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.     

Inter-annual variability in larval supply to populations of three invertebrate taxa in the northern California Current

We investigated sources of inter-annual variability in larval supply to crab and sea urchin populations at Bodega Head and Point Reyes in northern California. During the spring and summer upwelling seasons of the years 1992 through 1997 we monitored the weekly settlement rates of nine species of crabs and two species of sea urchins. As observed in previous studies, daily values of alongshore windstress, temperature and salinity provided evidence for the poleward flow of relatively warm, low salinity water from south of Point Reyes, an apparent retention zone, during upwelling relaxation events. In years dominated by these events (1992, 1993, 1995 and 1996) we observed that alongshore windstress, temperature and salinity were coherent and temperature was significantly correlated with cancrid crab settlement. During these years the magnitude of cancrid crab settlement and the fraction of cancrid crabs relative to other crab species settling were high. Over four years of concurrent sampling there was consistently greater cancrid crab settlement at the Point Reyes site, within the retention zone, than at Bodega Head. Settlement of non-cancrid crabs (porcellanids, grapsids, pagurids and majids) was not as closely linked to intra-annual patterns of upwelling and relaxation, possibly due to the shorter seasonal availability of larvae allowing for the influence of fewer relaxation events. Settlement of this group among years was positively correlated with environmental indicators of strong seasonal upwelling; high salinity, Bakun upwelling index and low temperature. Sea urchin settlement events were observed in June and July of 1992, 1994 and 1997 during warming periods when salinity and temperature were increasing and alongshore windstress was low. Across the six years of the study, we found that cancrid crab larvae had a more even seasonal availability than larvae of non-cancrid species, which settled in greatest numbers during the early portion of the upwelling season. Sea urchins settled in greatest numbers during the later part of the upwelling season. Together these patterns demonstrate the taxon-specific way that inter-annual variability in larval supply is forced by the coincidence of larval availability with favorable physical transport mechanisms.     

Multi-bioindicator study of a small estuary in Vendée (France)

Surficial sediment (about 5 mm) was scraped off in 15 stations selected in the Vie Estuary, a small estuary on the French Atlantic coast. The samples, prepared using the suitable methods, were used for comparing the behaviour of periphytic algae, sporopollinic and other palynologic material, ostracoda and foraminifera for proposing a synthetic evaluation of the information provided by each of them. Dinoflagellate cysts, which are found in an almost monospecific assemblage in low-salinity water, are dispersed by tidal currents, but the location of tintinnids in only the lower reaches shows a limited inward transport. Sporopollinic material is clearly related to the adjacent vegetation, indicating a local origin, and then little influence of transport on the microbenthos, even if fragments of freshwater crustaceans and of Pediastrum alga are found down to the mouth in the sporopollinic deposits. This limited transport of microbenthos allows the use of periphytic algae, benthic ostracoda and benthic foraminifera as indicators of local environmental conditions. It was then possible to determine the extent of marine influence in the estuary, to discriminate between the main channel and adjacent basins, and between different stages of evolution of the basins, from a recently dug basin to a eutrophicated one.     

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.     

Recent developments in “added-mass” planing theory

The results of several recent isolated investigations in planing theory are consolidated in this paper, together with new insights generated by a recent numerical solution of the vertically impacting wedge problem by Zhao and Faltinsen [(1992), Water entry of two-dimensional bodies. J. Fluid Mech. 246, 593–612]. As a result, in contrast to some earlier studies, it is found that the “wetted width” associated with the added mass is not that of the intersection of the wedge with the undisturbed water surface, but the wetted width of the splashed-up water, as originally proposed by Wagner [(1932), Uber Stoss-und Gleitvorgange an der Oberflache von Flussig-Keiten, Zeitschrift für Angewandte Mathematik und Mechanik, Band 12, Heft 4 (August)]. However, the splash-up ratio is not the value of (π/2–1) which he proposed, but a value which decreases with increasing deadrise, originally proposed in the late-1940s by Pierson (“Pierson's hypothesis” in the paper). For 30° deadrise, for example, Pierson's splash-up ratio is two-thirds that of Wagner's.The new equations are employed to determine the increase in the “added mass” of prismatic hull sections due to chine immersion, using experimental data. If m_o^′ is the added amss of the hull section whose chines are just wetted, Payne [(1988), Design of High-speed Boats. Volume 1: Planing. Fishergate, Inc., Annapolis, Maryland, U.S.A.] postulated that the increase in added mass due to a chine submergence (z_c) would be

