39,539 research outputs found
Alternative statistical-mechanical descriptions of decaying two-dimensional turbulence in terms of "patches" and "points"
Numerical and analytical studies of decaying, two-dimensional (2D)
Navier-Stokes (NS) turbulence at high Reynolds numbers are reported. The effort
is to determine computable distinctions between two different formulations of
maximum entropy predictions for the decayed, late-time state. Both formulations
define an entropy through a somewhat ad hoc discretization of vorticity to the
"particles" of which statistical mechanical methods are employed to define an
entropy, before passing to a mean-field limit. In one case, the particles are
delta-function parallel "line" vortices ("points" in two dimensions), and in
the other, they are finite-area, mutually-exclusive convected "patches" of
vorticity which in the limit of zero area become "points." We use
time-dependent, spectral-method direct numerical simulation of the
Navier-Stokes equations to see if initial conditions which should relax to
different late-time states under the two formulations actually do so.Comment: 21 pages, 24 figures: submitted to "Physics of Fluids
Rotor dynamic state and parameter identification from simulated forward flight transients, part 1
State and parameter identifications from simulated forward flight blade flapping measurements are presented. The transients were excited by progressing cyclic pitch stirring or by hub stirring with constant stirring acceleration. Rotor dynamic inflow models of varying degree of sophistication were used from a one parameter inflow model (equivalent Lock number) to an eight parameter inflow model. The maximum likelihood method with assumed fixed measurement error covariance matrix was applied. The rotor system equations for both fixed hub and tilting hub are given. The identified models were verified by comparing true responses with predicted responses. An optimum utilization of the simulated measurement data can be defined. From the numerical results it can be anticipated that brief periods of either accelerated cyclic pitch stirring or of hub stirring are sufficient to extract with adequate accuracy up to 8 rotor dynamic inflow parameters plus the blade Lock number from the transients
Methods Studies on System Identification from Transient Rotor Tests
Some of the more important methods are discussed that have been used or proposed for aircraft parameter identification. The methods are classified into two groups: Equation error or regression estimates and Bayesian estimates and their derivatives that are based on probabilistic concepts. In both of these two groups the cost function can be optimized either globally over the entire time span of the transient, or sequentially, leading to the formulation of optimum filters. Identifiability problems and the validation of the estimates are briefly outlined, and applications to lifting rotors are discussed
A note on multi-dimensional Camassa-Holm type systems on the torus
We present a -component nonlinear evolutionary PDE which includes the
-dimensional versions of the Camassa-Holm and the Hunter-Saxton systems as
well as their partially averaged variations. Our goal is to apply Arnold's
[V.I. Arnold, Sur la g\'eom\'etrie diff\'erentielle des groupes de Lie de
dimension infinie et ses applications \`a l'hydrodynamique des fluides
parfaits. Ann. Inst. Fourier (Grenoble) 16 (1966) 319-361], [D.G. Ebin and J.E.
Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid.
Ann. of Math. 92(2) (1970) 102-163] geometric formalism to this general
equation in order to obtain results on well-posedness, conservation laws or
stability of its solutions. Following the line of arguments of the paper [M.
Kohlmann, The two-dimensional periodic -equation on the diffeomorphism group
of the torus. J. Phys. A.: Math. Theor. 44 (2011) 465205 (17 pp.)] we present
geometric aspects of a two-dimensional periodic --equation on the
diffeomorphism group of the torus in this context.Comment: 14 page
- …