An oceanographically generic problem of the interaction of a boundary current with bathymetric features such as a gap in the ridge or a strait between two islands is considered. Multiple flow patterns (penetrating or leaping the gap) and hysteresis (dependence on prior evolution) may exist in such systems. Examples include the Gulf Stream leaping from the Yucatan to Florida and the Kuroshio leaping from Luzon to Taiwan. Using numerical analysis, Sheremet earlier found that multiple steady states can be explained by variation in the balance between the inertia (which promotes leaping state) and the  effect (which promotes penetrating state). In the present work a verification of the multiple states and hysteresis in a laboratory model are offered. To set up a gap-leaping current, a circular tank with a sloping bottom (simulating the  effect) is used, and the flow is driven using a new method of pumping fluid through sponges (thus generating a Sverdrup flow in the interior). A semicircular ridge with a gap is inserted into the western part of the tank. Using a dye release flow visualization method, the existence of multiple flow patterns over varying boundary current transport values differing by a factor of more than 2 are dramatically shown. An associated numerical model in bipolar curvilinear coordinates, which allows for the matching of all the boundaries, reproduces the laboratory results very well. This idealized problem offers a very useful geophysical test case for numerical models involving flow separation and reattachment.
A thermoacoustic interpretation of Mack's second-mode instability is proposed. It is demonstrated that the fundamental mechanism of second-mode wave growth in hypersonic boundary layers is consistent with standingwave thermoacoustically driven instability. The resonant nature of such modes is sustained by an acoustic impedance well between the wall (infinite impedance) and near the sonic line (secondary peak in impedance). A Lagrangian approach is adopted to show that such resonant standing waves derive energy from the base flow through thermoacoustic Reynolds stress, which results from the divergence of acoustic power inside the impedance well, and thermodynamic work. This treatment does not represent a complete energy closure (due to the neglect of viscosity), but it does provide insight toward a fundamental energy source and the physical mechanisms governing Mack's acoustic second mode.
Langmuir turbulence is a boundary layer oceanographic phenomenon of the upper layer that is relevant to mixing and vertical transport capacity. It is a manifestation of imposed aerodynamic stresses and the aggregate horizontal velocity profile due to orbital wave motion (the so-called Stokes profile), resulting in streamwise-elongated, counterrotating cells. The majority of previous research on Langmuir turbulence has focused on the open ocean. Here, we investigate the characteristics of coastal Langmuir turbulence by solving the grid-filtered Craik–Leibovich equations where the distinction between open and coastal conditions is a product of additional bottom boundary layer shear. Studies are elucidated by visualizing Langmuir cell vortices using isosurfaces of Q. We show that different environmental forcing conditions control the length scales of coastal Langmuir cells. We have identified regimes where increasing the Stokes drift velocity and decreasing surface wind stress both act to change the horizontal size of coastal Langmuir cells. Furthermore, wavenumber is also responsible in setting the horizontal extent Ls of Langmuir cells. Along with that, wavenumber that is linked to the Stokes depth δs controls the vertical extent of small-scale vortices embedded within the upwelling limb, while the downwelling limb occupies the depth of the water column H for any coastal surface wave forcing (i.e., and ). Additional simulations are included to demonstrate insensitivity to the grid resolution and aspect ratio.
The problem of oceanic gap-traversing boundary currents, such as the Kuroshio current crossing the Luzon Strait or the Gulf Stream traversing the mouth of the Gulf of Mexico, is considered. Systems such as these are known to admit two dominant states: leaping across the gap or penetrating into the gap forming a loop current. Which state the system will assume and when transitions between states will occur are open problems. Sheremet (J. Phys. Oceanogr., vol. 31, 2001, pp. 1247–1259) proposed, based on idealized barotropic numerical results, that variation in the current’s inertia is responsible for these transitions and that the system admits multiple states. Generalized versions of these results have been confirmed by barotropic rotating-table experiments (Sheremet & Kuehl, J. Phys. Oceanogr., vol. 37, 2007, 1488–1495; Kuehl & Sheremet,J. Mar. Res., vol. 67, 2009, pp. 25–42). However, the typical structure of oceanic boundary currents, such as the Gulf Stream or Kuroshio, consists of an upper-layer intensified flow riding atop a weakly circulating lower layer. To more accurately address this oceanic situation, the present work extends the above findings by considering two-layer rotating table experiments. The flow is driven by pumping water through sponges and vertical seals, creating a Sverdrup interior circulation in the upper layer which impinges on a ridge where a boundary current is formed. The $\beta $ effect is incorporated in both layers by a sloping rigid lid as well as a sloping bottom and the flow is visualized with the particle image velocimetry method. The experimental set-up is found to produce boundary currents consistent with theory. The existence of multiple states and hysteresis, characterized by a cusp topology of solutions, is found to be robust to stratification and various properties of the two-layer system are explored.
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