Internal tides in Monterey Submarine Canyon R. A. Hall1 and G. S. Carter1 1Department of Oceanography, University of Hawai'i at Manoa, Honolulu, Hawaii, USA. Abstract The M2 internal tide in Monterey Submarine Canyon is simulated using a modified version of the Princeton Ocean Model. Most of the internal tide energy entering the canyon is generated to the south, on Sur Slope and at the head of Carmel Canyon. The internal tide is topographically steered around the large canyon meanders. Depth-integrated baroclinic energy fluxes are up-canyon and largest near the canyon axis, up to 1.5 kW m−1 at the mouth of the upper canyon and increasing to over 4 kW m−1 around Monterey and San Gregorio Meanders. The up-canyon energy flux is bottom-intensified, suggesting topographic focusing occurs. Net along-canyon energy flux decreases almost monotonically from 9 MW at the canyon mouth to 1 MW at Gooseneck Meander, implying high levels of internal tide dissipation occur. The depth-integrated energy flux across the 200 m isobath is of order 10 W m−1 along the majority of the canyon rim, but increases by over an order of magnitude near the canyon head where internal tide energy escapes onto the shelf. Reducing the size of the model domain to exclude remote areas of high barotropic-to-baroclinic energy conversion decreases the depth-integrated energy flux in the upper canyon by 20%. However, quantifying the role of remote internal tide generation sites is complicated by a pressure perturbation feedback between baroclinic energy flux and barotropic-to-baroclinic energy conversion. 1 Introduction approach a slope from deep water, the onshore/offshore direction of propagation after reflection is determined by Submarine canyons are a common feature along conti- the ratio of the topographic slope to the internal wave nental shelves. They are estimated to cover approxi- characteristic slope, mately 20% of the shelf along the west coast of North s @H=@x America (Hickey, 1995). Canyons can be efficient gen- α = topog = ; (1) 1=2 erators of internal tides (internal gravity waves with swave [(!2 − f 2) = (N 2 − !2)] tidal frequencies) through scattering of the barotropic tides from sloping topography (Bell, 1975; Baines, 1982). where H is the total depth, x is distance, ! is the angular They are also thought to trap internal waves from out- frequency of the wave, f is the inertial frequency, and N side the canyon, through reflection from the sloping to- is the buoyancy frequency. If α < 1 (subcritical) waves pography, and channel the energy towards the canyon will continue to shoal after reflection. If α > 1 (super- head (Gordon and Marshall, 1976; Hotchkiss and Wun- critical) reflected waves will propagate back into deeper sch, 1982). water. If α = 1 (critical) linear theory breaks down, Unlike internal tide generation, which may be dom- leading to nonlinear effects and potentially wave break- inated by topographic blocking (Garrett and Kunze, ing. In a three-dimensional ocean it is more apt to vi- 2007), reflection of internal tide beams is entirely de- sualize internal wave `sheets' rather than beams (Carter termined by the topographic slope. Reflection is often et al., 2006; Jachec, 2007). The slope of an internal wave considered in only two-dimensions; when internal waves beam in a horizontal/vertical section will depend on the orientation of the section with respect to the internal Corresponding author address: Dr. Rob Hall, Department wave sheet. If section is in the same plane as the sheet of Oceanography, University of Hawai'i at Manoa, Marine Sci- ence Building, 1000 Pope Road, Honolulu, HI 96822, USA. the slope of the beam will equal swave. If the section is ([email protected]) perpendicular to the sheet the beam will be horizontal. 1 HALL AND CARTER: INTERNAL TIDES IN MSC 37oN 0 1 2 3 4 Depth (km) 55’ Monterey Meander 50’ Soquel Canyon 25 Smooth 45’ Ridge Gooseneck Meander 50 40’ San Gregorio Carmel Canyon Meander 35’ 100 75 30’ Sur Slope 30’ 25’ 20’ 15’ 10’ 5’ 122o W 55’ 50’ Figure 1: Bathymetry of Monterey Submarine Canyon. The contour interval is 100 m. The line along the axis of the canyon is the thalweg. Distance along the thalweg from Moss Landing is marked with a cross at 5 km intervals. Internal waves above the rim of the canyon are focused density increases upon reflection because the separation towards the canyon floor by supercritical reflection from between adjacent internal wave characteristics narrows, the steep canyon walls (Gordon and Marshall, 1976), concentrating the energy into a smaller area. Increases while internal waves entering the canyon from offshore in internal wave energy density have been observed in are focused towards the canyon head by subcritical re- Hydrographers Canyon (Wunsch and Webb, 1979), Hud- flection along the typically gentle sloping canyon floor son Canyon (Hotchkiss and Wunsch, 1982), and recently (Hotchkiss and Wunsch, 1982). In both cases, energy in Gaoping Canyon off Taiwan (Lee et al., 2009). 