Predicting significant wave height off the northeast coast of the United States

To develop a simple method to predict the significant wave height, we analyze 18 years of hourly observations from 12 different buoys that are off the northeast coast of the United States. Water depths ranged from 19 to 4427 m for these moored buoys. We find that, on average, all of these buoys exhibit a region of constant wave height for 10-m wind speeds between 0 and 4 m s⁻¹. That wave height does, however, depend on water depth. For wind speeds above 4 m s^–1, the wave height increases as the square of the wind speed; but the multiplicative factor is again a function of water depth. We synthesize these results in a prediction scheme that yields the significant wave height from simple functions of water depth and 10-m wind speed for wind speeds up to 25 m s^–1.     

On wavelet analysis of nonstationary turbulence

Wavelets are new tools for turbulence analysis that are yielding important insights into boundary-layer processes. Wavelet analysis, however, has some as yet undiscussed limitations: failure to recognize these can lead to misinterpretation of wavelet analysis results. Here we discuss some limitations of wavelet analysis when applied to nonstationary turbulence. Our main point is that the analysis wavelet must be carefully matched to the phenomenon of interest, because wavelet coefficients obscure significant information in the signal being analyzed. For example, a wavelet that is a second-difference operator can provide no information on the linear trend in a turbulence signal. Wavelet analysis also yields no meaningful information about nonlinear behavior in a signal — contrary to claims in the literature — because, at any instant, a wavelet is a single-scale operator, while nonlinearity involves instantaneous interactions among many scales.     

The minimum gap-opening planet mass in an irradiated circumstellar accretion disc

We consider the minimum mass planet, as a function of radius, that is capable of opening a gap in an α-accretion disc. We estimate that a half-Jupiter mass planet can open a gap in a disc with accretion rate     for viscosity parameter  α= 0.01  , and solar mass and luminosity. The minimum mass is approximately proportional to     . This estimate can be used to rule out the presence of massive planets in gapless accretion discs. We identify two radii at which an inwardly migrating planet may become able to open a gap and so slow its migration; the radius at which the heating from viscous dissipation is similar to that from stellar radiation in a flared disc, and the radius at which the disc becomes optically thin in a self-shadowed disc. In the inner portions of the disc, we find that the minimum planet mass required to open a gap is only weakly dependent on radius. If a migrating planet is unable to open a gap by the time it reaches either of the transition radii, then it is likely to be lost on to the star. If a gap-opening planet cuts off disc accretion allowing the formation of a central hole or clearing in the disc then we would estimate that the clearing radius would approximately be proportional to the stellar mass.