ALBERT

Description: In order to gain insight into the hydraulics of rotating-channel flow, a set of initial-value problems analogous to Long's towing experiments is considered. Specifically, we calculate the adjustment caused by the introduction of a stationary obstacle into a steady, single-layer flow in a rotating channel of infinite length. Using the semigeostrophic approximation and the assumption of uniform potential vorticity, we predict the critical obstacle height above which upstream influence occurs. This height is a function of the initial Froude number, the ratio of the channel width to an appropriately defined Rossby radius of deformation, and a third parameter governing how the initial volume flux in sidewall boundary layers is partitioned. (In all cases, the latter is held to a fixed value specifying zero flow in the right-hand (facing downstream) boundary layer.) The temporal development of the flow according to the full, two-dimensional shallow water equations is calculated numerically, revealing numerous interesting features such as upstream-propagating shocks and separated rarefying intrusions, downstream hydraulic jumps in both depth and stream width, flow separation, and two types of recirculations. The semigeostrophic prediction of the critical obstacle height proves accurate for relatively narrow channels and moderately accurate for wide channels. Significantly, we find that contact with the left-hand wall (facing downstream) is crucial to most of the interesting and important features. For example, no instances are found of hydraulic control of flow that is separated from the left-hand wall at the sill, despite the fact that such states have been predicted by previous semigeostrophic theories. The calculations result in a series of regime diagrams that should be very helpful for investigators who wish to gain insight into rotating, hydraulically driven flow.

Description: Oceanic observations indicate that abyssal mixing tends to be localized to regions of rough topography. How localized mixing interacts with the ambient fluid in a stratified, rotating system is an open question. To gain insight into this complicated process laboratory experiments are used to explore the interaction of mechanically induced boundary mixing and an interior body of linearly stratified rotating fluid. Turbulence is generated by a single vertically oscillating horizontal bar of finite horizontal extent, located at mid-depth along the tank wall. The turbulence forms a region of mixed fluid which quickly reaches a steady-state height and collapses into the interior. The mixed-layer thickness, hm ∼ γ(ω/N1/2, is spatially uniform and independent of the Coriolis frequency f. N is the initial buoyancy frequency, ω is the bar oscillation frequency, and γ ≈ 1 cm is an empirical constant determined by the bar geometry. Surprisingly, the export of mixed fluid does not occur as a boundary current along the tank perimeter. Rather, mixed fluid intrudes directly into the interior as a radial front of uniform height, advancing with a speed comparable to a gravity current. The volume of mixed fluid grows linearly with time, V α (N/f 32h3mft, and is independent of the lateral extent of the mixing bar. Entrainment into the turbulent zone occurs principally through horizontal flows at the level of the mixing that appear to eliminate export by a geostrophic boundary flow. The circulation patterns suggest a model of unmixed fluid laterally entrained at velocity ue ∼ Nhm, into the open sides of a turbulent zone with height hm and a length, perpendicular to the boundary, proportional to Lf ≡ γ(ω/f)1/2. Here Lf is an equilibrium length scale associated with rotational control of bar-generated turbulence. The model flux of exported mixed fluid Q ∼ hmLfue is constant and in agreement with the experiments. © 2004 Cambridge University Press.

Description: Laboratory and numerical experiments are used to study flow of a uniform-density fluid on the β-plane around a thin zonally elongated island (or ridge segment in the abyss). This orientation is chosen specifically to highlight the roles of the zonal boundary layer dynamics in controlling the circulation around the island. There are examples of deep ocean topography that fall into this category which make the work directly applicable to oceanic flows. Linear theory for the transport around the island and the flow structure is based on a modification of the Island Rule (Pedlosky et al. 1997; Pratt & Pedlosky 1999). The linear solution gives a north-south symmetric flow around the island with novel features, including stagnation points which divide the zonal boundary layers into eastward and westward flowing zones, and a western boundary layer of vanishing length, and zonal jets. Laboratory experiments agree with the linear theory for small degrees of nonlinearity, as measured by the ratio of the inertial to Munk boundary layer scales. With increasing nonlinearity the northsouth symmetry is broken. The southern stagnation point (for anticyclonic forcing) moves to the eastern tip of the island. The flow rounding the eastern tip from the northern side of the island now separates from the island. Time-dependence emerges and recirculation cells develop on the northern side of the island. Mean transport around the island is relatively unaffected by nonlinearity and given to within 20% by the modified Island Rule. Numerical solutions of the shallow water equations are in close agreement with the laboratory results. The transition from zonal to meridional island orientation occurs for island inclinations from zonal greater than about 20°.