Maurice Rattray

Salt flux and mixing in the Columbia River Estuary

The Columbia River Estuary at low discharge falls in classes 1b and 2b of the Hansen & Rattray (1966) classification system with the former occurring upstream where the salinity gradients are weakest. During high discharge it falls in the relatively unexplored region bounding classes 1b, 2b and 4. It is typified by both strong tidal and mean currents modified by bathymetry and channel curvature. The dominant lateral dynamic balance is between the pressure gradient, centrifugal and Coriolis forces. The estuary has a strong vertical salinity gradient and also a marked transverse gradient required for the lateral dynamic balance. More than half the upstream salt flux, balancing the downstream mean flow advective salt flux is directly due to correlations between tidal components of velocity and salinity and between each of these and the tidal variation of cross-sectional area. The remaining upstream salt flux arises from the vertical gravitational circulation. The mean stratification and circulation for both high and low discharges yield theoretical estimates of the diffusive fraction of the upstream salt flux in reasonable agreement with the observed values. They also lead to reasonable estimates of P and F m for low discharge condition but for high discharge only the estimate of P is reasonable. Neither the high discharge estimate of F m nor the vertical profiles of velocity, U , and salinity, S , fit the theoretical models.

Generation and dissipation of coastal internal tides

Abstract Long surface waves passing over a depth discontinuity approximating the continental shelf can generate internal waves of significant amplitudes. In the ocean the internal waves are progressive with seaward components of both phase and group velocities. They form a wave beam whose vertical depth is twice the shelf depth and whose center aligns along the characteristic emanating from the surface above the shelf break. Coupling between the oceanic and shelf internal waves causes fine structure within the beam. The position and magnitude of the fine structure depends upon the geometric configuration of the continental shelf and the amount of friction present. As the beam propagates away from the shelf break, the more rapid spatial decay of the higher modes causes it to widen and take on a rounded form. Over the shelf, the internal motion is composed of one or two narrow beams. One emanates from the bottom of the shelf break and reflects back and forth between the surface and the bottom as it progresses up the shelf. The other, when it occurs, is its reflection from the coast which moves out across the shelf. For viscous cases, the reflected shelf beam is damped nearly completely before it returns to the shelf break. When the slope of the bottom is nowhere greater than that of the characteristics, no backward reflection occurs and the incident beam must be completely absorbed in the nearshore region. In the presence of friction, the sharp gradients of phase and amplitude found at the edges of the shelf and oceanic beams in the inviscid case have disappeared and the internal wave beams are widened.

Effects of continental slope and variable Brunt-Väisälä frequency on the coastal generation of internal tides☆

Abstract Internal waves of significant amplitudes can be generated when long surface waves pass over a depth profile approximating the continental shelf. In addition to the shelf-generated beam with a vertical depth twice the shelf depth and its center along the characteristics emanating from the surface above the shelf, wave energy is generated from an inclined slope that interferes with the oceanic beam constructively sloping below and destructively above the center of the downwards propagating beam. After reflection from the oceanic bottom the additional energy adds to the oceanic beams energy above its center and substracts below its center. The magnitude of this effect increases as the inclination of the slope approaches that to the internal wave characteristics. For a Brunt-Vaisala frequency decreasing with depth, the vertical extent of the oceanic beam increases as it propagates downward from the generating region. The spreading of the adjacent characteristics with the depth decreases the energy density; however, because of the simulataneous steepening of the characteristics, the vertical displacements are notso strongly affected.

Theoretical analysis of conditions in a salt wedge

Abstract Theoretical results are obtained for salt-wedge estuaries which give the velocity profile, stress distribution, shape and length of the wedge for steady-state flow conditions. It is assumed that the cross-section is rectangular. Cases are presented for both constant depth and uniformly sloping bottom. The dynamics resemble those found in open channel flow with the addition of a laminar boundary layer at the interface between the wedge and the upper layer. The theory gives reasonable predictions for the length and shape of salt wedges observed in flumes and in the Mississippi and Duwamish Rivers.

Comparison of methods for analysis of the transverse and vertical circulation contributions to the longitudinal advective salt flux in estuaries

Three different sampling designs, based upon the manner in which the total cross-sectional area is decomposed into sub-areas, are explored for their applicability to assessing the transverse and vertical variations of properties in an estuary cross-section. Three hypotheses on the nature of the distribution are used to test the designs. The procedures are applied to Southampton Water where it is found that although both the salinity and velocity have important transverse and vertical variations, the longitudinal advective salt flux is almost totally due to their vertical deviations. This results, which contrasts with previous analyses, follows from the effect of gravity in vertically stratifying both the salinity and velocity distributions.

Distribution of a non-conservative constituent in an estuary with application to the numerical simulation of dissolved silica in the San Francisco Bay

Abstract A simplified relation between the distribution of a non-conservative quantity and the distribution of salinity in an estuary is developed analytically from the conservation equations. The relation is tested against a numerical simulation of the same problem using a two-dimensional gravitational circulation model.

Discussion of trace metals in the waters of a partially-mixed estuary

A general relation for the determination of losses of miscible constituents in an estuary is derived. The relation is applicable to the steady state, tidally-averaged conditions in a partially-mixed estuary where both the advective fluxes from the net circulation and the tidal, non-advective fluxes are important.

Interpolation errors and oceanographic sampling

Abstract Formulae are derived which can be used to give an interpolated value for an oceanographic variable and to estimate the accuracy of the interpolation. The interpolated value is obtained by taking the average of the values obtained from two Lagrange interpolation polynomials: one utilizing two points above and one below the depth of interpolation; and the other, one above and two points below this depth. The error of an interpolated value is composed of two parts, one part which is due to measurement error of the observations, and another part which is the error of the interpolation itself. The difference in the values given by the two interpolation polynomials provides a measure of the error of interpolation. Expressions for the errors resulting from measurement errors, given as the ratio of the standard deviation of the interpolated values to the standard deviation of the individual measurements, depend only on the sampling and interpolation depths. Utilization of these formulae permits the determination of optimum sampling programmes which, with a minimum number of observations, yield the distribution of a variable to a prescribed accuracy.

A comparison of methods for forecasting wave generation

Abstract Wave heights and periods in the generating areas of an unusually severe storm and its forerunner were hindcast by three different methods and compared with observations. Wave height agreement was good for all methods. Period agreement was poor; however, all reported periods fell within the spectral range determined by the Pierson-Neuman-James method. The description of a sea in terms of its spectrum is indicated.

On the predictability of the 137Cs distribution in the Severn Estuary

Abstract The observed distribution of 137Cs resulting from known sources in the Severn Estuary permits the testing of simple predictive models for the one-dimensional distribution of non-conservative substances in an estuary. These models either use a known distribution of salinity to infer corresponding ones for other substances, or else directly solve mass balance equations utilizing previously determined dispersion coefficients. Both methods are shown to previously determined dispersion coefficients. Both methods are shown to provide results comparing favorably with observations. Stokes drift plays an important role in the circulation of the Severn. A modified densimetric Froude number, including this drift, is therefore used to estimate the circulation and stratification of the estuary. A new equation is used for calculating the 137Cs distribution from the observed salinity distribution. It generalizes previous formulations to permit variation of the net runoff with position along the estuary.