Geometric focusing of internal waves

Maas, Leo R. M.; Lam, Frans‐Peter A.

doi:10.1017/s0022112095003582

Cited by 165 publications

(270 citation statements)

References 29 publications

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“…9. different depths at each ITEX2 along-canyon station suggests that the internal tide during this period is standing along the characteristic, in the manner of the basin internal seiches depicted in Maas and Lam (1995). This pattern is seen clearly in Fig.…”

Section: Volume 28 J O U R N a L O F P H Y S I C A L O C E A N O G R mentioning

confidence: 76%

“…Internal seiches in basins have been the subject of recent studies (Maas and Lam 1995;Münnich 1996), but they have rarely been observed in the ocean. Niiler (1968) discusses a seiching internal tide in the Straits of Florida, Winant and Bratkovich (1981) identify internal tides standing in the cross-shelf plane on the narrow southern California shelf, and Griffin and Middleton (1992) discuss standing internal wave patterns in the nearshore region off Sydney, Australia.…”

Section: A Possible Internal Tide Generation Sitesmentioning

confidence: 99%

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Observations of the Internal Tide in Monterey Canyon

Petruncio¹,

Rosenfeld²,

Paduan³

1998

J. Phys. Oceanogr.

153

117

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Data from two shipboard experiments in 1994, designed to observe the semidiurnal internal tide in Monterey Canyon, reveal semidiurnal currents of about 20 cm s Ϫ1 , which is an order of magnitude larger than the estimated barotropic tidal currents. The kinetic and potential energy (evidenced by isopycnal displacements of about 50 m) was greatest along paths following the characteristics calculated from linear theory. These energy ray paths are oriented nearly parallel to the canyon floor and may originate from large bathymetric features beyond the mouth of Monterey Bay. Energy propagated shoreward during the April experiment (ITEX1), whereas a standing wave, that is, an internal seiche, was observed in October (ITEX2). The difference is attributed to changes in stratification between the two experiments. Higher energy levels were present during ITEX1, which took place near the spring phase of the fortnightly (14.8 days) cycle in sea level, while ITEX2 occurred close to the neap phase. Further evidence of phase-locking between the surface and internal tides comes from monthlong current and temperature records obtained near the canyon head in 1991. The measured ratio of kinetic to potential energy during both ITEX1 and ITEX2 was only half that predicted by linear theory for freely propagating internal waves, probably a result of the constraining effects of topography. Internal tidal energy dissipation rate estimates for ITEX1 range from 1.3 ϫ 10 Ϫ4 to 2.3 ϫ 10 Ϫ3 W m Ϫ3 , depending on assumptions made about the effect of canyon shape on dissipation. Cross-canyon measurements made during ITEX2 reveal vertical transport of denser water from within the canyon up onto the adjacent continental shelf.

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Section: Volume 28 J O U R N a L O F P H Y S I C A L O C E A N O G R mentioning

confidence: 76%

Section: A Possible Internal Tide Generation Sitesmentioning

confidence: 99%

Observations of the Internal Tide in Monterey Canyon

Petruncio¹,

Rosenfeld²,

Paduan³

1998

J. Phys. Oceanogr.

153

117

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“…Recent observations and more complex models support Munk's inference (Garrett 1991;Toole et al 1994;Ledwell and Hickey 1995;Lueck and Mudge 1997). Processes causing mixing at lateral boundaries include internal waves shoaling at the sediment-water interface, shear from the upward and downward movement of the pycnocline, geometric focusing of internal waves, and flow over topographic features (Ericksen 1982(Ericksen , 1985(Ericksen , 1998Thorpe 1987Thorpe , 1995Taylor 1993;Imberger 1994;Ivey et al 1995;Maas and Lam 1995). Enhanced mixing has also been observed in deep basins when the topography is rough .…”

