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Essentially two classes of free edge waves can exist on a sloping continental shelf in the presence of Coriolis force. For small longshore wave length, fundamental waves of the first class behave like Stokes edge waves. However, for great wave lengths (of several hundred kilometers or more) the characteristics of the first class are significantly altered. In the northern hemisphere the phase speed for waves moving to the right (facing shore from the sea) exceeds the speed for waves which move to the left. Also, the group velocity for a given edge wave mode has a finite upper limit. Waves of the second class are essentially quasigeostrophic boundary waves with very low frequency and, like Kelvin waves, move only to the left (again facing shore from the sea). Unlike Stokes edge waves, those of the quasigeostrophic class are associated with large vorticity. Examination of the formal solution for forced edge waves indicates that those of the second class may be excited significantly by a wind stress vortex. Also, in contrast to the conclusion of Greenspan (1956), it is proposed that a hurricane can effectively excite the higher order edge wave modes in addition to the fundamental if wind stress is considered.

The well-known Rhines theory of bottom-trapped topographic Rossby waves (TRW) in a uniformly stratified ocean over a sloping seabed, and its dispersion relation between wave frequency and wavenumber components, have served a very useful purpose in prompting recognition of the existence of TRW in the ocean and in motivating the search for sources of such disturbances. However, in quantitative studies of backward ray tracing of bottom-trapped Rossby waves for source search purposes, a realistic profile of the buoyancy frequency N(z) within the water column ought to be taken into account. Toward this goal an analytic solution for linear, quasigeostrophic, topographic Rossby waves for an ocean having regionally distinct exponential profiles of buoyancy frequency is offered.

We describe observations of large amplitude wind-driven current oscillations of 24-hr period occurring in the near-surface layer of waters of the Texas-Louisiana continental shelf. The near-surface anti-cyclonic current amplitudes can reach 60 cm s−1 and represent the largest non-storm induced high-frequency currents on the shelf. These currents can persist for a week or more, as long as driving diurnal winds persist with uninterrupted phase. The latitude of the shelf and the diurnal period of the wind-forcing combine to produce conditions for a near-resonant response of the surface currents to the wind stress, such that, the resulting currents are almost an order of magnitude greater than those found from steady Ekman drift. The oscillations are phase-locked to time of day suggesting a connection to the daily cycle of heating and cooling. The oscillations generally occur during the summer months when there is a shallow mixed layer, strong vertical stratification, maximum insolation, and infrequent frontal passages.

The primary objective of this work is to formulate surface meteorological fields over the northwestern Gulf of Mexico for the period from April 1992 through November 1994 useful for the study of mesoscale processes and for model forcing of the near-coastal circulation. Observations were adjusted to standard heights, and a method of statistical interpolation was applied to time series of in situ observations to produce the required surface fields. Resulting monthly and seasonal mean fields show two principal patterns over the Texas-Louisiana shelf region—for summer and nonsummer. From June through August, surface winds are relatively constant, with alongshore wind components generally directed upcoast (from Mexico toward the Mississippi Delta). In other (nonsummer) months, surface winds are much more variable with alongshore wind components generally directed downcoast. The relatively large interannual variability is illustrated. Using these meteorological fields together with rather complete ocea...

Hourly wind fields for the northwestern Gulf of Mexico (here called LATEX winds) were constructed from in situ measurements for the period April 1992 through November 1994 using statistical (optimal) interpolation. Here the LATEX winds are compared with the National Centers for Environmental Prediction (NCEP) and the European Remote Sensing Satellite (ERS-1) scatterometer winds for the same period and region. Comparisons show no significant bias between LATEX and ERS-1 wind speeds or directions. LATEX and ERS-1 wind fields nearly coincide except during extreme meteorological events when ERS-1 fields may show noncoherent patterns over distances for which coherence is expected; for those situations, LATEX winds appear more realistic. Although there is no significant bias between wind speeds, the direction bias is more than 10° between the LATEX and NCEP winds. The largest differences between LATEX and NCEP winds occurred near the coast. In summer, the NCEP and LATEX winds showed larger differences ...

