Internal Bore Evolution Across the Shelf Near Pt. Sal CA interpreted as a Gravity Current

Off the central California coast near Pt. Sal, a large amplitude internal bore was observed for 20 h over 10 km cross-shore, or 100 m to 10 m water depth (D), and 30 km alongcoast by remote sensing, 39 in situ moorings, ship surveys, and drifters. The bore is associated with steep isotherm displacements representing a significant fraction of D. Observations were used to estimate bore arrival time tB, thickness h, and bore and non-bore (ambient) temperature difference ΔT, leading to reduced gravity g′. Bore speeds c, estimated from mapped tB, varied from 0.25 m s−1 to 0.1 m s−1 from D = 50 m to D = 10 m. The h varied from 5 to 35 m, generally decreased with D, and varied regionally alongisobath. The bore ΔT varied from 0.75 to 2.15 °C. Bore evolution was interpreted from the perspective of a two-layer gravity current. Gravity current speeds U, estimated from the local bore h and g− compared well to observed bore speeds throughout its cross-shore propagation. Linear internal wave speeds based on various stratification estimates result in larger errors. On average bore thickness h = D/2, with regional variation, suggesting energy saturation. From 50–10 m depths, observed bore speeds compared well to saturated gravity current speeds and energetics that depend only on water depth and shelf-wide mean g′. This suggests that this internal bore is the internal wave analogue to a saturated surfzone surface gravity bore. Alongcoast variations in pre-bore stratification explain variations in bore properties. Near Pt. Sal, bore Doppler shifting by barotropic currents is observed.

Lifecycle of a Submesoscale Front Birthed from a Nearshore Internal Bore

The ocean is home to many different submesoscale phenomena, including internal waves, fronts, and gravity currents. Each of these processes entail complex nonlinear dynamics, even in isolation. Here we present shipboard, moored, and remote observations of a submesoscale gravity current front created by a shoaling internal tidal bore in the coastal ocean. The internal bore is observed to flatten as it shoals, leaving behind a gravity current front that propagates significantly slower than the bore. We posit that the generation and separation of the front from the bore is related to particular stratification ahead of the bore, which allows the bore to reach the maximum possible internal wave speed. After the front is calved from the bore, it is observed to propagate as a gravity current for ≈4 hours, with associated elevated turbulent dissipation rates. A strong cross-shore gradient of along-shore velocity creates enhanced vertical vorticity (Rossby number ≈ 40) that remains locked with the front. Lateral shear instabilities develop along the front and may hasten its demise.

Alongshore Variability of Shoaling Internal Bores on the Inner Shelf

Temperature and velocity measurements from 42 moorings were used to investigate the alongshore variability of nonlinear internal bores as they propagated across the central California inner shelf. Moorings were deployed September–October 2017 offshore of the Point Sal headland. Regional coverage was ~30 km alongshore and ~15 km across shore, spanning 9–100-m water depths. In addition to subtidal processes modulating regional stratification, internal bores generated complex spatiotemporal patterns of stratification variability. Internal bores were alongshore continuous on the order of tens of kilometers at the 50-m isobath, but the length scales of frontal continuity decreased to O(1 km) at the 25-m isobath. The depth-averaged, bandpass-filtered (from 3 min to 16 h) internal bore kinetic energy was found to be nonuniform along a bore front, even in the case of an alongshore-continuous bore. The pattern of along-bore variability varied for each bore, but a 2-week average indicated that was generally strongest around Point Sal. The stratification ahead of a bore influenced both the bore’s amplitude and cross-shore evolution. The data suggest that alongshore stratification gradients can cause a bore to evolve differently at various alongshore locations. Three potential bore fates were observed: 1) bores transiting intact to the 9-m isobath, 2) bores being overrun by faster, subsequent bores, leading to bore-merging events, and 3) bores disappearing when the upstream pycnocline was near or below middepth. Maps of hourly stratification at each mooring and the estimated position of sequential bores demonstrated that an individual internal bore can significantly impact the waveguide of the subsequent bore.

Automatic Expanding Mandrel with Air Sensing Device: Design and Analysis

In precision machining, expanding mandrels are used for jobs with close tolerances. An expanding mandrel consists of a tapered arbor or shaft, with a thin-slotted clamping sleeve or collet made of hardened steel. The internal tapered and external cylindrical surfaces are ground to a high degree of accuracy, and the mandrel expands to fit the internal bore of the workpiece. Expanding mandrels are, essentially, wedge mechanisms. This paper proposes an automatic expanding mandrel with a novel force transmission system for high stiffness within a novel air sensing system, which allows detection of the correct part position before starting machining. A computational model for determining the dynamic clamping force of the proposed mechanism is developed and implemented using MATLAB. This model considers the influence of the stiffness behaviors of the collet, force transmission structure and workpiece. Additionally, this paper presents the finite element method analyses which were conducted to check the proposed computational model. The amount of clamping force transmitted by a collet chuck holder depends strongly on: clearances, wedge angle, stiffness of the collet chuck holder and workpiece stiffness.

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.

Circulation-based models for Boussinesq internal bores

Existing control-volume models for predicting the front velocity of internal bores enforce the conservation of mass and streamwise momentum, but not vertical momentum. Instead, they usually invoke an empirical assumption relating the up- and downstream energy fluxes to obtain an additional equation required for determining the pressure jump across a bore. The present investigation develops a control-volume model for internal bores on the basis of mass and momentum conservation alone, without the need for considering energy. This is accomplished by combining the streamwise and vertical momentum equations to obtain a vorticity relation that no longer involves pressure. Hence, this vorticity equation, in combination with the conservation of mass, is sufficient for evaluating the bore velocity. The energy loss across the bore can then be predicted by the streamwise energy equation and compared to the assumptions underlying earlier models. The flux of vorticity across the internal bore predicted by the new model is seen to be in close agreement with direct numerical simulation results. Any discrepancies with experimentally measured bore velocities are shown to be due to the effects of downstream mixing.