On nonlinear wave groups and crest statistics

We present a second-order stochastic model of weakly nonlinear waves and develop theoretical expressions for the expected shape of large surface displacements. The model also leads to an exact theoretical expression for the statistical distribution of large wave crests in a form that generalizes the Tayfun distribution (Tayfun, J. Geophys. Res., vol. 85, 1980, p. 1548). The generalized distribution depends on a steepness parameter given by μ = λ3/3, where λ3 represents the skewness coefficient of surface displacements. It converges to the Tayfun distribution in narrowband waves, where both distributions describe the crests of all waves well. In broadband waves, the generalized distribution represents the crests of large waves just as well whereas the Tayfun distribution appears as an upper bound and tends to overestimate them. However, the theoretical nature of the generalized distribution presents practical difficulties in oceanic applications. We circumvent these by adopting an appropriate approximation for the steepness parameter. Comparisons with wind-wave measurements from the North Sea suggest that this approximation allows both distributions to assume an identical form with which we can describe the distribution of large wave crests fairly accurately. The same comparisons also show that third-order nonlinear effects do not appear to have any discernable effect on the statistics of large surface displacements or wave crests.

Cluster observations and theoretical identification of broadband waves in the auroral region

Broadband waves are common on auroral field lines. We use two different methods to study the polarization of the waves at 10 to 180 Hz observed by the Cluster spacecraft at altitudes of about 4 Earth radii in the nightside auroral region. Observations of electric and magnetic wave fields, together with electron and ion data, are used as input to the methods. We find that much of the wave emissions are consistent with linear waves in homogeneous plasma. Observed waves with a large electric field perpendicular to the geomagnetic field are more common (electrostatic ion cyclotron waves), while ion acoustic waves with a large parallel electric field appear in smaller regions without suprathermal (tens of eV) plasma. The regions void of suprathermal plasma are interpreted as parallel potential drops of a few hundred volts.

High-Order Optimized Numerical Schemes for Computational Aeroacoustics

This paper presents a new optimization approach for the high-order finite difference schemes. Due to the fact that it is common for a sound field to consist of several dominant wavenumbers, the proposed numerical schemes are optimized at these dominant wavenumbers instead of over a range of wavenumber. These optimized multi-component schemes, as referred to in this paper, give very accurate solutions if used to predict an acoustic wave traveling with these dominant wavenumbers. In addition, for broadband waves, it is shown that the performance of the optimized upwind multi-component scheme is comparable to that of the optimized upwind broadband scheme, which is optimized over a range of wavenumber. The results of the Fourier analysis also show that the optimized central multi-component schemes are at least comparable to if not better than the optimized central broadband schemes when solving broadband waves.

Multi-spacecraft observations of broadband waves near the lower hybrid frequency at the Earthward edge of the magnetopause

Broadband waves around the lower hybrid frequency (around 10 Hz) near the magnetopause are studied, using the four Cluster satellites. These waves are common at the Earthward edge of the boundary layer, consistent with earlier observations, and can have amplitudes at least up to 5 mV/m. These waves are similar on all four Cluster satellites, i.e. they are likely to be distributed over large areas of the boundary. The strongest electric fields occur during a few seconds, i.e. over distances of a few hundred km in the frame of the moving magnetopause, a scale length comparable to the ion gyroradius. The strongest magnetic oscillations in the same frequency range are typically found in the boundary layer, and across the magnetopause. During an event studied in detail, the magnetopause velocity is consistent with a large-scale depression wave, i.e. an inward bulge of magnetosheath plasma, moving tailward along the nominal magnetopause boundary. Preliminary investigations indicate that a rather flat front side of the large-scale wave is associated with a rather static small-scale electric field, while a more turbulent backside of the large-scale wave is associated with small-scale time varying electric field wave packets.Key words. Magnetospheric physics (magnetopause, cusp, and boundary layers) – Space plasma physics (waves and in-stabilities)