“…The streamwise spatial Fourier transform of this field performed across the whole experimental domain is shown in figure 3( b ), where a sharp peak is observed around , followed by secondary peaks at higher wavenumbers. Such behaviour of the Fourier transform of frequency-varying signals is common in other frequency modulated signals, such as chirps and linear time-delayed signals (Cook & Bernfeld 1967), and analytical assessment of such phenomena can be performed using asymptotic methods, such as the method of stationary phase (Murray 1984). Figure 3.Mean pressure at the centreline educed from data and from different fitting functions for .…”
Section: Spectral Characteristics Of the Shock-cell Structurementioning
This paper explores the screech closure mechanism for different axisymmetric modes in shock-containing jets. While many of the discontinuities in tonal frequency exhibited by screeching jets can be associated with a change in the azimuthal mode, there has to date been no satisfactory explanation for the existence of multiple axisymmetric modes at different frequencies. This paper provides just such an explanation. As shown in previous works, specific wavenumbers arise from the interaction of waves in the flow with the shocks. This provides new paths for driving upstream-travelling waves that can potentially close the resonance loop. Predictions using locally parallel and spatially periodic linear stability analyses and the wavenumber spectrum of the shock-cell structure suggest that the A1 mode resonance is closed by a wave generated when the Kelvin–Helmholtz mode interacts with the leading wavenumber of the shock-cell structure. The A2 mode is closed by a wave that arises owing to the interaction between the Kelvin–Helmholtz wave and a secondary wavenumber peak, which arises from the spatial variation of the shock-cell wavelength. The predictions are shown to closely match experimental data, and possible justifications for the dominance of each mode are provided based on the growth rates of the absolute instability.
“…The streamwise spatial Fourier transform of this field performed across the whole experimental domain is shown in figure 3( b ), where a sharp peak is observed around , followed by secondary peaks at higher wavenumbers. Such behaviour of the Fourier transform of frequency-varying signals is common in other frequency modulated signals, such as chirps and linear time-delayed signals (Cook & Bernfeld 1967), and analytical assessment of such phenomena can be performed using asymptotic methods, such as the method of stationary phase (Murray 1984). Figure 3.Mean pressure at the centreline educed from data and from different fitting functions for .…”
Section: Spectral Characteristics Of the Shock-cell Structurementioning
This paper explores the screech closure mechanism for different axisymmetric modes in shock-containing jets. While many of the discontinuities in tonal frequency exhibited by screeching jets can be associated with a change in the azimuthal mode, there has to date been no satisfactory explanation for the existence of multiple axisymmetric modes at different frequencies. This paper provides just such an explanation. As shown in previous works, specific wavenumbers arise from the interaction of waves in the flow with the shocks. This provides new paths for driving upstream-travelling waves that can potentially close the resonance loop. Predictions using locally parallel and spatially periodic linear stability analyses and the wavenumber spectrum of the shock-cell structure suggest that the A1 mode resonance is closed by a wave generated when the Kelvin–Helmholtz mode interacts with the leading wavenumber of the shock-cell structure. The A2 mode is closed by a wave that arises owing to the interaction between the Kelvin–Helmholtz wave and a secondary wavenumber peak, which arises from the spatial variation of the shock-cell wavelength. The predictions are shown to closely match experimental data, and possible justifications for the dominance of each mode are provided based on the growth rates of the absolute instability.
Abstract-Characterization of a propagation channel is essential in developing an optimum wireless system. Accurate prediction of field parameters, both stochastic and deterministic can greatly reduce the time and effort required to design and develop a progression of prototypes necessary to achieve the final system requirements. To accomplish this, a physics-based methodology must be considered. In this methodology, a series of scattering and diffraction models must be developed and integrated which accurately represent the effects of various terrain features on electromagnetic wave propagation. In this paper, diffraction of electromagnetic waves from a surface impedance discontinuity, which can represent a river or trough is considered. In order to more accurately represent the transmitter antenna, dipole excitation is used as the wave source. The river or trough is modeled as a variable impedance insert in an infinite plane with one-dimensional (1-D) variation. An integral equation for an impedance surface is formulated in the Fourier domain, which is solved iteratively using a perturbation technique. An analytical solution is provided to any desired order in terms of multifold convolution integrals of the Fourier transform of the impedance function. The far-field integral is then evaluated using the stationary phase technique. Next, the formulation is extended to a short dipole with arbitrary orientation by expanding the dipole field in terms of a continuous spectrum of plane waves. Results are then shown for both plane wave and dipole excitation. Scattering results for an impedance insert are generated up to second order. These results are then compared to geometrical theory of diffraction (GTD) results. The effect of varying both the width and perturbation parameter of the insert are described. Results from plane wave incidence at various oblique angles are shown. Effects of varying the impedance transition shape are shown and compared. Scattering results for dipole excitation show E-field components in a planar grid at a given height above the scattering plane. It is shown that theẑ component of the diffracted field is maximized for either a vertical or horizontal dipole orientation. Effects generated by varying the receiver height are also discussed.
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