On the basis of current measurements observed at 31 moorings during April 1992 through November 1994, as part of the Texas-Louisiana Shelf Circulation and Transport Processes Study, we describe the horizontally nondivergent part of the near-surface, shelf-wide-scale, low-frequency circulation and its variability on the Texas-Louisiana continental shelf by means of objectively fitted stream function fields. The 32-month mean velocity stream function patterns generally support the Cochrane and Kelly [1986] circulation schema for the shelf circulation, in which an elongated cyclonic gyre exists during the nonsummer period (September through May) but with flow in the summer (June to August) directed upcoast (toward the Mississippi delta) over the entire shelf. There exists significant interannual variability of the stream function fields, especially in the transition period from spring to summer to fall and along the shelf break. Strong upcoast (downcoast) currents dominate at the western shelf break associated with the presence of energetic anticyclones (cyclones). The dominant pattern of stream function variability deduced by empirical orthogonal function (EOF) analysis of 32 individual monthly mean patterns contains about 89% of the variance and shows a simple, shelf-wide, along-shelf pattern of circulation. The monthly evolution in amplitude of this dominant EOF pattern clearly mimics the monthly evolution of the along-shelf component of the wind with squared correlation of 0.83. This provides strong evidence that the seasonal variation of the shelf circulation is wind forced, in support of Cochrane and Kelly. The second and residual EOFs show more complex features near the shelf break that are associated with Loop Current eddies known to impact the continental slope and shelf break.

We analyzed 81 current meter records of varying lengths (3 to 30 months) to describe the principal diurnal (O1, K1, P1, and Q1) and semidiurnal (S2, M2, K2, and N2) tidal current constituents on the Texas-Louisiana continental shelf. The Louisiana-Texas Shelf Physical Oceanography Program (LATEX) had 81 current meters at 31 sites and varying depths from April 1992 to December 1994. The local inertial period range across the shelf (24.4 hours to 26.2 hours) and thermal diurnal cycling during the summer season make it difficult to estimate the diurnal tidal constituents. Dominant tidal modes on the shelf are K1, O1, and M2. Absolute and relative energy contained in each tidal constituent varies with shelf location. The northeast corner of the shelf, near Atchafalaya Bay, has the largest tidal currents with maximum surface current amplitudes (at 3 m depth) of about 9 cm s−1, while typical maximum tidal surface currents near the shelf break are between 1 and 2 cm s−1 for each of the K1, O1, and M2 components. In general, the surface tidal currents decrease in magnitude as water depth increases toward the shelf break, although the semidiurnal components are amplified more at midshelf locations than the diurnal components. Examination of tidal ellipses at different depths suggests that the M2 tide has less vertical structure, while the diurnal tides exhibit more shear, particularly at the more shallow locations. Sea surface height constituents estimated at five locations along the Texas-Louisiana coast are in agreement with historical values.

Low-frequency circulation over the Texas-Louisiana continental shelf is examined. Currents over the inner shelf are upcoast (Rio Grande to Mississippi River) in summer and downcoast in nonsummer and are driven by an annual cycle of winds. This results in an annual signal for salinity, with lowest salinity waters occurring (a) in late spring along the inner portion of the western shelf when downcoast flows carry the high discharges from the Mississippi-Atchafalya and other rivers to the Mexican border, and (b) in summer over the inner and outer eastern shelf when the upcoast flow causes a pooling of the discharges from the Mississippi-Atchafalya rivers over that shelf. Upcoast winds during summer also result in high salinities over the western shelf due to advection from off Mexico and upwelling. Currents over the outer shelf are variable, but predominantly upcoast throughout the year, probably a result of the integrated effects of anticy-clonic eddies impinging on the shelf edge. Comparison of currents in the weather band (2-10 d) with the mesoscale band (10-100 d) suggests the shelf is divided at approximately the 50-m isobath. The weather band predominates over the inner shelf, reflecting frequent passage of fronts over the region. The mesoscale band predominates over the outer shelf, indicating the presence of offshelf eddies that frequent this region.

We address four independent sources of observational evidence pertaining to circulation in the Bay of Campeche (BOC), located south of 23°N in the western Gulf of Mexico, with the objective of characterizing its mean circulation, its variability, and the probable forcing thereof. The observational information includes historic hydrographic and dissolved oxygen data, Lagrangian current data, satellite-derived sea surface height anomaly (SSHA), and special observations of marine winds in the BOC. The hydrographic data reveals that the mean surface circulation relative to 425 db and to 800 db includes a weak cyclone with cyclic transport of about 4x10 6 m 3 .s -1 . Ten years of near-surface drifter observations shows a statistically meaningful mean cyclonic pattern of current with westward intensification that is consistent with the mean surface dynamic topography relative to 800 db. Observations of mean currents in the BOC at 900 m based on deep floats by G. L. Weatherly and others allows estimation of the current shear from the Lagrangian data and this is geostrophically consistent with that from the dynamic topography relative to 800 m. The mean cyclonic wind stress curl field deduced from two sources of marine wind data indicate a forced Sverdrup transport consistent with that observed. Moreover a seasonal cycle is suggested in the near surface drifter data that is coherent with the seasonal signal in the wind stress curl. Finally, the historic SSHA for a period of over 8 years in the 1990s allows a characterization of the dominant empirical spatial patterns and their temporal variability.

