Simulation of green water flow on deck using non-linear dam breaking theory

Experiments carried out with models of floating production, storage and offloading platforms (FPSOs) showed that the flow of water over the deck edge, onto the deck resembled a suddenly released wall of water rather than a breaking wave. Therefore green water flow onto the deck was simulated using dam breaking theory, but the theory’s shallow-water assumptions may be limiting. In this paper a non-linear dam breaking problem is formulated. Equations of motion in the Lagrangian form are used and the solution is sought as an infinite series in time. Comparisons with the shallow water approximation are carried out.     

Robust adaptive control of underactuated ships on a linear course with comfort

This paper addresses an important problem in ship control application—the robust stabilization of underactuated ships on a linear course with comfort. Specifically, we develop a multivariable controller to stabilize ocean surface ships without a sway actuator on a linear course and to reduce roll and pitch simultaneously. The controller adapts to unknown parameters of the ship and constant environmental disturbances induced by wave, ocean current and wind. It is also robust to time-varying environmental disturbances, time-varying change in ship parameters and other motions of the ship such as surge and heave. The roll and pitch can be made arbitrarily small while the heading angle and sway are kept to be in reasonably small bounds. The controller development is based on Lyapunov’s direct method and backstepping technique. A Lipschitz continuous projection algorithm is used to update the estimate of the unknown parameters to avoid the parameters’ drift due to time-varying environmental disturbances. Simulations on a full-scale catamaran illustrate the effectiveness of our proposed controller.     

A nitrate and silicate budget in the equatorial Pacific Ocean: a coupled physical–biological model study

A coupled physical–biological model was developed to simulate the low-silicate, high-nitrate, and low-chlorophyll (LSHNLC) conditions in the equatorial Pacific Ocean and used to compute a detailed budget in the Wyrtki box (5°N–5°S, 180–90°W) for the major sources and cycling of nitrogen and silicon in the equatorial Pacific. With the incorporation of biogenic silicon dissolution, NH₄ regeneration from organic nitrogen and nitrification of ammonia in the model, we show that silicon recycling in the upper ocean is less efficient than nitrogen. As the major source of nutrients to the equatorial Pacific, the Equatorial Undercurrent provides slightly less Si(OH)₄ than NO₃ to the upwelling zone, which is defined as 2.5°N–2.5°S. As a result, the equatorial upwelling supplies less Si(OH)₄ than NO₃ into the euphotic zone in the Wyrtki box, having a Si/N supply ratio of about 0.85 (2.5 vs. 2.96 mmolm⁻² day⁻¹). More Si(OH)₄ than NO₃ is taken up with a Si/N ratio of 1.17 (2.72 vs. 2.33 mmolm⁻² day⁻¹) within the euphotic zone. The difference between upwelling supply and biological uptake is balanced by nutrient regeneration and horizontal advection. Excluding regeneration, the net silicate and nitrate uptakes are nearly equal (1.76 vs. 1.84 mmolm⁻² day⁻¹). However, biogenic silica export production is slightly higher than organic nitrogen (1.74 vs. 1.59 mmolm⁻² day⁻¹) following a 1.1 Si/N ratio. In the central equatorial Pacific, low silicate concentrations limit diatom growth; therefore non-diatom new production accounts for most of the new production. Higher silicate supply in the east maintains elevated diatom growth rates and new production associated with diatoms dominate upwelling zone. In contrast, the new production associated with small phytoplankton is nearly constant or decreases eastward along the equator. The total new production has a higher rate in the east than in the west, following the pattern of surface silicate. This suggests that silicate regulates the diatom production, total new production, and thereby carbon cycle in this area. The modeled mean primary production is 48.4 mmolCm⁻² day⁻¹, representing the lower end of direct field measurements, while new production is 15.0 mmolCm⁻² day⁻¹, which compares well with previous estimates.     

Modeling bed-load transport of coarse sediments in the Great Bay Estuary, New Hampshire

Current, sea level and bed-load transport are investigated in the Lower Piscataqua River section of the Great Bay Estuary, New Hampshire, USA—a well-mixed and geometrically complex system with low freshwater input, having main channel tidal currents ranging between 0.5 and 2 m s⁻¹. Current and sea level forced by the M₂M₄M₆ tides at the estuarine mouth are simulated by a vertically averaged, non-linear, time-stepping finite element model. The hydrodynamic model uses a fixed boundary computational domain and accounts for flooding–drying of tidal flats by making use of a groundwater component. Inertia terms are neglected in comparison with pressure gradient and bottom friction terms, which is consistent with the observed principal dynamic balance for this section of the system. The accuracy of hydrodynamic predictions in the study area is demonstrated by comparison with four tidal elevation stations and two cross-section averaged current measurements. Simulated current is then used to model bed-load transport in the vicinity of a rapidly growing shoal located in the main channel of the lower system. Consisting of coarse sand and gravel, the shoal must be dredged every five to eight years. Two approaches are taken—an Eulerian parametric method in which nodal bed-load flux vectors are averaged over the tidal cycle and a Lagrangian particle tracking approach in which a finite number of sediment particles are released and tracked. Both methods yield pathways and accumulations in agreement with the observed shoal formation and the long-term rate of sediment accumulation in the shoal area.     

Thermal structures in the Kuroshio extension measured with a towed thermistor chain

Two-dimensional temperature data observed by use of a 275 meter towed thermistor chain deployed from an oceanographic research vessel USS MARYSVILLE, which cruised with a speed of 6.2 knots in July 1966 across the Kuroshio Extension in the North Pacific, are investigated. Two-dimensional variations of the distribution of the isotherms along the ship's track are analyzed with special reference to their slope, wavelength and wave height. The results show that the slope and wave height of isotherms have a tendency to increase as the temperature decreases. Even if the contribution of wave heights smaller than 1.5 m is neglected, i.e., contribution of large scale slope with a horizontal scale of 5–30 km is subtracted, this tendency is still detected. In contrast to this, the wavelength evaluated by the crest to crest method has no dependency on the temperature. Power spectrum of the isotherm depth is proportional tok ^–1.87 for 13°C andk ^–2.13 for 27°C, wherek is the wave number. It is shown that the spectra of warmer isotherms are relatively well approximated by –2 power law (Garrett and Munk spectrum) for internal waves rather than the –5/3 power law (Kolmogorov spectrum) for three dimensional isotropic turbulence.