Ocean currents may cause vortex induced vibrations (VIV) of deep-water umbilicals and cables. Since the VIV response may give significant contributions to the total fatigue damage it is important to know the structural damping for relevant curvature levels.
A laboratory test has been performed on a 12.5 m long test specimen to determine the damping for a range of curvature levels that are in the vicinity of the stick-slip transition region. The energy input to maintain steady state oscillations with curvature amplitudes in the range 0.0002–0.001 m−1 was measured. The steady state energy input is consistent with damping ratios obtained using the free decay method.
The structural damping depends on construction temperature and curvature and is less for typically low seawater temperature and low curvatures. The transition between the stick- and the slip regime is seen for typical seawater temperature.
An algorithm for solving the steady-state Schrödinger equation for a complex piecewise-constant potential in the presence of theE-field is developed and implemented. The algorithm is based on the consecutive matching of solutions given by the Airy functions at the band boundaries with the matrix rank increasing by no more than two orders, which enables the characteristic solution to be obtained in the convenient form for search of the roots. The algorithm developed allows valid solutions to be obtained for the electric field magnitudes larger than the ground-state energy level, that is, when the perturbation method is not suitable.
Inertial-range scaling laws for two- and three-dimensional turbulence are re-examined within a unified framework. A new correction to Kolmogorov's k−5/3 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.
Calculating the Energy Spectrum of Complex Low-Dimensional Heterostructures in the Electric Field
