Generation of Internal Lee Waves by Lateral Circulation in a Coastal Plain Estuary

Recent mooring observations at a cross-channel section in Chesapeake Bay showed that internal solitary waves regularly appeared during certain phases of a tidal cycle and propagated from the deep channel to the shallow shoal. It was hypothesized that these waves resulted from the nonlinear steepening of internal lee waves generated by lateral currents over channel-shoal topography. In this study numerical modeling is conducted to investigate the interaction between lateral circulation and cross-channel topography and discern the generation mechanism of the internal lee waves. During ebb tides, lateral bottom Ekman forcing drives a counterclockwise (looking into estuary) lateral circulation, with strong currents advecting stratified water over the western flank of the deep channel and producing large isopycnal displacements. When the lateral flow becomes supercritical with respect to mode-2 internal waves, a mode-2 internal lee wave is generated on the flank of the deep channel and subsequently propagates onto the western shoal. When the bottom lateral flow becomes near-critical or supercritical with respect to mode-1 internal waves, the lee wave evolves into an internal hydraulic jump. On the shallow shoal, the lee waves or jumps evolve into internal bores of elevation.

Application of a model of internal hydraulic jumps

A model devised by Thorpe & Li (J. Fluid Mech., vol. 758, 2014, pp. 94–120) that predicts the conditions in which stationary turbulent hydraulic jumps can occur in the flow of a continuously stratified layer over a horizontal rigid bottom is applied to, and its results compared with, observations made at several locations in the ocean. The model identifies two positions in the Samoan Passage at which hydraulic jumps should occur and where changes in the structure of the flow are indeed observed. The model predicts the amplitude of changes and the observed mode 2 form of the transitions. The predicted dissipation of turbulent kinetic energy is also consistent with observations. One location provides a particularly well-defined example of a persistent hydraulic jump. It takes the form of a 390 m thick and 3.7 km long mixing layer with frequent density inversions separated from the seabed by some 200 m of relatively rapidly moving dense water, thus revealing the previously unknown structure of an internal hydraulic jump in the deep ocean. Predictions in the Red Sea Outflow in the Gulf of Aden are relatively uncertain. Available data, and the model predictions, do not provide strong support for the existence of hydraulic jumps. In the Mediterranean Outflow, however, both model and data indicate the presence of a hydraulic jump.

A model for internal bores in continuous stratification

We describe a model for the speed of an internal bore as a function of amplitude in continuous stratification of arbitrary form. The model is developed from the Dubreil-Jacotin–Long theory for nonlinear solitary waves in the conjugate flow limit, which represents an internal hydraulic jump, by allowing dissipation across the jump. The bore speeds predicted by the model are consistent in both the small- and large-amplitude limits with the waveguide intrinsic to the ambient stratification. The model therefore represents a significant advancement over previous theories limited to sharp two-layer stratification. The model shows good agreement with Navier–Stokes simulations of both undular and turbulent internal bores generated by dam break into a continuously stratified ambient with a finite pycnocline, predicting both the front speed as well as the velocity and density structure through the bore. A model is required for the structure of the energy dissipation, and we introduce a one-parameter closure that produces excellent agreement with numerical results, particularly in the parameter limit that maximizes the overall dissipation. By varying the dissipation parameter, the model reproduces previous two-layer theories in the thin-pycnocline limit, and suggests an improved two-layer front speed relationship. It is demonstrated that, even for the sharp two-layer limit, continuous stratification, and particularly the nonlinear waveguide, must be accounted for in order to accurately predict the bore speed and structure.

High-Resolution Doppler Lidar Observations of Transient Downslope Flows and Rotors

The authors present observations of the temporal evolution of downslope windstorms with rotors and internal hydraulic jumps of unprecedented detail and spatiotemporal coverage. The observations were carried out by means of a coherent Doppler lidar in the lee of the southern Sierra Nevada range during the sixth intensive observational period of the Terrain-induced Rotor Experiment (T-REX) in 2006. Two representative flow regimes are analyzed and juxtaposed in this paper. The first case shows pulses of high-momentum air that propagate eastward through the valley with an internal hydraulic jump on the leading edge. The region downstream of the transient internal hydraulic jump is characterized by turbulence but no coherent rotor circulation was observed. During the second case, the strongest windstorm of the field campaign T-REX occurred. The observed features of this event resemble the classical notion of a rotor. Altogether, the Doppler lidar observations of both downslope flow events reveal a complex, turbulent flow that is highly transient, intermittent, 3D, and interacts with a significant along-valley flow.

The Descending Stratified Flow and Internal Hydraulic Jump in the Lee of the Sierras

Cross-barrier density differences and westerly flow established a descending stratified flow across the Sierra Nevada (United States) on 9–10 April 2006. Downslope flow and an internal hydraulic jump occurred only when the potential temperature of the westerly descending flow was at least as cold as the existing upvalley-flowing valley air mass. The onset was observed in sequences of visible satellite images and with weather stations. The University of Wyoming King Air flew through the stratified flow and imaged the structure of the internal hydraulic jump with its cloud radar. Shear-layer instabilities, which first developed near the jump face, grew and paired downstream, mixing the internal hydraulic jump layer. A single wave response to the downslope flow and internal hydraulic jump was observed aloft, but only after the downslope flow had become established.

Underwater sand bed erosion and internal jump formation by travelling plane jets

Theory and experiments are used to investigate the water and sediment motion induced along a sea bed by travelling plane jets. Steadily moving jets are considered, and represent an idealization of the tools mounted on ships and remotely operated vehicles (ROVs) for injection dredging and trenching. The jet-induced turbulent currents simultaneously suspend sand from the bed and entrain water from the ambient. To describe these processes, a shallow-flow theory is proposed in which the turbulent current is assumed stratified into sediment-laden and sediment-free sublayers. The equations are written in curvilinear coordinates attached to the co-evolving bed profile. A sharp interface description is then adopted to account rigorously for mass and momentum exchanges between the bed, current and ambient, including their effects on the balance of mechanical energy. Travelling-wave solutions are obtained, in which the jet-induced current scours a trench of permanent form in a frame of reference moving with the jetting tool. Depending on the operating parameters, it is found that the sediment-laden current may remain supercritical throughout the trench, or be forced to undergo an internal hydraulic jump. These predictions are confirmed by laboratory experiments. For flows with or without jump in which the current remains attached to the bed, bottom profiles computed by the theory compare favourably with imaging measurements.