We analyzed 1397 drifter records collected in the Gulf of Mexico and northwestern Cayman Basin between the years 1989 and 1999 to describe the general features of the upper ocean circulation. These drifters were generally drogued at 50 m below the surface and exclude those of the Surface CUrrent Lagrangian Program (SCULP). In addition to the dominant flows through the Yucatan Channel and Straits of Florida, robust circulation features clearly seen include: a weak cyclone south of 21°N in the Bay of Campeche, westward zonal flow across the Gulf between 21°N and 24°N, a northward western boundary current between 95°W and 97°W and 24°N and 26°N, mean downcoast (westward) flow on the Texas-Louisiana shelf, highly variable mean flow on the shelves and slope of the northeastern Gulf, mean upcoast (southward) flow on the lower West Florida Shelf, and a large region of high variability in the deep regions of the central Gulf of Mexico. Although much of the driving of the Gulf of Mexico is attributed to currents associated with the Loop Current and its associated Loop Current Eddies (particularly in the deep waters), other features can be directly correlated with seasonal wind driving, particularly on the shelves of the northern Gulf, near the western boundary, and in the Bay of Campeche.

On the basis of hydrographic data collected by the Texas-Louisiana Shelf Circulation and Transport Processes Study (LATEX A) and on earlier cruises, we examined the energetic scales of spatial variability over the Texas-Louisiana continental shelf. Shelf-scale spatial reference fields were sought to represent the general distributions of circulation and water properties over the shelf at the time of the observations. Various methods were explored for determining such reference fields of potential temperature, salinity, and geopotential anomaly at the sea surface relative to 70 dB. Spatial reference fields obtained from mean May fields and from polynomials fitted to individual May cruise data were compared. On the basis of those comparisons, quadratics were selected to fit property distributions from individual cruises and so to yield reference fields. Smaller-scale anomaly fields were obtained by removing the reference fields from the observed distributions. Calculation of correlation versus separation distance based on these anomaly fields then allowed estimation of spatial scales of anomaly fields for cross-shelf and along-shelf transects. The zero-crossing scale and the Gaussian decay scale are shown to be essentially the same, and the zero-crossing scale is used. The principal results for the anomaly scales are (1) cross-shelf scales over the western shelf are shorter (order 15 km) than those in the eastern and central regions (order 20 km), (2) along-shelf spatial scales are of the order of 35 km, (3) there is no significant difference in cross-shelf scales at the surface, middepth, and bottom, and (4) along-shelf scales are essentially the same over the western and eastern regions of the shelf, over the midshelf (50-m isobath) and along the shelf break (200-m isobath), and at different depths along the 200-m isobath. The same spatial scales are found when using data with spatial resolution of 1–10 km cross shelf and 10–20 along shelf to obtain the anomaly fields, so the data resolution used is adequate to represent the scales. The variances of the observed (shelf-wide) salinity, temperature, and geopotential anomaly are greater cross shelf than along shelf. The variance of the cross-shelf anomaly fields is around 10% of the shelf-wide fields; that of the along-shelf anomaly fields is about 35% of that in the shelf-wide fields. The analysis of scales when grouped by season did not show persuasive evidence of seasonal variation.

Wind-induced, near-inertial oscillations over the Texas-Louisiana shelf in spring and summer 1992 are described using the current and wind observations taken during the first year of the Texas-Louisiana Shelf Circulation and Transport Processes Study (LATEX A). Rotary spectral analysis shows clockwise-rotating energy peaks at near-inertial frequencies for records from all current meter moorings after the suppression of principal tidal signals. The vertical structure of near-inertial oscillations is characterized by a first baroclinic mode with a near 180° phase difference between the upper mixed layer and the lower stratified layer. The oscillations are intermittent with a modulation timescale of about 5–10 days. They are surface-intensified and have maximum values near the shelf break, decaying gradually toward the coast but rapidly offshore. Near-inertial oscillations appear to accompany a sudden change of the wind stress during frontal passages. Diagnostic analysis suggests that the large near-inertial oscillations over the LATEX shelf are mainly generated by high-frequency (near-inertial) variation of the wind stress accompanying the passage of atmospheric fronts. When the downward transfer of the near-inertial energy to the deep stratified layer is small, a simple mixed layer model forced by the observed wind stress provides a reasonable prediction of the near-inertial currents in the mixed layer.

