Journal of Hydraulic Engineering

The arrested saline wedge geometry is characterized by two major internal demarcation lines, the density interface and the zero velocity line (ZVL). As a complement to earlier two‐layer model formulations that are based upon the density interface, a two‐layer model using the ZVL is developed. The advantage of this model is that it divides the flow into an active upper zone with high kinetic energy content and a passive lower zone as suggested by detailed experiments. Net entrainment across the ZVL drives the flow in the passive salt zone. An entrainment model is developed on the basis of stability theory and similarity theory for turbulent buoyant shear flows but includes an empirical transition to purely laminar flow in the low Reynolds number range. The model depends on two local parameters, a bulk Richardson number (or densimetric Froude number) and a bulk Reynolds number. Predicted entrainment rates agree well with available data over the range of parameters. Furthermore, the model can be extended to predict the interfacial shear in the complementary formulation that is based on the density interface and, again, shows good agreement with published data. In part 2, the proposed model is applied to the prediction of overall wedge properties, i.e., length, shape, and internal circulation, in estuary flows.

The theoretical formulations developed in part 1 for entrainment at the zero velocity line (ZVL) and for interfacial friction of the density interface have been implemented in a two‐layer model of the arrested salt wedge. Assuming constant densities in each layer, the equations are integrated numerically to predict overall wedge properties, including total intrusion length, the strength of salt circulation, wedge shape, and critical exit conditions. Good agreement is found with available data spanning the full Reynolds number range from laboratory to field conditions with relative intrusion lengths between orders $10-{10}^4\text{.}$ This supports the theoretical development of part 1. Furthermore, the model documents the importance of including in wedge analysis the lower‐layer dynamics (bottom shear stress and convective effects) in contrast to the earlier Schijf and Schonfeld formulation.

The mean flow characteristics immediately downstream of solid and porous fences submerged in turbulent boundary layers have been studied using two‐dimensional fences of different porosities. The flow downstream of the fence within and above the standing eddy was found to be well described by Goertler's half‐jet model. The dimensionless spread parameter σ was found to vary systematically with $X/{\delta }_0$ and the porosity of the fence. The intrinsic axis from which the coordinates are measured was found to follow a similarity law. The scaling parameters used in such similarity analysis are shown to be functions of $U_{*0}H/\nu$ and porosity. The model developed in this paper has been found to be applicable to the flow past both solid wedges and quadrant‐edged roughness. A method of predicting the mean velocity field downstream of solid and porous bodies has been proposed as a result of the analysis presented in the paper.

Analytical solutions for free‐surface swirling flows in a vertical dropshaft are presented. The swirling flows are governed by the circulation number and the Froude number. Two types of flow problems are analyzed. The transition flow problem, where the shaft diameter varies, is solved using specific energy curves. In the gradually varied‐flow problem, the shaft diameter is kept constant. Some results of practical interest are presented.

An analysis of the response of a density‐stratified reservoir to surface shear stress is presented. The reservoir is assumed to be two‐dimensional and to have a constant depth. In the limit that the bulk Wedderburn number $W_B$ and the bulk Richardson number ${\mathrm{Ri}}_B$ are both infinite, the resulting equations are linear and solutions can be found in terms of the individual responses of a set of orthogonal normal modes. For the case of a steady wind stress, the solution consists of periodic motions and steady isopycnal displacements. However, the steady‐state isopycnal slope at the base of the mixed layer is infinite, implying that upwelling can occur when the Wedderburn number is quite large. This is attributed to blocking of the stratified fluid below the mixed layer by the endwall. The modal theory presented in this paper is compared with experimental observations made using a belt to impart shear stress to a stratified fluid contained in a box. The comparison shows that the present theory is qualitatively correct in that upwelling is observed when $W_B\gg 1\text{.}$ However, the modal theory best predicts the first‐mode seiche amplitude; the higher‐mode response is not accurately predicted.

Detailed measurements on the internal flow structure of the arrested saline wedge over a horizontal bottom have been performed together with observations of its overall appearance. The experiments covered a channel Reynolds number range between 4,000 and 10,000 and a densimetric Froude number range between 0.39 and 0.49. Measurements included overall shape, internal circulation, velocity, density and gradient Richardson number profiles, entrainment rates, and shear stresses. The major portion of the saline wedge, excluding the wedge tip and the exit regions, is a quasi‐equilibrium region in which internal flow properties are nearly similar. The flow dynamics are controlled by the turbulent freshwater overflow with a downward cascading process of energy toward the salt layer. Conditions at the two major internal dividing lines, the density interface and the zero velocity line, are elucidated. The density interface is a highly stable zone with intermittent wave breaking, mixing, and entrainment. The zone is in a state of marginal instability consistent with linear stability theory. Viscous and turbulent shear stresses are of about equal magnitude at the interface, while the net upward entrainment is small. The zero velocity line, in contrast, experiences a large upward entrainment of salt water but has small shear stresses.

Entrainment and deposition fluxes were measured in Central Long Island Sound. Data were collected with a 3‐MHz acoustic transceiver range gated to sample the sediment concentration in 1‐cm intervals in the bottom 70 cm of the water column. Horizontal and vertical velocities were sampled 68 cm above the bottom. A turbulent control volume derivation was used to estimate the fluxes and their variation over one 3.5‐hr deployment and a second deployment that spanned a tidal cycle. Time histories of three measures of the shear stress as well as the turbulent and wave kinetic energy were correlated with the entrainment fluxes. Turbulent and wave kinetic energy was the most reliable correlate with entrainment while the Reynolds' stress and drag coefficient estimates fared less well, the former failing at ebb tide, and the latter during periods of low average velocity.

A methodology has been presented by which field data on spatial variations in the hydraulic conductivity and local dispersivity may be utilized to determine the macrodispersion coefficient tensor of the formation. This technique has been applied to an idealized stratified formation, and the relative importance of several nondimensional parameters that influence the macrodispersivity have been studied. It has been shown that for flows parallel to the stratification the macrodispersivity may be several orders of magnitude greater than the local dispersivity. This effect is significantly reduced as the flow direction is rotated. In utilizing the macroscopic advection‐dispersion equation, it has been shown that the macrodispersion coefficient may be dependent on grid scale, source location, and flow direction, although scale and source dependence will generally disappear as the grid scale becomes very large.