Internal Hydraulic Theory Research Articles

Hydraulic modelling of stratified bi-directional flow in a river mouth

Analytical results from internal hydraulic theory are presented for a horizontal channel connecting river- and sea-basin waters of slightly different densities. The maximal exchange of inviscid, two-layer flow is analysed for such a system, for the case of a non-rectangular channel. The internal hydraulic theory has been extended to include internal energy losses and related net barotropic flow components in the surface layer. The hydraulic model is tested using archival field measurements in the Pärnu River mouth, where stratified bi-directional flow, accompanied by variable sea-level conditions and river water discharges, was observed. The study demonstrates that internal hydraulic theory predicts satisfactorily the stratified bi-directional fluxes and density-interface depths observed in the river mouth. In this study the two-layer exchange problem is solved with two control points, but the theory can be applied quite generally to predict the layer depths of the river and marine waters in the estuarine interaction zone.

Exchange flow through an opening

This paper presents a theoretical and experimental study of the exchange of fluids of different densities through an opening. Three types of openings are examined: a bottom opening (the opening is at the bottom of a gate), a middle opening (in the middle) and a window opening (the opening is in the middle but does not extend across the width). Simultaneous measurements of velocity field and interface position were obtained using flow visualization and image processing techniques. Experimental results confirm the predictions of the internal hydraulic theory that there are two internal hydraulic controls in the flow through bottom openings, but one control in the middle and window opening experiments. The neglect of non-hydrostatic forces and interfacial mixing in the theory, however, results in a significant underestimate of the exchange rate by more than 50 % in the middle and window opening experiments. The fluctuations in the interface position were caused by Kelvin-Helmholtz instabilities as well as basin-scale internal seiche, and the transition of internally supercritical flow to subcritical flow was caused by the mixing generated by these instabilities.

Linear internal waves and the control of stratified exchange flows

Internal hydraulic theory is often used to describe idealized bi-directional exchange flow through a constricted channel. This approach is formally applicable to layered flows in which velocity and density are represented by discontinuous functions that are constant within discrete layers. The theory relies on the determination of flow conditions at points of hydraulic control, where long interfacial waves have zero phase speed. In this paper, we consider hydraulic control in continuously stratified exchange flows. Such flows occur, for example, in channels connecting stratified reservoirs and between homogeneous basins when interfacial mixing is significant. Our focus here is on the propagation characteristics of the gravest vertical-mode internal waves within a laterally contracting channel.Two approaches are used to determine the behaviour of waves propagating through a steady, continuously sheared and stratified exchange flow. In the first, waves are mechanically excited at discrete locations within a numerically simulated bi-directional exchange flow and allowed to evolve under linear dynamics. These waves are then tracked in space and time to determine propagation speeds. A second approach, based on the stability theory of parallel shear flows and examination of solutions to a sixth-order eigenvalue problem, is used to interpret the direct excitation experiments. Two types of gravest mode eigensolutions are identified: vorticity modes, with eigenfunction maxima centred above and below the region of maximum density gradient, and density modes with maxima centred on the strongly stratified layer. Density modes have phase speeds that change sign within the channel and are analogous to the interfacial waves in hydraulic theory. Vorticity modes have finite propagation speed throughout the channel but undergo a transition in form: upwind of the transition point the vorticity mode is trapped in one layer. It is argued that modes trapped in one layer are not capable of communicating interfacial information, and therefore that the transition points are analogous to control points. The location of transition points are identified and used to generalize the notion of hydraulic control in continuously stratified flows.

Hydraulics of Exchange Flows

Basic internal hydraulic theory has been extended to include frictional and nonhydrostatic effects for the case of flow over a sill in a channel connecting two reservoirs of slightly different density. The predictions of the extended theory compare well with laboratory experiments. The inclusion of frictional and nonhydrostatic effects was found to be necessary to accurately predict the flow rate, the along-channel variations in interfacial position, the composite and stability Froude numbers, and the internal energy. The accuracy of predictions of the extended theory is limited by uncertainty in estimates of the interfacial friction factor.

Echange flow through a channel with an underwater sill

Abstract We have performed theoretical and laboratory studies of the exchange of two fluids of slightly different density over an underwater sill in a channel of constant width. After extending internal hydraulic theory to incorporate frictional and non-hydrostatic forces, we obtained excellent agreement with experimental results. Both Kelvin-Helmholtz and Holmboe instabilities were observed in the experiments. Measurements of the wavelength and speed of the Holmboe instabilities were consistent with the theoretical predictions.

Tidal Intrusion Fronts

A tidal intrusion front forms as a dense seawater inflow plunges (subducts) beneath ambient estuarine water during flood tide. The associated foam lines and color changes have been observed on many smaller estuaries with constricted mouths. Internal hydraulic theory and laboratory experiments are reviewed and expressions are obtained for the position of plunging and the amount of associated mixing. The existence of a tidal intrusion front and its structure are discussed in terms of densimetric Froude numbers. These fronts are particularly important in smaller estuaries in which the intrusion process may dominate wind and tidal mixing and thus determine the overall stratification of the estuary. Three classes of three-dimensional plunging flow are identified and discussed. In particular, it is suggested that the peculiar, cursive V-shape plunge line is characteristic of strongly plunging flow.

Aerial Observations of the Yugoslavian Bora

Abstract The first aircraft observations of the bora in Yugoslavia were accomplished during the ALPEX project in 1982. Data from all five ALPEX bora flights have been analyzed in a comparative study of bora structure. Although the bora varies considerably in depth, in the strength of the incoming low level flow, and in the direction of the winds aloft, several common features are evident. These include: upstream descent and acceleration beginning where the mountains rise; an approximate coincidence between the depth of the uppermost descending streamline and the wind reversal level upstream (when a reversal exists); a decoupling of the flow aloft associated with a splitting of the inversion and the formation of a thick mixed layer downstream; a narrow region of intense turbulence and an ascending jet just downstream of the plunging bora. The bora structure is similar in many respects to the Boulder windstorm. Internal hydraulic theory, taking into account the decoupling effect of the intermediate layer, a...

Resonant flow of a stratified fluid over topography

The flow of a stratified fluid over topography is considered in the long-wavelength weakly nonlinear limit for the case when the flow is near resonance; that is, the basic flow speed is close to a linear long-wave phase speed for one of the long-wave modes. It is shown that the amplitude of this mode is governed by a forced Korteweg-de Vries equation. This equation is discussed both analytically and numerically for a variety of different cases, covering subcritical and supercritical flow, resonant or non-resonant, and for localized forcing that has either the same, or opposite, polarity to the solitary waves that would exist in the absence of forcing. In many cases a significant upstream disturbance is generated which consists of a train of solitary waves. The usefulness of internal hydraulic theory in interpreting the results is also demonstrated.