The continuous dynamical modes of the exchange flow in the Bab al Mandab are computed in an attempt to assess the hydraulic character of the flow at the sill. First, an extended version of the Taylor-Goldstein equation for long waves that accounts for cross-channel topographic variations, is developed. A series of calculations using idealized background velocity U(z) and buoyancy frequency N(z) are presented to illustrate the effects of simple topographic cross sections on the internal modes and their speeds. Next, hydrographic and direct velocity measurements from April to November 1996 using moored CTDs and a bottom-mounted ADCP are utilized to construct monthly mean vertical profiles of N 2 (z) and at the U(z) sill. An analytical approximation of the true topography across the strait is also constructed. The observed monthly mean profiles are then used to solve for the phase speeds of the first and second internal modes. Additional calculations are carried out using a selection of ''instantaneous'' (2-h average) profiles measured during extremes of the semidiurnal tide. The results are compared with a three-layer analysis of data from the previous year. Many of the authors' conclusions follow from an intriguing observation concerning the long-wave phase speeds. Specifically, it was nearly always observed that the calculated speeds c Ϫ1 and c 1 of the two waves belonging to the first internal mode obey c Ϫ1 Ͻ U min Ͻ U max Ͻ c 1 , where U min and U max are the minimum and maximum of the velocity profile. An immediate consequence is that neither wave has a critical level. For monthly mean profiles, each of which have U min Ͻ 0 Ͻ U max , the flow is therefore subcritical (the phase speeds of the two waves have opposite signs). For instantaneous profiles this relationship continues to hold, although the velocity profile can be unidirectional. Thus the flow can be critical (c Ϫ1 ϭ 0 and/or c 1 ϭ 0) or even supercritical (c Ϫ1 and c 1 have the same sign) with respect to the first mode. Similar findings follow for the second baroclinic mode phase speeds (c Ϫ2 and c 2). The authors conclude that hydraulically critical flow is an intermittent feature, influenced to a great extent by the tides. It is noted that the phase speed pairs for each mode lie very close to U min and U max. As suggested by the analysis of idealized profiles, this behavior is characteristic of flows that are marginally stable, perhaps as a result of prior mixing. This suggestion is supported by Richardson number (Ri) profiles calculated from the monthly mean and instantaneous data. Middepth values of Ri were frequently found to be O(1) and sometimes Ͻ1/4, a result consistent with the presence of mixing over portions of the water column.
The expanding deployment of sensor systems that capture location, time, and multiple thematic variables is increasing the need for exploratory spatio-temporal data analysis tools. Geographic information systems (GIS) and time series analysis tools support exploration of spatial and temporal patterns respectively and independently, but tools for the exploration of both dimensions within a single system are relatively rare. The contribution of this research is a framework for the visualization and exploration of spatial, temporal, and thematic dimensions of sensor-based data. The unit of analysis is an event, a spatio-temporal data type extracted from sensor data. The conceptual framework suggests an approach for design layout that can be flexibly modified to explore spatial and temporal trends, temporal relationships among events, periodic temporal patterns, the timing of irregularly repeating events, event–event relationships in terms of thematic attributes, and event patterns at different spatial and temporal granularities. Flexible assignment of spatial, temporal, and thematic categories to a set of graphical interface elements that can be easily rearranged provides exploratory power as well as a generalizable design layout structure. The framework is illustrated with events extracted from Gulf of Maine Ocean Observing System data but the approach has broad application to other domains and applications in which time, space, and attributes need to be considered in conjunction.
Chaotic advection is suggested as a possible mechanism for fluid exchange and mixing among a western boundary current and subbasin recirculation gyres. Applications include the North Atlantic Deep Western Boundary Current and its adjacent mesoscale recirculation gyres. Visualization and quantification of certain aspects of chaotic advection in a laboratory analog are described. Depending on the strength of the forcing, recirculating fluid offshore of the western boundary layer may be contained in a single gyre (not favorable for chaotic advection) or twin gyre with a ''figure-eight'' geometry (favorable for chaotic advection). When time dependence is imposed on these steady flows by varying the forcing periodically, the resulting fluid exchange, stirring, and mixing is most dramatic in the case of the twin gyre. A template for these processes can be formed by highlighting certain material contours (invariant manifolds) using dye and other techniques. These objects can be used to identify blobs of fluid (turnstile lobes) that are carried into and out of the gyres. The associated transports and flushing times can be estimated. The preferential stirring and mixing in the twin-gyre case is quantified by calculating the effective diffusivity of the flow field based on snapshots of the dye fields at longer times. The experiment suggests how tracers in a western boundary current might be transported into and out of neighboring recirculations and where regions of strong zonal or meridional transport might occur.
This paper presents capabilities of the EventViewer, a graphical user interface for visualizing and exploring patterns in events. The EventViewer supports queries on events stored in an events database and exploration of various temporal and spatial patterns in events. Interactions in the EventViewer interface allow users to select events from the database, assign spatial, temporal and thematic categories to graphic display elements called bands, stacks, and panels which causes events to be displayed according to their associations with the user selected categories. The spatial, temporal and thematic categories can be rearranged among the bands, stacks and panels thus changing the view of events and causing different patterns to become apparent. The EventViewer support exploration of periodic patterns, spatial and temporal trends, and event-event relationships. The EventViewer functionality is illustrated with oceanographic events extracted from the Gulf of Maine Ocean Observing system sensor data. Events are extracted from multiple time series variables collected at a number of locations and depths in the Gulf of Maine.
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