A major difficulty with two‐layer ocean models, except in the linear approximation, is encountered in situations where the interface intersects the seabed. For the single mode, reduced‐gravity version it is assumed that a passive deep lower layer exists everywhere, which in fact precludes any influence by bathymetry. These restrictions can be removed by employing a realistic continuous density stratification. Discussed here is a generalized, equivalent barotropic model in isopycnic coordinates that is based on the gravest vertical structure function E(σ) for current determined by the global, levelled‐state density distribution. The eigenvalue problem employs a rigid‐lid condition at the sea surface and requires E = 0 (a vanishing current) at the seabed for each local depth h. The gravest mode has monotonie E(σ) and an associated eigencelerity that is typical of a first baroclinic mode. Both the structure function and the celerity (hence the Rossby deformation radius) depend on the local depth h. ...

Oil spill trajectory models are one of the few tools that can help response teams stay ahead of an oil slick, but the process of trajectory modeling requires many time-consuming steps. Hydrodynamic modeling, used to generate the current forecasts required by trajectory models, can consume hours of operator and computer run-time. The Texas General Land Office and the Texas Water Development Board have automated the daily operation of hydrodynamic models to produce current forecasts for two Texas bays. Each midnight, computers running the hydrodynamic models for Galveston Bay and Corpus Christi Bay download the latest water level measurements from a real time tide gage network. The models use this data to produce a 2-day forecast of the currents for the two bay systems. In the event of a spill, the trajectory modeling team retrieves the recently generated current forecasts for immediate input to the trajectory model. Model automation saves two hours in computer run-time alone for these two bays. Along similar lines for the offshore environment, Texas A&M University is developing an automated gridded wind forecasts and a wind-driven, shelf circulation (spectral) model to predict near-surface current patterns and velocities along the inner Texas shelf on an operational basis.

Abstract Discussed are mean vectors and variance ellipses for currents at selected levels, from the sea surface to 2000 m, as well as near bottom in the Gulf of Mexico. The fields presented are based on record-length mean currents from a circulation model hindcast for model years 1993-1998. Background We have examined more than eight million hours of current meter records from the deep water region of the Gulf of Mexico (water depths greater than 200 m). However, the spatial and temporal coverage represented by that information is woefully inadequate to characterize the general circulation of the region. Here we characterize the principal features of the mean circulation based on the output from a numerical circulation model for the Gulf of Mexico developed by Dr. Lakshmi Kantha and colleagues at the University of Colorado with partial support from an industry-sponsored study on Climatology and Simulation of Eddies (CASE). The model is a version of the Princeton Ocean Model adapted for the Gulf of Mexico, referred to by the acronym CUPOM. The horizontal resolution is 1/12° and the vertical resolution is 24 sigma levels. The model hindcast used was for the years 1993 through 1998. The model assimilates altimeter data for the region with water depth of 1000 m or more. It also assimilates satellite sea surface temperature data, but uses climatological sea surface salinity. The 6-hourly wind stresses from the European Centre for Medium-range Weather Forecasting at 1.125° resolution are used for the wind forcing. The inflow boundary is at 21.333°N across the Yucatan Channel, with a physically balanced inflow prescribed using typical monthly temperature and salinity profiles. The outflow boundary is at the Florida Straits; the boundary condition is set to be balanced and in phase with the inflow boundary. The data assimilation module is the same as in Horton et al. (1997) and Clifford et al. (1997). Details of the specifics with respect to the Gulf of Mexico can be found in Kantha et al. (1999). Results Using the CUPOM hindcasts for 1993-1998, we produced time series animations and record-length mean fields of current vectors and variance ellipses at the sea surface, 500 m, 1000 m, 2000 m, and the first sigma level above the sea bed. Fig. 1 shows record-length current vectors at the sea surface for the Gulf of Mexico. The principal feature in the surface field is the Loop Current, and within the loop there is a closed anticyclone just northwest of Cuba. In contrast to observations, no southward flow to the Caribbean Sea is seen west of Cape San Antonio, Cuba, because the boundary conditions just to the south specify only flow into the Gulf. Strong flow is also seen over the continental shelves of the southern and western Gulf as well as within the deepwater portion of the western basin. The variance ellipses (not shown) for the surface currents are largest for the region of the Loop Current and indicate highest variability in a direction normal to the inflowing and outflowing limbs of that current.

