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Wave-induced bottom shear stress estimation in shallow water exemplified by using deep water wind statistics

Myrhaug D.

Oceanologia

2017

No. 59 (2)

102--107

The paper provides a simple and analytical method which can be used to give estimates of the wave-induced bottom shear stress for very rough beds and mud beds in shallow water based on wind statistics in deep water. This is exemplified by using long-term wind statistics from the northern North Sea, and by providing examples representing realistic field conditions. Based on, for example, global wind statistics, the present results can be used to make estimates of the bottom shear stress in shallow water.

The influence of wave-noise on wave speeds and amplitudes of surface-gravity waves

Murawski K., Zawada A.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2004

Vol. 8, No 3

321-326

We have analytically examined surface-gravity waves which propagate in space- and time-dependent random velocity fields. Using a perturbative method, we have derived a dispersion relation which is solved for the case of wave-noise whose spectrum E(k,omega) ~ E(k)delta(omega-crk), where delta is Dirac's delta-function and cr is the random phase speed. We have found that for a dispersionless noise resonance occurs when cr is equal to the group velocity cg of the surface-gravity wave. In this resonance the real part of the wave frequency is finite, but its imaginary part exhibits the characteristic 1/x singularity. The wave-noise interacts with a packet of the surface-gravity waves in such a way that the waves are attenuated for cr < cg and are amplified for cr > cg. As the real part is positive for high values of k, the surface-gravity waves are accelerated by the wave-noise.

Sound waves in a wave noise

Murawski K., Tarnowski M.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2004

Vol. 8, No 1

103-108

We examine by analytical and numerical means sound waves which propagate in a space- and time-dependent random mass density field in the form of dispersionless wave noise of its spectrum E(kappa,omega) ~ E(kappa) delta (omega-crk), where cr is a random speed. Numerical simulations are in agreement with the analytical theory which shows that at cr=omega/k resonance occurs and the cyclic frequency omega tends to infinity. For values of cr which are close to the resonance point, the sound waves are slowed down and attenuated (accelerated and amplified) for cr < omega/k (cr > omega/k).

Numerical simulations of sound wave generation in a random medium

Murawski K., Selwa M.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2004

Vol. 8, No 1

109-114

In turbulent media, both sound wave sources and the speed of sound can be stochastic variables. By means of numerical simulations of one-dimensional Euler equations with random source terms we have studied two cases in a homogeneous stochastic random medium for which the speed of sound and sound sources are: (1) correlated and (2) uncorrelated. The numerical simulations indicate that, if the source and the speed of sound fluctuations are uncorrelated, the acoustic field is incoherent, with a zero expectation value. The mean field is non-zero in the correlated case. The correlated and uncorrelated cases are clearly distinguishable by the mean field, but also - to some extent - in the power spectrum, which displays a modified Lorentzian profile with a shift in frequency.