Number Of Wavenumbers Research Articles

Multiscaled inviscid Taylor-Green vortex flow for examining energy conservation error in incompressible flows

This study investigates kinetic energy conservation errors in incompressible flows using multiplexed inviscid Taylor-Green vortices. Fourth-order precision Runge-Kutta methods, specifically five- and six-step methods, were employed and an inviscid two-dimensional periodic flow field was used as a test case. This method allows the energy conservation error to be suppressed to a very low level. Recent previous studies have dealt with turbulence generation using a multi-scale turbulence grid. In this study, the Taylor-Green vortex of the analytical solution is multiplexed to generate a flow field with a number of wavenumbers. Visualisation results of the initial field and the energy distribution over time were obtained. It was observed that the errors in the time evolution of the fluid energy were extremely small, and that the errors actually increased with time. However, the influence of the time step range was limited and the analytical and numerical solutions were in general agreement. As a result, it was confirmed that the inviscid Taylor-Green vortex is effective in examining the energy conservation error for incompressible flows.

High Resolution Wavenumber Analysis (HRWA) for the mechanical characterisation of viscoelastic beams

The High-Resolution Wavenumber Analysis (HRWA) is presented. It identifies complex wavenumbers and amplitudes of waves composing the harmonic response of a beam. Based on the frequency dependence of these wavenumbers, experimental dispersion equations of various beam mechanisms (e.g bending, torsion) can be retrieved. The HRWA method is compared to the Mc Daniel and the Inverse Wave Correlation (IWC) methods. It overcomes some drawbacks of these methods: the wavenumber resolution is enhanced. Also, the wavenumber search problem is expressed as a linear problem, making the method computationally efficient. A number of wavenumbers can be identified automatically, thanks to a statistical criterion. First, the noise sensitivity of each method is investigated in the basis of synthesised measurements. For this criterion, the HRWA and Mc Daniel method performances are close and much better than IWC. Moreover, the HRWA is five to twenty times faster to compute than other methods, depending on the mesh size. Second, an experimental case is presented where bending and torsion waves are identified, yielding an apparent viscoelastic Young and shear moduli on a wide-frequency range.

On the stability of two-dimensional convection rolls in an infinite Prandtl number fluid with stress-free boundaries

Numerical solutions for two-dimensional convection rolls in a fluid layer of infinite Prandtl number are obtained by the Galerkin method. Stress-free, isothermal boundaries are assumed at the horizontal boundaries of the fluid layer. The stability of the steady solutions with respect to three-dimensional disturbances is analyzed in the Rayleigh number-wave number space. It is found that even for Rayleigh numbers as high as several millions there appears to exist a region of the wavenumber α where the convection rolls are stable. This result contrasts with the well known transition to three-dimensional bimodal convection in the presence of no-slip boundaries, but it agrees with simple arguments about the stability of the thermal boundary layers.

Barotropic instability of flow along a trench

Abstract The linear stability of a laterally sheared barotropic flow along a trench is analyzed. The depth and mean flow profiles used in the model are piecewise constant and piecewise linear, respectively. As a consequence the stream function and dispersion relation describing the perturbation field can be written in terms of elementary functions. The dispersion relation, being a quartic in the wave frequency, yields four neutral wave modes: two shear waves, a shelf wave and a trench wave. An instability arises when two shear wave dispersion curves coalesce or when one of the shear wave curves coalesces with either a shelf or a trench wave dispersion curve. Further, because of the quartic nature of the dispersion relation, the stability diagrams can have overlapping regions of instability in Rossby number—wavenumber space. The model is applied to the Alaskan Stream off Kodiak Island, where infrared satellite images reveal the presence of wavelike temperature fronts with scales of either 90–100 km or 30–4...