We describe the numerical implementation of a phase-resolving, nonlinear spectral model for shoaling directional waves over a mild sloping beach with straight parallel isobaths. The model accounts for non-linear, quadratic (triad) wave interactions as well as shoaling and refraction. The model integrates the coupled, nonlinear hyperbolic evolution equations that describe the transformation of the complex Fourier amplitudes of the deep-water directional wave field. Because typical directional wave spectra (observed or produced by deep-water forecasting models such as WAVEWATCH III™) do not contain phase information, individual realizations are generated by associating a random phase to each Fourier mode. The approach provides a natural extension to the deep-water spectral wave models, and has the advantage of fully describing the shoaling wave stochastic process, i.e., the evolution of both the variance and higher order statistics (phase correlations), the latter related to the evolution of the wave shape. The numerical implementation (a Fortran 95/2003 code) includes unidirectional (shore-perpendicular) propagation as a special case. Interoperability, both with post-processing programs (e.g., MATLAB/Tecplot 360) and future model coupling (e.g., offshore wave conditions from WAVEWATCH III™), is promoted by using NetCDF-4/HD5 formatted output files. The capabilities of the model are demonstrated using a JONSWAP spectrum with a cos 2s directional distribution, for shore-perpendicular and oblique propagation. The simulated
Using a dusty plasma ratchet, one can realize the rectification of charged dust particle in a plasma. To obtain the ratchet potential dominating the rectification, here, we perform quantitative simulations based on a two-dimensional fluid model of capacitively coupled plasma. Plasma parameters are firstly calculated in two typical cross sections of the dusty plasma ratchet which cut vertically the saw channel at different azimuthal positions. The balance positions of charged dust particle in the two cross sections then can be found exactly. The electric potentials at the two balance positions have different values. Using interpolation in term of a double-sine function from previous experimental measurement, an asymmetrical ratchet potential along the saw channel is finally obtained. The asymmetrical orientation of the ratchet potential depends on discharge conditions. Quantitative simulations further reproduce our previous experimental phenomena such as the rectification of dust particle in the dusty plasma ratchet.
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