2 HALL AND CARTER: INTERNAL TIDES IN MSC Monterey Submarine Canyon (MSC) is located within sured depth-varying velocities and so considered all ve- and offshore of Monterey Bay in central California. It is locities to be baroclinic. However, numerical model sim- the largest submarine canyon along the west coast of the ulations of the tides in Monterey Bay (Jachec, 2007; United States, extending over 100 km from the abyssal Rosenfeld et al., 2009; Wang et al., 2009; Carter, 2010) plain at the base of the continental slope to within and have suggested barotropic M2 velocities may be sig- 100 m of Moss Landing in the centre of the bay. The nificantly larger. Jachec (2007) showed barotropic veloc- bathymetry of the canyon is very complex, with several ities in the upper canyon reach 0.06 m s−1. Both Rosen- sharp meanders in the upper reaches and two smaller feld et al. (2009) and Wang et al. (2009) quote barotropic side-canyons (Fig. 1). Following the canyon thalweg (the current magnitudes in the range 0.03{0.04 m s−1 for deepest part of the canyon axis) from Moss Landing, the Monterey Bay area. Most recently, Carter (2010) the first major meander is between 12 and 20 km, re- showed depth-averaged velocities in the bay can exceed ferred to as Gooseneck Meander. Between 30 and 55 km, 0.1 m s−1 and are spatially variable. there are two large meanders, Monterey and San Gre- Kunze et al. (2002) measured depth-integrated inter- gorio Meanders, that form an S-shaped bend. Soquel nal tide energy fluxes of 5 kW m−1 around San Gregorio Canyon merges with MSC from the north at around and Monterey Meanders, decreasing to order 1 kW m−1 32 km, just up-canyon of the apex of Monterey Mean- around Gooseneck Meander. Other energy flux measure- der. Carmel Canyon merges with MSC at around 60 km, ments have been made up-canyon of Monterey Mean- down-canyon of San Gregorio Meander. Further down- der. Petruncio et al. (1998) estimated the semi-diurnal canyon the canyon intersects two regions of smooth shelf internal tide energy flux to be 1.3 kW m−1 at a sta- slope, Smooth Ridge to the north and Sur Slope to the tion 22 km along the thalweg, slightly down-canyon of −1 south. The canyon floor is gently sloping (stopog = 0:03 Gooseneck Meander, and 0.8 kW m at 6 km, near to 0.06) and is subcritical to semi-diurnal internal tides the canyon head. Carter and Gregg (2002) made sev- down-canyon of San Gregorio Meander; up-canyon of eral measurements of internal tide energy flux, between the meander, the floor is near-critical. The canyon walls 2 and 11 km along the thalweg1, ranging from 0.3 to are steep (slopes up to 0.7) and supercritical along the 1.9 kW m−1. These internal tide energy fluxes are larger whole length of the canyon. than those typically found at continental shelf edges (or- The currents in MSC are dominated by a semi-diurnal der 0.1 W m−1, Sherwin, 1988; Green et al., 2008), but internal tide. Velocity amplitudes > 0.2 m s−1 have been less than half that observed at the mouth of Gaoping observed in the canyon (Shepard et al., 1974; Rosenfeld Canyon (Lee et al., 2009). et al., 1994; Petruncio et al., 1998) and are intensified Previous measurements of internal tide energy fluxes near the bottom (Xu et al., 2002). Key (1999) observed have been predominantly in a net up-canyon direction, strongly bottom-intensified currents near the head of the suggesting the majority of internal tide generation oc- canyon that were associated with internal tidal bores. curs offshore or in the lower reaches of the canyon. On Semi-diurnal vertical isopycnal displacements with 30 the basis of internal tide characteristics, Petruncio et al. to 60-m amplitudes have also been observed near the (1998) suggested Smooth Ridge and the steep ridge in- canyon head (Broenkow and McKain, 1972; Petruncio side San Gregorio Meander as likely generation sites, but et al., 1998; Carter and Gregg, 2002). later studies found no evidence for internal tide gen- The M2 is the dominant tidal constituent in the eration at these locations (Kunze et al., 2002; Jachec canyon and four largest constituents (M2, S2, K1, and et al., 2006; Carter, 2010). Kunze et al. (2002) and O1) account for 90% of the total current variability (Xu Carter and Gregg (2002) identifed along-canyon flux di- and Noble, 2009). Near-inertial oscillations are absent vergences and down-canyon energy fluxes near Goose- (Kunze et al., 2002), possibly due to the presence of neck Meander, suggestive of local internal tide genera- the steep canyon walls.