Abstract Empirical orthogonal function (EOF) analysis was performed on current meter records and model outputs in the deep regions of the Gulf of Mexico. The results of the EOF analysis were similar for model and observation stations located on the continental slope and rise. The vertical structure of modes, generally, shows a surface-intensified mode containing a high percentage of total variance and a bottom-intensified nearbarotropic mode beginning at roughly 800 m and extending to the bottom. Introduction We examined current meter records and model outputs of the University of Colorado Princeton Ocean Model (CUPOM) to construct empirical orthogonal functions (EOFs) which describe the vertical current structure in the deep Gulf of Mexico. EOF analysis, also known as principal component analysis, has become an accepted tool to quantify patterns of variability present in large sets of time-series data1. To facilitate analysis of the EOF modal time series, all EOFs done in this paper used singular value decomposition (SVD) to provide both the modal amplitudes and principal component time series. Further, both east-west (U) and north-south (V) current velocity EOFs were done simultaneously. Therefore, percentages of variance reported are based on the variance contained in both the U and V time series. Data Current meter observations. Analyzed were datasets that consisted of simultaneous point measurements of current velocity of 5 or more distinct depths and which lasted at least 4 months2. Initial EOF analysis concentrated on observations in water depths greater than 700 m during the period 1980-1988. The analysis was done on raw unfiltered data from the eastern, central, and western Gulf of Mexico. The analysis was performed using those data that were available at all depth levels, i.e., irrespective of any temporal gaps. CUPOM data. Model data were generated from a version of the Princeton Ocean Model adapted for the Gulf of Mexico. The model has 1/12° horizontal resolution and 24 vertical sigma levels. The model hindcast covered the years 1993-1998. EOF analysis of model output was performed using data from cross-and along-isobaths as well as from single locations. The across-isobath lines went from 200-3000 m total depth across the continental slope at longitudes 88°, 90°, 92°, 94°, and 96°W and across the slope meridionally in the eastern and western Gulf at 26°N. Along-isobath lines were in the central Gulf along the 500, 1000, and 2000-m isobaths between 89°W and 94°W. In this paper we concentrate on the along-isobath line at 2000 m and the cross-slope line at 90°W (Fig. 1). Results Fig. 2 illustrates the typical modal structure seen from slope locations around the northern Gulf of Mexico. The data used to construct the modes of Fig. 2 were from CUPOM model year 1993 and taken near 27.2°N and 89.9°W and at the edge of the Sigsbee Escarpment. Unfiltered hourly current velocity time series at all 24 sigma levels were used to construct the EOF modes.

Abstract Energetic current events occurring in the deep water region of the Gulf of Mexicoare identified, including especially: surface-intensified eddies; deep barotropic motions, sometimes with bottom intensification; atmospheric storm-generated motions, and mid-water current jets. We have searched for such events in the literature, measurements, and numerical model output, seeking situations where the magnitudes of currents over the period of an event are considerably greater than the background currents for the region or for situations where the current characteristics were known to be associated with a particular class of event. Examples of the major classes of energetic current events are shown. Suggestions are made for additional measurements and knowledge needed. Introduction With the exception of a few individuals (e.g., Pequegnat1), the common belief of a decade or more ago was that energetic currents in the Gulf of Mexico were confined to the upper waters-surely no deeper than the sill of the Yucatan Channel (approximately 2000 m) and perhaps not much deeper than the sill at the Florida Straits (800 m). Now we recognize a number of classes of currents in the deep waters of the Gulf, and some are known to extend to the greatest depths in that basin. These currents have been the focus of many recent measurements and studies supported by the oil and gas industry and the Minerals Management Service of the U.S. Department of the Interior. Improved characterization of these currents and their causal mechanisms will lead to improved design criteria for, and to estimation and mitigation of impacts on, technology for ultra-deep water oil and gas exploration and production. Here we briefly discuss and present examples of currents from the deep water region of the Gulf. Classes of currents considered are:currents resulting from energetic, episodic atmospheric events (e.g., tropical cyclones such as hurricanes, extratropical cyclones, and cold air outbreaks);surfaceintensified currents arising from major surface circulation features (i.e., the Loop Current, the anticyclonic eddies derived there from, both cyclonic and anticyclonic eddies spun up in the Gulf; and other low-frequency circulation features driven by local wind stress distributions);currents extending from about 800 m through the deeper water column, sometimes with bottom intensification; andhigh-speed, subsurface-intensified currents. Observations Currents caused by energetic atmospheric events. Perhaps the class of phenomena that longest has been of concern to oil and gas operators comprises those currents resulting from strong, episodic wind events. In the Gulf of Mexico there are three general classes of such events: tropical cyclones (especially hurricanes), extratropical cyclones, and cold air outbreaks. These episodic events can result in extreme waves and can cause currents with speeds of 100-150 cm/s over the continental shelves. Recent examples are given in Nowlin et al.2 who also show that such currents reach significant speeds even at depths of 500 m over the slope.

