always spatially almost periodic at any time provided that the solution exists. No restriction on the space dimension is imposed. This fact follows from continuous dependence of the solution with respect to initial data in uniform topology. Similar result is also established for Cauchy problem of the three-dimensional Navier-Stokes equations in a rotating frame

Energy-dependent Neutron Transport Theory In The Fast Domain.

PhDEnergyNuclear physicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/185268/2/6813370.pd

The Cauchy problem for the Navier-Stokes equations with spatially almost periodic initial data

A unique classical solution of the Cauchy problem for the Navier-Stokes equa- tions is considered when the initial velocity is spatially almost periodic. It is shown that the solution is always spatially almost periodic at any time provided that the solution exists. No restriction on the space dimension is imposed. This fact follows from continuous dependence of the solution with respect to initial data in uniform topology. Similar result is also established for Cauchy problem of the three- dimensional Navier-Stokes equations in a rotating frame

Energy-dependent neutron transport theory in the fast domain : technical report

http://deepblue.lib.umich.edu/bitstream/2027.42/6822/5/bac9792.0001.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/6822/4/bac9792.0001.001.tx

National Aeronautics and

Turbulence under strong stratification and rotation is usually characterized as quasi-two dimensional turbulence. We develop a "quasi-two dimensional" energy spectrum which changes smoothly between the Kolmogorov-5/3 law (no stratification), the-2 scalings of Zhou for the case of strong rotation, as well as the-2 scalings for the case of strong rotation and stratification. For strongly stratified turbulence, the model may give the-2 scaling predicted by Herring; and the-5/3 scaling indicated by some mesoscale observations

ENERGY SPECTRA OF STRONGLY STRATIFIED AND ROTATING TURBULENCE

Turbulence under strong stratification and rotation is usually characterized as quasi-two dimensional turbulence. We develop a “quasi-two dimensional” energy spectrum which changes smoothly between the Kolmogorov-5/3 law (no stratification), the-2 scalings of Zhou for the case of strong rotation, as well as the-2 scalings for the case of strong rotation and stratification. For strongly stratified turbulence, the model may give the-2 scaling predicted by Herring; and the-5/3 scaling indicated by some mesoscale observations

Fast Singular Oscillating Limits and Global Regularity for the 3D Primitive Equations of Geophysics

Fast singular oscillating limits of the three-dimensional "primitive" equations of geophysical fluid flows are analyzed. We prove existence on infinite time intervals of regular solutions to the 3D "primitive" Navier-Stokes equations for strong stratification (large stratification parameter N). This uniform existence is proven for periodic or stress-free boundary conditions for all domain aspect ratios, including the case of three wave resonances which yield nonlinear "$2\frac{1}{2}$ dimensional" limit equations for N → +∞; smoothness assumptions are the same as for local existence theorems, that is initial data in Hα, α ≥ 3/4. The global existence is proven using techniques of the Littlewood-Paley dyadic decomposition. Infinite time regularity for solutions of the 3D "primitive" Navier-Stokes equations is obtained by bootstrapping from global regularity of the limit resonant equations and convergence theorems