A layered numerical model for simulating the generation and propagation of internal tides over continental slope II stability analysis

1999 ◽  
Vol 17 (3) ◽  
pp. 252-257
Author(s):  
Du Tao ◽  
Fang Guo-hong ◽  
Fang Xin-hua
2007 ◽  
Vol 37 (11) ◽  
pp. 2740-2763 ◽  
Author(s):  
Sybren Drijfhout ◽  
Leo R. M. Maas

Abstract The generation and propagation of internal tides has been studied with an isopycnic three-dimensional ocean model. The response of a uniformly stratified sea in a channel, which is forced by a barotropic tide on its open boundary, is considered. The tide progresses into the channel and forces internal tides over a continental slope at the other end. The channel has a length of 1200 km and a width of 191.25 km. The bottom profile has been varied. In a series of four experiments it is shown how the cross-channel geometry affects the propagation and trapping of internal tides, and the penetration scale of wave energy, away from the continental slope, is discussed. In particular it is found that a cross-channel bottom slope constrains the penetration of the internal tidal energy. Most internal waves refract toward a cross-channel plane where they are trapped. The exception is formed by edge waves that carry part of the energy away from the continental slope. In the case of rotation near the continental slope, the Poincaré waves that arise in the absence of a cross-channel slope no longer bear the characteristics of the wave attractor predicted by 2D theory, but are almost completely arrested, while the right-bound Kelvin wave preserves the 2D attractor in the cross-channel plane, which is present in the nonrotating case. The reflected, barotropic right-bound Kelvin wave acts as a secondary internal wave generator along the cross-channel slope.


2006 ◽  
Vol 36 (6) ◽  
pp. 1165-1183 ◽  
Author(s):  
Craig M. Lee ◽  
Thomas B. Sanford ◽  
Eric Kunze ◽  
Jonathan D. Nash ◽  
Mark A. Merrifield ◽  
...  

Abstract Full-depth velocity and density profiles taken along the 3000-m isobath characterize the semidiurnal internal tide and bottom-intensified turbulence along the Hawaiian Ridge. Observations reveal baroclinic energy fluxes of 21 ± 5 kW m−1 radiating from French Frigate Shoals, 17 ± 2.5 kW m−1 from Kauai Channel west of Oahu, and 13 ± 3.5 kW m−1 from west of Nihoa Island. Weaker fluxes of 1–4 ± 2 kW m−1 radiate from the region near Necker Island and east of Nihoa Island. Observed off-ridge energy fluxes generally agree to within a factor of 2 with those produced by a tidally forced numerical model. Average turbulent diapycnal diffusivity K is (0.5–1) × 10−4 m2 s–1 above 2000 m, increasing exponentially to 20 × 10−4 m2 s–1 near the bottom. Microstructure values agree well with those inferred from a finescale internal wave-based parameterization. A linear relationship between the vertically integrated energy flux and vertically integrated turbulent dissipation rate implies that dissipative length scales for the radiating internal tide exceed 1000 km.


2010 ◽  
Vol 40 (6) ◽  
pp. 1338-1355 ◽  
Author(s):  
Matthew H. Alford ◽  
Ren-Chieh Lien ◽  
Harper Simmons ◽  
Jody Klymak ◽  
Steve Ramp ◽  
...  

Abstract In the South China Sea (SCS), 14 nonlinear internal waves are detected as they transit a synchronous array of 10 moorings spanning the waves’ generation site at Luzon Strait, through the deep basin, and onto the upper continental slope 560 km to the west. Their arrival time, speed, width, energy, amplitude, and number of trailing waves are monitored. Waves occur twice daily in a particular pattern where larger, narrower “A” waves alternate with wider, smaller “B” waves. Waves begin as broad internal tides close to Luzon Strait’s two ridges, steepening to O(3–10 km) wide in the deep basin and O(200–300 m) on the upper slope. Nearly all waves eventually develop wave trains, with larger–steeper waves developing them earlier and in greater numbers. The B waves in the deep basin begin at a mean speed of ≈5% greater than the linear mode-1 phase speed for semidiurnal internal waves (computed using climatological and in situ stratification). The A waves travel ≈5%–10% faster than B waves until they reach the continental slope, presumably because of their greater amplitude. On the upper continental slope, all waves speed up relative to linear values, but B waves now travel 8%–12% faster than A waves, in spite of being smaller. Solutions of the Taylor–Goldstein equation with observed currents demonstrate that the B waves’ faster speed is a result of modulation of the background currents by an energetic diurnal internal tide on the upper slope. Attempts to ascertain the phase of the barotropic tide at which the waves were generated yielded inconsistent results, possibly partly because of contamination at the easternmost mooring by eastward signals generated at Luzon Strait’s western ridge. These results present a coherent picture of the transbasin evolution of the waves but underscore the need to better understand their generation, the nature of their nonlinearity, and propagation through a time-variable background flow, which includes the internal tides.


2020 ◽  
Vol 197 ◽  
pp. 07008
Author(s):  
Federico Colombo ◽  
Luigi Mazza ◽  
Giuseppe Pepe ◽  
Terenziano Raparelli ◽  
Andrea Trivella

This paper deals with the stabilization of an inverted pendulum on cart; the latter is pneumatically actuated by a double acting cylinder controlled by low cost proportional valves. In particular, a numerical model of whole system is developed in order to find the ability of the pneumatic actuation in stabilizing the pendulum and evaluate its bandwidth. A cascade of two control loops (the inner one for the pendulum angle, the outer one for the cart displacement) are analyzed and proper compensators are defined. The possibility of introducing an additional loop to control the force exerted by the actuator on the cart is evaluated.


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