Abstract Currents were generally surface intensified, with speeds reaching ~200 cm/s in association with energetic events such as passage of a Loop Current Eddy or intense atmospheric storm. A minimum in current speed occurred at about 800-1000 m depth. But maximum speeds can reach 120 cm/s at about 2000 m. Bottom intensification was present. Horizontal spatial decorrelation scales were smaller in the transverse direction than longitudinal. Introduction Over 8 million hours of current records were assembled as part of the Gulf of Mexico Deepwater Physical Oceanography Reanalysis and Synthesis of Historical Data Study, sponsored by the Minerals Management Service (MMS). Data assembled were from the area bounded by the shelf edge (approximately the 200-m isobath) of the northern Gulf of Mexico and the 25°N latitude line. Data extended from the sea surface to the sea floor in water depths from 200 m to over 3000 m. Additionally, a seven year (1993-1999) circulation model run was completed using the high-resolution University of Colorado Princeton Ocean Model (CUPOM) for the Gulf of Mexico1. Current records and the output of the CUPOM run were examined to characterize currents and estimate horizontal scales of deep flow in the Gulf of Mexico. Results The characterization of the currents was examined using the observational data base. Because of a lack of concurrent observational data with adequate spatial resolution, the horizontal scales were estimated using the CUPOM output for 1993. Observations. All current records of good quality were compiled to show the percentage of time that unfiltered currents exceeded various speed thresholds as a function of depth ranges. Because currents below about 800 m in the Gulf generally are nearly barotropic, and because deep observations are scarce, we used the large depth range of 1200 m to the sea bed to obtain a reasonable sample size for the deep layer. Results indicate that currents above 200 m exceed 75 cm/s about 2% of the time and 100 cm/s almost 1% of the time. The fastest currents are near surface and percents for all speed bins decrease rapidly with depth above 800 m. Currents below 800 m are normally rather coherent in the vertical, sometimes with bottom intensification. Below 1200 m the currents exceeded 40 cm/s about 0.6% of the time, which is greater than for the depth interval of 800–1200 m; this is evidence of bottom intensification. For each current record, a current rose and persistence table were produced. These can be examined to study the effects of energetic current events, such as occur with passage of the Loop Current, associated eddies, or hurricanes and other intense atmospheric storms. For example, mooring I1 was deployed for MMS in water depth of 2001 m in the northcentral Gulf just south of the Sigsbee Escarpment.

The proper design of a pipe line for the transport of gas or oil from sea to land requires the solution of a number of engineering problems either not encountered in pipe line engineering on land or found to be of a different nature in the marine environment than in the terrestrial environment. These include: (l) consideration of the vertical stability of the pipe, (2) consideration of the lateral stability of the pipe and its vertical risers in the presence of wave-induced forces, and (3) consideration of the longitudinal stability of the pipe in the presence of thermally induced tensile and compressive forces. The first of these considerations is treated in the present paper.

Dispersion of a dense effluent continuously discharged into a stream of constant velocity is considered. The Navier-Stokes equations and advection-diffusion equation for density are solved numerically for the fields of flow and density downstream from the discharge port. The numerical results appear to simulate the dispersal of effluents within a broad density range, they satisfy certain conservation requirements and approach analytical solutions of the linearized equations for effluents of low density anomaly.

Frequency-wavenumber spectra of sea surface temperature and wind-stress curl are computed from 11 years of surface marine observations taken in the eastern North Pacific. These data were averaged by month and 2° quadrangles to yield spectra with periods from 2 to 48 months and zonal wavelengths from 400 to 4000 km. Spectra were computed for all 2° zonal bands between 16 and 40°N using data from the area between 120 and 160°W. Missing monthly values led to the computation of these spectra using a least-squares Fourier expansion which eliminated the need for temporal interpolation. Frequency spectra computed with this technique compare well with spectra using standard Fourier methods. The resulting spectra were found to separate naturally into two regions; one between 29 and 40°N and the second between 15 and 29°N. Even within these zonal bands there were some important north–south changes. The annual signal was found to dominate the spectra of sea surface temperature at almost all wavelengths. The...

A finite difference approximation to the equations of motion without the field acceleration terms, and the salt conservation equation with an isotropic diffusion coefficient, are used to model the circulation of a rectangular basin having the gross dimensional characteristics of a bar-built estuary. The recursion relations include the dynamic effects of horizontal salinity variations. Two cases are examined; in the first case the basin has a constant depth and in the second case the bottom slope varies linearly across the basin. The resulting patterns of circulation are qualitatively analyzed using a vorticity equation. The analysis indicates that the dynamic effects of horizontal salinity gradients can be significant in controlling the circulation in localized sections of the basin.