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confidence: 86%

Boundary mixing and nutrient fluxes in Mono Lake, California

MacIntyre

Flynn

Jellison

et al. 1999

Limnology & Oceanography

262

261

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Temperature-gradient microstructure and nutrient profiling were undertaken at both an inshore and an offshore site on Mono Lake, California, to determine whether boundary mixing occurred and the effects on nutrient flux within the lake. Turbulence, as quantified by rates of dissipation of turbulent kinetic energy, was two to three orders of magnitude higher at the inshore site where the pycnocline intersected the bottom than at the same depths at an offshore station. The intense turbulence primarily occurred within 3.5 m of the sediment-water interface. In addition, temperature profiles were more incrementally stepped in the pycnocline inshore than offshore. The Turner angle indicated that double-diffusive processes may have augmented turbulent transport in the upper 10 m, where temperatures were inversely stratified, but not in the main pycnocline. Within the pycnocline, ⑀ exceeded the threshold value for buoyancy flux (⑀ thr ϭ 15N2 ) in 21% of the turbulent layers inshore but in only 1% of the layers offshore. The coefficient of vertical eddy diffusivity, K z , was two to four orders of magnitude higher within 4 m of the bottom inshore than offshore at the same depths. Spatially averaged values of K z , obtained from the heat-flux method using data obtained from both conductivity-temperature-depth (CTD) profiles and moored thermistor chains, were two orders of magnitude less than those obtained nearshore with microstructure profiling. From the differences in K z , we inferred that most heat flux occurred due to boundary mixing at the base of the pycnocline inshore with the heat redistributed laterally by advection. Boundary mixing was initiated after winds were strong enough for the Lake number to decrease to a value of 2; thermocline compression and steepening of internal waves at the base of the pycnocline occurred, followed by packets of high-frequency internal waves critical for wave breaking. Calculated ammonium fluxes at the inshore site were sufficient to support daily rates of primary productivity in the deep chlorophyll maximum throughout the lake. These results indicate the vertical flux of nutrients across the nutricline in Mono Lake occurs over a limited area during intense mixing events initiated by high winds.Whether mixing events occur as frequently throughout the pycnocline as they do near lateral boundaries has implications for heat and nutrient fluxes and spatial heterogeneity of ecological processes. The importance of mixing near boundaries was inferred by Munk (1966), who determined

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“…New interest into the singular solutions to the Poincaré equation was put forward with the work of Maas & Lam (1995) on gravity modes in two-dimensional basins. The pressure fluctuations of internal gravity modes also satisfy Poincaré equation, and Maas & Lam (1995) showed the crucial role of characteristic trajectories and coined the concept of attractor to describe the convergence of characteristics to special limit cycles.…”

Section: Introductionmentioning

confidence: 99%

“…The pressure fluctuations of internal gravity modes also satisfy Poincaré equation, and Maas & Lam (1995) showed the crucial role of characteristic trajectories and coined the concept of attractor to describe the convergence of characteristics to special limit cycles. At the same time, Hollerbach & Kerswell (1995) and Kerswell (1995) investigated the internal shear layers spawned by the critical latitude singularity (another singularity different from that of the attractors), in relation with the precession flows of a spherical shell.…”

Section: Introductionmentioning

confidence: 99%

Inertial waves in a differentially rotating spherical shell

2013

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We investigate the properties of small-amplitude inertial waves propagating in a differentially rotating incompressible fluid contained in a spherical shell. For cylindrical and shellular rotation profiles and in the inviscid limit, inertial waves obey a second-order partial differential equation of mixed type. Two kinds of inertial modes therefore exist, depending on whether the hyperbolic domain where characteristics propagate covers the whole shell or not. The occurrence of these two kinds of inertial modes is examined, and we show that the range of frequencies at which inertial waves may propagate is broader than with solid-body rotation. Using high-resolution calculations based on a spectral method, we show that, as with solid-body rotation, singular modes with thin shear layers following short-period attractors still exist with differential rotation. They exist even in the case of a full sphere. In the limit of vanishing viscosities, the width of the shear layers seems to weakly depend on the global background shear, showing a scaling in E 1/3 with the Ekman number E, as in the solid-body rotation case. There also exist modes with thin detached layers of width scaling with E 1/2 as Ekman boundary layers. The behavior of inertial waves with a corotation resonance within the shell is also considered. For cylindrical rotation, waves get dramatically absorbed at corotation. In contrast, for shellular rotation, waves may cross a critical layer without visible absorption, and such modes can be unstable for small enough Ekman numbers.

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Geometric focusing of internal waves

Cited by 165 publications

References 29 publications

Observations of the Internal Tide in Monterey Canyon

Observations of the Internal Tide in Monterey Canyon

Boundary mixing and nutrient fluxes in Mono Lake, California

Inertial waves in a differentially rotating spherical shell

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