1,031 research outputs found
On inertial-range scaling laws
Inertial-range scaling laws for two- and three-dimensional turbulence are
re-examined within a unified framework. A new correction to Kolmogorov's
scaling is derived for the energy inertial range. A related
modification is found to Kraichnan's logarithmically corrected two-dimensional
enstrophy-range law that removes its unexpected divergence at the injection
wavenumber. The significance of these corrections is illustrated with
steady-state energy spectra from recent high-resolution closure computations.
Implications for conventional numerical simulations are discussed. These
results underscore the asymptotic nature of inertial-range scaling laws.Comment: 16 pages, postscript (uncompressed, not encoded
Large-scale energy spectra in surface quasi-geostrophic turbulence
The large-scale energy spectrum in two-dimensional turbulence governed by the
surface quasi-geostrophic (SQG) equation
is studied. The nonlinear transfer of this system conserves the two quadratic
quantities and
(kinetic energy), where denotes
a spatial average. The energy density is bounded and its spectrum
is shallower than in the inverse-transfer range. For
bounded turbulence, in the low-wavenumber region can be bounded by
where is a constant independent of but dependent on the domain
size. Results from numerical simulations confirming the theoretical predictions
are presented.Comment: 11 pages, 4 figures, to appear in JF
Exactly Conservative Integrators
Traditional numerical discretizations of conservative systems generically
yield an artificial secular drift of any nonlinear invariants. In this work we
present an explicit nontraditional algorithm that exactly conserves these
invariants. We illustrate the general method by applying it to the three-wave
truncation of the Euler equations, the Lotka--Volterra predator--prey model,
and the Kepler problem. This method is discussed in the context of symplectic
(phase space conserving) integration methods as well as nonsymplectic
conservative methods. We comment on the application of our method to general
conservative systems.Comment: 30 pages, postscript (1.3MB). Submitted to SIAM J. Sci. Comput
Robust Exponential Runge-Kutta Embedded Pairs
Exponential integrators are explicit methods for solving ordinary
differential equations that treat linear behaviour exactly. The stiff-order
conditions for exponential integrators derived in a Banach space framework by
Hochbruck and Ostermann are solved symbolically by expressing the Runge--Kutta
weights as unknown linear combinations of phi functions. Of particular interest
are embedded exponential pairs that efficiently generate both a high- and
low-order estimate, allowing for dynamic adjustment of the time step. A key
requirement is that the pair be robust: if the nonlinear source function has
nonzero total time derivatives, the order of the low-order estimate should
never exceed its design value. Robust exponential Runge--Kutta (3,2) and (4,3)
embedded pairs that are well-suited to initial value problems with a dominant
linearity are constructed.Comment: 24 pages, 8 figures. The Mathematica scripts mentioned in the paper
can be found in: https://github.com/stiffode/expint
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Nonlinear symmetric stability of planetary atmospheres
The energy–Casimir method is applied to the problem of symmetric stability in the context of a compressible, hydrostatic planetary atmosphere with a general equation of state. Formal stability criteria for symmetric disturbances to a zonally symmetric baroclinic flow are obtained. In the special case of a perfect gas the results of Stevens (1983) are recovered. Finite-amplitude stability conditions are also obtained that provide an upper bound on a certain positive-definite measure of disturbance amplitude
Case History of Seismic Base Isolation of a Building –The Foothill Communities Law and Justice Center
The Foothill Communities Law and Justice Center, located in seismically active Southern California, is the first building in the United States to be base isolated for seismic resistance. Natural rubber isolators with layers of steel plates were used to make the fundamental period of vibration of the base isolated building about twice as long as that for a comparable conventional fixed base building. Most earthquake energy is present in the shorter period ranges, and at longer periods, a building should be subjected to less earthquake input; this will allow buildings to be designed more economically and increase the likelihood of less damage, both structural and non- structural. The experience of the Law and Justice Center after three small earthquakes suggest that the concept is not only feasible, but may be the wave of the future for what would be relatively short period buildings
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