A radiational condition compatible with a weakly dispersive governing equation for tsunami waves is developed for use at the open lateral boundaries of a limited-domain propagation model. A Boussinesq-type governing equation for the interior is adopted. The resulting open boundary condition (OBC) is a modified Sommerfeld condition, in which the effects of weak dispersion, geometric spreading and shoaling are allowed. The OBC is applied along wave ray characteristics which intersect the open boundary obliquely. The numerical implementation employs Lagrange interpolations in two dimensions from information on a regular grid in the interior region. Test results indicate that the numerical boundary is highly transparent to incident waves in the absence of bottom topography. Weak dispersion effects (Airy dispersion, Poincare dispersion and nonlinear dispersion) are faithfully reproduced in the test simulations. The effects of topography (reflection, refraction, and diffraction), which are not included in the OBC, result in some contamination of the solutions. However, the first few leading waves are free from serious error. Also the contamination due to topography near the open boundaries is sporadic and does not produce a cumulative effect. The modified OBC is shown to be a very significant improvement over the simple nondispersive Sommerfeld radiation condition.

In order to clarify some inconsistencies in the literature, on ocean energetics, the evaluation of the available potential energy (APE) is reconsidered. Attention is focused on the baroclinic APE under conditions in which the hydrostatic approximation prevails. Following Margules and Lorenz (ML), we define this as the difference between the total enthalpy of a given sample state of the fluid and that of an isentropically leveled state having the same mass. It is partly gravitational potential energy and partly elastic internal energy. For emphasis, we denote this as the ML APE. It differs from the gravitational part (APEg) by an amount that depends on whether the elastic internal energy is released (as in the atmosphere) or stored (as in the ocean) during an isentropic leveling process. In the ocean the ML APE is found to be somewhat less than the APEg, in contrast to the atmosphere where the ML APE greatly exceeds the APEg. This difference is ascribed to the temperature dependency of compressibi...

In evaluating current environmental protection policy, economists often note that current regulations are more costly than necessary to meet environmental quality standards. While the a priori case is strong that current regulatory approaches are resulting in higher-than-necessary costs to attain environmental standards, there is relatively little empirical evidence to support this claim. The purpose of this paper is to supply some of the missing evidence by presenting the results of one study that assesses some of the potential savings associated with implementing economic, rather than command-and-control, regulatory approaches to abate one type of air pollution in one region of the country. Specifically, the paper examines the costs of meeting a prospective short-term standard for nitrogen dioxide under a range of alternative emissions control strategies for stationary sources of nitrogen oxide emissions in the Chicago Air Quality Control Region. The alternative strategies that are considered range from those that might result under current regulatory policy to those that economic policy approaches (such as emissions charges or marketable permits) are designed to implement. The analysis shows that the most efficient program of emissions controls may be more than an order of magnitude less costly than current regulatory strategies, and that economic approachesmore » have additional advantages over more conventional regulatory approaches. 12 references, 3 tables« less

A time-dependent numerical model, which treats fully evolved wind-driven canopy flow as a coupled two-layer system, is developed. The interfacial stress is formulated in terms of a coupling coefficient and the flow differential. The resistance afforded by a vegetative canopy is parameterized in terms of a drag coefficient and dimensional properties of the canopy elements. With flow confined strictly to the canopy, the calming effect of the canopy is introduced through a sheltering coefficient. The canopy is modeled as a set of rigid uniform structures orientated normal to the flow and evenly distributed with specified density over the bottom. The algorithm is tested by simulating the steady-state water-surface profiles observed in a laboratory channel containing wire screen obstructions. The model is applied next to a wind-driven rectangular basin with simulated vegetation specified over half the bottom.

The decay of mesoscale eddies can be attributed to either frictional dissipation of kinetic energy through viscous effects or through dispersive spreading of the different constituent Rossby wave components at their own characteristic wave speeds. Several previous investigations of eddy decay have examined the role of variable friction in the spindown process. In addition to frictional results, these studies have shown that nonlinear advective processes can stabilize the vortex against dispersive effects. The quantification of this relation between nonlinear stabilization and beta dispersion is the primary focus of this paper. Results are obtained using a finite difference “equivalent barotropic” numerical model with a fixed biharmonic friction formulation. Variable parameters in the study are vortex size and strength. Initial conditions are in the form of a Gaussian height field in gradient balance. Nonfrictional vortex decay is parameterized in terms of lateral spreading. This spreading is dete...