where b is the chine beam and k is a constant which Payne [(1988), Design of High-speed Boats. Volume 1: Planing. Fishergate, Inc., Annapolis, Maryland, U.S.A.] gave as .The present analysis includes the “one-sided flow” correction introduced in Payne [(1990), Planing and impacting forces at large trim angels. Ocean Engng 17, 201–234]. Partly for that reason and partly because of the more precise analysis of the experimental data, the present paper revises the value to k = 2 for wetted length to beam ratios normally employed. For deadrise angles in excess of 40° and wetted keel to beam ratios in excess of 2.0, there is some evidence that k < 2.0.The revised theoretical formulation is compared with eight different sets of experimental data for flat plate and prismatic hull forms and is found to be in excellent agreement when the speed is high enough for “dynamic suction” (a loss of buoyancy at low speeds and low wetted lenghts) to be unimportant. This is true for “chines-dry” operation with deadrise angles up to 50° and chines-wet operation at length to beam ratios far in excess of the most extreme conventional practice.The research involved in performing this analysis led to the realization that different towing tanks measure different wetted chine lengths for the same hulls and test conditions. Some consistently measure more splash-up than “theory” (based on Pierson's splash-up hypothesis) predicts and others measure somewhat less than the theory. Some examples are given in Appendix B. The reason for this is not understood.     

Dissolved carbon and 33-133-133-1anomalies in the water column caused by hydrocarbon seeps on the northwestern Gulf of Mexico slope

Alkalinity, dissolved inorganic carbon (DIC), and ¹³C profiles from seep sites on the northwestern Gulf of Mexico upper slope show anomalously negative ¹³C values of up to –4.5 PDB, increased levels of DIC of up to 2.45 mmole/liter, and slight alkalinity rises of up to 2.54 meq/liter, relative to water column profiles from a seep-free site (0.63, 2.04 mmole/liter, and 2.39 meq/liter). The observed DIC enrichments coupled with the¹³C-depletions are attributed to the release of CO₂ by microbial oxidation of crude oil in the seep environment, and its migration into the water column. The ¹³C composition of the migrating CO₂ is estimated to be –26.0 on the basis of dissolved carbon inventory. Manifestation of DIC and ¹³C anomalies in the water column caused by hydrocarbon seepage holds promise to be useful for hydrocarbon reconnaissance surveys over large offshore tracts on account of the simplicity of sampling acquisition, and rapidity of analytical techniques in the laboratory.     

Particulate flux in the water column overlying Santa Monica Basin

Fluxes of particulate carbon, nitrogen, phytoplankton pigments, biogenic silica and dry mass were measured using free-floating and moored sediment trap arrays in the Santa Monica Basin during the period from October 1985 to August 1990 as part of the California Basin Study (CaBS) Program. In field testing for potential sources of sediment trap biases, we found little significant or consistent difference in rate estimates between short-term drifting traps and long-term moored traps, between preserved and unpreserved traps in short-term experiments, between different preservatives (mercury or formalin) in long-term experiments, between different designs of small cylindrical traps, and between deep-moored cylindrical traps and large conical traps. We did, however, find that sediment trap samples collected and analyzed on 0.45 μm silver filters gave estimates of carbon and nitrogen fluxes about 25% higher than samples collected on GF/F glass-fiber filters. Concurrent trap deployments at two stations 18km apart revealed low mesoscale variability in flux estimates. Seasonal patterns in carbon and nitrogen flux were not evident in our data, but strong seasonality, with spring maxima and summer minima, were observed for fluxes of phaeopigments and biogenic silica out of the euphotic zone.Time-averaged rates of particulate flux for long-term trap deployments from January to August 1990, were 121, 18.8, 1.5, 67 and 633mg m⁻²d⁻¹ at 110–135m for carbon, nitrogen, phaeopigment, biogenic silica and mass, respectively. Flux estimates to the basin floor (835–860m) were 50, 6.5, 0.64, 41.6 and 575mg m⁻²d⁻¹ for the same parameters. The former estimates are constrained by and in good agreement with independent assessments of new production from nitrate uptake in the euphotic zone. The latter agree with rates previously inferred from the sedimentary record using ²¹⁰Pb as a tracer. In addition, the difference in carbon estimates in the water column between the euphotic zone and the basin floor is consistent with the requirements for bacterial growth and metabolism at intermediate depths as measured by the thymidine method.