Dynamics of “critical” trajectories

Two diagnostic dynamic models for flow in hyperbolic and elliptic regions of a geophysical fluid are developed and compared. As the main interest here is in local dynamical processes, these models are used to study trajectories near stagnation points in the flow field. The simplest model presumes a balance between the Coriolis and geopotential accelerations. This model is equivalent to the classic approach that characterizes these regimes by the quadratic equation for the eigenvalues of the velocity gradient. However, since that model imposes geostrophic dynamics, the eigenvalues of the velocity gradient can be replaced by the local curvature or Hessian of the geopotential scaled by Coriolis. The general model adds both local and inertial accelerations to the dynamical balance. In contrast to the classic result the consequent frequency equation is a quartic that involves both the Hessian of the geopotential field, the components of the velocity gradient, and Coriolis. Roots of this equation give two distinct time scales, which are interpreted as Lagrangian time scales. Motion of the geopotential field produces a third Eulerian time scale. Critical trajectories are those whose initial positions and velocities are such that they are independent of the Lagrangian time scales. These simple models establish that within hyperbolic and elliptic regions of the geopotential field there may be trajectories whose time scales differ radically from even their nearest neighbors.A characteristic of critical trajectories in the ocean is that they often are found near stagnation points. These may be hard to identify even in model simulations, but a similar quantity, the null in the geopotential gradient, might be easier to obtain. To analyze the relation between the critical trajectories, stagnation points, and gradient null, evolution models for the later two objects are proposed. For a steady geopotential all three coincide. However with a time varying geopotential, they are distinct even though all have the same time scale. The analysis provides a metric for the separation of all three objects.     

A note on “overfishing”

The continuing public concern with overfishing ignores the underlying problems that face fishery mangers. Attention needs to be given to (1) the transitory nature of the ocean environment, (2) the natural variation in fish stocks, (3) the role of the fishing industry and market forces in fishery management, and (4) the failure to focus on what it is we most need from the oceans, in what form we need it, and at what price.     

The “separation formula” and its application to the Pacific Ocean

The “separation formula”, a new method for computing the adiabatic inter-hemispheric meridional transport, is applied to the Pacific Ocean. The method involves an integration of the wind stress along a “horseshoe” path. It begins at the separation point of the East Australian Current, continues eastward across the ocean, progresses northward along the continental boundary, and then turns back westward across the ocean to the separation point of the Kuroshio. Since the Pacific is closed on the northern side, such an integration gives the wind-driven Indonesian throughflow.The analytical formulas show that, in order for the adiabatic wind-driven throughflow to exist, it is necessary that there be an asymmetry in the winds associated with the two zonal cross-sections connecting the (northern and southern) separation points in the west to the continents in the east. It turns out that these asymmetries in the Pacific are relatively small and, consequently, do not allow for a significant (i.e. more than one Sverdrup) Indonesian transport. Specifically, in the Pacific, this wind-driven transport is directed to the south, implying a very small net Indian-to-Pacific transport rather than a Pacific-to-Indian transport. The adiabatic model fails, therefore, to explain the observed Pacific-to-Indian throughflow of 5-6 Sv.When an upwelling is added to the model (to simulate diabatic processes), then one obtains the result that all the water upwelled in the Pacific must exit the Pacific via the Indonesian seas, i.e. the wind field is effectively blocking the oceanic region between Australia and South America, forcing the upwelled water into the Indian Ocean. This model suggests, therefore, that the observed Pacific-to-Indian throughflow is a measure of the upwelling in the Pacific.     

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.     

A correcting “prism” for underwater viewpoints

The angular field observable in water by an observer in air depends on the configuration of the air-water interface. When the interface is a plane, the absolute limit to observable field is about from the normal to the interface. A practical limit, because of lateral chromatic aberration is considerably less, approximately 30°. A conventionally used configuration in research submersibles, is a polymethyl methacrylate port with inner and outer surfaces parallel. This has the same optical limitations as the plane air-water interface. It is shown that if the inner and outer surfaces are not required to be parallel to each other, there are solutions which permit extending the observable field to nearly a full hemisphere with acceptably small distortion and lateral chromatic aberration.     

Sealevel changes associated with hurricane “Gloria”

Gloria was a fast-moving, intense hurricane that grazed the North Carolina coastline in September, 1985. The resulting storm surge was measured remotely using a telephone-linked wave data system as well as a local tide gage. The surge was hindcast using the model of Jelesnianski (1967) which was developed for shore-parallel storm tracks. The agreement with measurement was quite satisfactory. The data suggest extremely rapid rise times for the peak surge of hurricanes moving at high speed along the coast.     