The Karman-Prandtl mixing-length theory for fluid flow over a flat surface with a laminar sublayer near the boundary is adapted to the flow along an infinite circular cylinder on the supposition that, in the nature of the radial inward convection of momentum towards the boundary, there is no accumulation of the momentum within any arbitrary finite volume of fluid. Experimental results for smooth and rough pipe flows are invoked in order to develop the nature of the boundary flow over a range of conditions from the quasi-smooth to the fully turbulent regimes. The drag coefficient for tangential friction is evaluated as a function of Reynolds number and surface roughness and is shown to lie within the limits 0.002 and 0.02, depending on roughness, for diameter Reynolds numbers greater than 103. Theoretical indications compare favorably with results from towing tests of stranded cables.

A conformal transformation of the equations that constitute the boundary value problem of permanent-form finite gravity waves from the x, y plane to the velocity-potential-stream-function plane is presented. After the resulting equations are given in a nondimensional form the Fourier coefficients of the solutions to this problem are determined for a representative sampling of theoretical waves of various heights at different depths of water through a numerical iterative process. A comparison of the results is made with existing Stokes first, third, and fifth order theories and with Chappelear's [1961] direct numerical calculations. The approach presented has the following advantages: (a) simplification of the boundary conditions through the mapping transformation, (b) one set of coefficients to define the wave characteristics, (c) easy evaluation of the particle trajectories, and (d) a wide range of depths of water and heights of waves to which it can be applied.

A numerical scheme for computation of two-dimensional, nonlinear storm surges and tides is applied to Galveston Bay, Tex. Allowance is made for the overflow of low-lying barrier islands and for the flooding of and recession from low-lying land areas adjacent to the bay. The initial surge or tide, or both, at the seaward end of the bay outside the barrier islands is prescribed. The system has been calibrated for spring tide conditions and for the surge produced by hurricane Carla (September, 1961). Verification of the system is carried out for hurricane Cindy (September, 1963).

Preliminary results are presented of an investigation of the applicability of Prandtl's equation to the determination of wind stresses from the vertical wind gradient in the Atchafalaya Bay region. A study of the correlation of water-level oscillations with barometric pressure and wind speed is discussed briefly.

Two indices for tagging hurricanes with respect to their capacity for producing storm tides and waves on a continental shelf are suggested. Application of these indices to the hurricane data of the United States since 1900 indicates that the logarithms of these indices possess nearly Gaussian distribution. This affords an approximate means of evaluating the average rate of occurrence of storms having a given level of intensity, defined by either the wave energy index or storm tide potential for a particular site. A rate of occurrence is computed for the northwestern Gulf of Mexico shelf area.

The equation for the conservation of total mechanical energy (kinetic, gravitational, and elastic energy) is derived from the conservation of momentum and mass and averaged over the volume of the oceans to equate the production and dissipation of mechanical energy in a statistically steady ocean. The work done by the atmosphere dominates production and is estimated as 0.1 W/m2 from synoptic data which is consistent with most (but not all) of the reported observations of turbulent dissipation. Potential energy production contributes only .0.2% to the total production implying an eddy diffusivity of buoyancy of 10−5 m2/s and a thermal Cox number of 200. The “low” values of diffusivity derived from microstructure observations appear to reflect a relatively small potential energy production.

An analytical, normal mode, two-layer model is presented that gives the response of a coastal region to local wind forcing. The model is linear and is developed in frequency space, the latter allowing one to compare the model responses directly with the results of current meter/wind data spectral and coherence analyses. The theoretical development indicated the requirement of a frictional parameter in both the barotropic and baroclinic modes to balance the wind stress at lower frequencies. Experimentation with the model and current and wind data collected 20 km off the Texas coast showed the requirement for both frictional effects throughout the subinertial frequency range. With appropriate frictional parameters, the model predicts the response of the Texas coastal region to local wind forcing quite well, using data from the fall and winter of 1978–1979. However, during the summer of 1978, the model consistently underpredicted the energy levels of the currents. Since the summer is a period of low wind stress energy for the Texas shelf, this underprediction most likely indicates the presence of nonlocally generated shelf wave phenomena.

This report, while concerning primarily those analytical and numerical models of quasi-steady circulation of the oceans and adjacent seas, also recognizes similar important studies pertaining to lakes, estuaries, and the continental shelf. (Note, however, that coastal upwelling studies are covered in a separate report.) The accompanying bibliography includes representative papers from abroad as well as from the United States. Several review papers are included with the new contributions, published since the beginning of 1971; moreover, the list includes some papers that this reporter is aware of which will be published in 1975. Several of the latter, although carrying the date 1975, are papers presented at the Symposium on Numerical Models of Ocean Circulation which was held in October 1972, at Durham, New Hampshire; the proceedings will appear as a publication of the U.S. National Academy of Science.