Over the past four decades, the combination of in situ and remote sensing observations has demonstrated that long nonlinear internal solitary-like waves are ubiquitous features of coastal oceans. The following provides an overview of the properties of steady internal solitary waves and the transient processes of wave generation and evolution, primarily from the point of view of weakly nonlinear theory, of which the Korteweg-de Vries equation is the most frequently used example. However, the oceanographically important processes of wave instability and breaking, generally inaccessible with these models, are also discussed. Furthermore, observations often show strongly nonlinear waves whose properties can only be explained with fully nonlinear models.

/pdf/long-nonlinear-internal-waves-126jyzwpra.pdf

Long Nonlinear Internal Waves

Results of laboratory experiments are presented in which a finite volume of homogeneous fluid was released instantaneously into another fluid of slightly lower density The experiments were performed in a channel of rectangular cross-section, and the two fluids used were salt water and fresh water As previously reported, the resulting gravity current, if viscous effects are negligible, passes through two distinct phases: an initial adjustment phase, during which the initial conditions are important, and an eventual self-similar phase, in which the front speed decreases as t−1/3 (where t is the time measured from release) The experiments reported herein were designed to emphasize the inviscid motion From our observations we argue that the current front moves steadily in the first phase, and that the transition to the inviscid self-similar phase occurs when a disturbance generated at the endwall (or plane of symmetry) overtakes the front If the initial depth of the heavy fluid is equal to or slightly less than the total depth of the fluid in the channel, the disturbance has the appearance of an internal hydraulic drop Otherwise, the disturbance is a long wave of depression Measurements of the duration of the initial phase and of the speed and depth of the front during this phase are presented as functions of the ratio of the initial heavy fluid depth to the total fluid depth These measurements are compared with numerical solutions of the shallow-water equations for a two-layer fluid

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112083002979

Gravity currents produced by instantaneous releases of a heavy fluid in a rectangular channel

The dynamics of gravity currents are believed to be strongly influenced by dissipation due to turbulence and mixing between the current and the surrounding ambient fluid. This paper describes new theory and experiments on gravity currents produced by lock exchange which suggest that dissipation is unimportant when the Reynolds number is sufficiently high. Although there is mixing, the amount of energy dissipated is small, reducing the current speed by a few percent from the energy-conserving value. Benjamin (J. Fluid Mech. vol. 31, 1968, p. 209) suggests that dissipation is an essential ingredient in gravity current dynamics. We show that dissipation is not important at high Reynolds number, and provide an alternative theory that predicts the current speed and depth based on energy-conserving flow that is in good agreement with experiments. We predict that in a deep ambient the front Froude number is 1, rather than the previously accepted value of √ 2. New experiments are reported for this case that support the new theoretical value. This paper provides an analysis of the motion of a gravity current produced by lock exchange. In a lock exchange experiment, fluids of different densities initially at rest are separated by a vertical barrier – the lock gate – in a tank. When the gate is removed, differences in the hydrostatic pressure cause the denser fluid to flow in one direction along the bottom boundary of the tank, while the lighter fluid flows in the opposite direction along the top boundary of the tank. Figure 1 shows the initial configurations for lock exchange flows: a full-depth release when the depths of heavy and light fluid on both sides of the gate are equal is shown in (a )a nd apartial-depth release when the dense fluid occupies only a fraction of the full depth is shown in (b). Figure 2 shows the flow resulting from a full-depth lock release experiment. In this case the densities on the two sides of the lock gate are very similar (the density ratio γ = ρ1/ρ2 < 1 is close to unity). A dense gravity current travels to the right along the lower boundary and a buoyant current travels to the left along the upper boundary. Visually the flows are very nearly symmetric, and the dense and light fronts travel at almost the same speeds (figure 2b). The currents occupy about half the channel depth in each case, although they may be shallower immediately behind the head where there is mixing. The speeds of the two currents are constant within experimental resolution. Previous similar observations led Benjamin (1968) to develop a theory for the propagation of a steadily advancing current. He considered one half of the flow shown in figure 2(a), say the dense current only. In a frame of reference moving with the current, the front