Heated diver decompression shelter: The “womb concept”

A hybrid thermal protection method using waste heat from a surface-mounted outboard motor is shown to create a warm “micro-climate” environment for divers. The effects of surface heater capacities, water flow rates, shelter volume and shelter insulation on micro-climate temperatures are characterized. During long, cold-water decompression stops this method offers a reliable, low-cost alternative to surface-supplied hot water suits or diver-carried heating systems. An added bonus for divers using closed-circuit breathing apparatus is prolonged durations of their carbon dioxide scrubbers when surrounded by the warm water “micro-climate”. Closed-circuit and open-circuit options of this diver decompression shelter concept are evaluated.     

Multiple “stable” states and the conservation of marine ecosystems

Marine ecosystems were among the first to provide potential examples of multiple stable states. However, remarkably few of these have been explored in detail, and none have been rigorously confirmed. This may be because differences between alternative states are too subtle to document in the context of regular disturbance, because one state is naturally far more likely to occur than any other, or because most environments naturally support only one type of stable community. It is also possible that the temporal and spatial criteria required to document alternate stable states rigorously may be too difficult to meet in most circumstances. Nevertheless, the possibility of alternative stable states has recently received renewed attention in the context of marine conservation biology. People may be widening the range of habitats in which alternate stable states are possible, or they may be shifting communities to new domains of attraction that rarely occur in the absence of massive anthropogenic perturbations. The ability of people now to alter ocean ecosystems on global scales may eliminate “edge effects” that might otherwise rescue perturbed communities. Ecosystems with alternate stable states are characterized by positive feedback mechanisms that stabilize transitions; even if return to original conditions is predicted (that is, the alternate states are not stable), the same mechanisms will retard recovery. This may explain in part why return to original conditions following anthropogenic disturbance is slower than expected. Slow recovery times and transitions to new states are both potentially costly to human societies. Thus, from a conservation perspective the indefinite persistence of an alternate state may be less important than the presence of feedback loops that slow recovery. Both possibilities reinforce the arguments for application of the precautionary principle in managing marine ecosystems.     

Age of settlement and accumulation rate of submarine “coralligène” (−10 to −60 m) of the northwestern Mediterranean Sea; relation to Holocene rise in sea level

Morphological and chronological studies have been carried out on coralline algal buildups (“coralligène”) situated between 10 and 60 m depth near Marseilles, and in Corsica (France). Despite the presence of occasionally sizeable quantities of iron hydroxide, these constructions prove to be a reliable material for radiocarbon dating. Ages obtained using this method range from 640±120 yrs B.P. (Corsica, Scandola Natural Reserve, −15 m) to 7760±80 yrs B.P. (Marseilles, Grand Congloue, −52 m). Internal erosion surfaces within the buildups give evidence of discontinuous development. The accumulation rate of the coralligène constructions is very low (0.006–0.83 mm yr⁻¹ according to the depth and time period). The higher values (0.53–0.83 mm yr⁻¹) were recorded for the deeper constructions. They correspond to a period between 8000 and 6000 yrs B.P. After 6000 yrs B.P., the only appreciable accumulation rates (0.11–0.42 mm yr⁻¹) were recorded for constructions situated between 10 and 35 m depth, whereas the accumulation rates of deep coralligène (> 50 m) appear to be low or zero. The age of the large constructions (overhang: 80 cm in width) is positively correlated with depth (r = 0.95; p < 0.005). Their development occurred during the Flandrian transgression. The oldest structures, today situated at 50 to 60 m depth, started to develop when water depth was probably no greater than 10 to 15 m. Apart from in strongly shaded fissures on rocky coasts and areas subjected to heavy sedimentation, the main framework building algal species was initially Mesophyllum lichenoides (Ellis) Lemoine, a high tolerant species to light, hydrodynamic energy and temperature. With the rise in sea level, the coralligène structure gradually became available to other less tolerant algal species (Lithophyllum, Lithothamnion), and the crustforming population diversified. Because of the good preservation of coralligène structures, the reliability of radiocarbon dating and the correlation between the age and bathymetric position of the large coralligène structures (except in areas of heavy sedimentation and fissures in shallow rocky coasts), these buildups are considered to be of use as biological indicators of variations in sea level.