/pdf/gravity-currents-produced-by-lock-exchange-5dnj5lmlup.pdf

Gravity currents produced by lock exchange

The physical oceanography of fjords

This is a theoretical and experimental study of the basic hydraulics of two flowing layers. Unlike single-layer flows, two-layer flows respond quite differently to bottom depth as opposed to width variations. Bottom-depth changes affect the lower layer directly and the upper layer only indirectly. Changes in width can affect both layers. In fact for flows through a contraction control two distinct flow configurations are possible; which one actually occurs depends on the requirements of matching a downstream flow. Two-layer flows can pass through internally critical conditions at other than the narrowest section. When the two layers are flowing in the same direction, the result is a strong coupling between the two layers in the neighbourhood of the control. For contractions a particularly simple flow then exists upstream in which there is no longer any significant interfacial dynamics; downstream in the divergent section the flow remains internally supercritical, causing one of the layers to be rapidly accelerated with a resulting instability at the interface. A brief discussion of internal hydraulic jumps based upon the energy equations as opposed to the more traditional momentum equations is included. Previous uniqueness problems are thereby avoided.

The hydraulics of two flowing layers with different densities

This paper examines a region of rapidly varied flow in a two-layered density stratified system with one layer flowing, and the other stationary. The analogous phenomenon in open channel hydraulics is the hydraulic jump. In density stratified flows the phenomenon is referred to as a density jump because it is generally accompanied by a change in density of the flowing layer.It is shown there is a fundamental difference between the hydraulic jump and the density jump in that flow conditions on either side of a density jump are not uniquely related. A density jump with given flow conditions upstream has a range of possible states which may be attained downstream. The rate of entrainment of ambient fluid into a density jump, and the conditions downstream of the jump, are determined by the downstream control and the upsteam conditions. The particular case of a density jump controlled by a broad crested weir downstream is examined in detail.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112071001034

A rapidly varied flow phenomenon in a two-layer flow

This paper describes an experimental study of the flow associated with the intrusion of an air cavity into a long horizontal duct as water was allowed to drain from one end. Flows of this nature were discussed by Benjamin (1968), who showed that throttling of the flow of water from the end of the duct would cause both the celerity and the depth of the cavity to reduce. However, the experiments described in this paper revealed that the celerity of the cavity was not reduced from its unthrottled value until the water depth beneath the cavity was 0·78 of the duct depth. For values of this depth ratio between 0·5 and 0·78, the flow as a whole was unsteady. It is shown that Benjamin's model can be modified to allow for the unsteady nature of the flow. Benjamin's original model was found to describe accurately the form and behaviour of the cavity in the case of unthrottled flow, when the flow was steady, and also when the depth beneath the cavity exceeded 0·78 of the duct height, when the flow was again steady. Surface-tension effects were found to reduce the celerity of the cavity and to modify its shape as described by Gardner & Crow (1970).

Motion of air cavities in long horizontal ducts

The behavior of large and small-scale bubble plumes is compared with that of plumes in which the buoyancy is miscible with the surrounding fluid. It is found that the structure of bubble plumes is determined by the value of a Weber number based on the ratio of buoyant and surface tension forces at the source. At low Weber numbers the structure tends to be self-preserving and the current generating capability is otpimized.

Two-Dimensional Bubble Plumes

This paper describes the nature of saline wedge formation in tunnelled ocean sewage outfalls. A momentum flux equation is used to determine the sewage discharge required to purge a saline wedge from an outfall tunnel in which the risers leave from the soffit. It is shown that the purging discharge is generally much greater than the flow required to prevent saline intrusion into the risers. Laboratory experiments are described which confirm the validity of the purging criterion. Means by which the purging flow may be minimized are also considered.

Purging of Saline Wedges from Ocean Outfalls

When the flow rate from a port discharging buoyant fluid into a denser environment is less than a critical value, a counter flow of dense fluid will become established through the port. Experiments were conducted at near prototype scales which confirmed that the critical rate of discharge could be expressed in terms of a densimetric Froude number based on the port diameter and the buoyancy of the discharge. The value of the critical Froude number was found to depend primarily on the port orientation and shape.

Closure of "Avoidance of Seawater Intrusion into Ports of Ocean Outfalls"

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