We show that discrete lenses of anomalously high-salinity water, originating from the shelf edge and trapped within the seasonal pycnocline, are advected 100 km or more onto the Celtic Sea continental shelf. We propose that the lenses are created by increased diapycnal mixing at the shelf edge associated with breaking high-frequency internal wave packets. Quasi-synoptic hydrography sections show the lenses to be 3–5 km wide, their temporal persistence confirmed by moored instrumentation and a series of CTD casts. Estimates of the propagation speed of these features (∼0.020 m s−1) compare favorably with the magnitude of observed residual currents. Residual current variability within the pycnocline is dominated by vertical structures most consistent with the second baroclinic mode. The residual flow is therefore thought to be predominantly driven by non-linear second mode internal tidal waves. These are observations of a shelf edge exchange process not previously identified.
 The exchange of water between the deep ocean and continental shelf plays an important role in the cycling of carbon and nutrients [Liu et al., 2010], and in flushing of fresh water and sediments from the shelf [McCave et al., 2001]. Here we present observations of a new shelf edge exchange process: lenses of high-salinity slope water, trapped within the pycnocline, being transferred 100 km or more onto the continental shelf. Historical data confirms that salinity anomalies within the pycnocline are a common occurrence, but never before has this signature been reliably captured in high resolution hydrography sections.
 The observations were made in the Celtic Sea, a 500 km wide section of the NW European shelf (Figure 1a). Depths on the shelf are typically 100–150 m and increase rapidly to more than 2000 m beyond the shelf edge. Internal tides are prominent during the stratified summer months, having peak-to-trough amplitudes of >50 m at the shelf edge during spring tides [Pingree et al., 1986]. With wavelengths of the order 35 km, they may coherently propagate 170 km or more on-shelf [Inall et al., 2011].
 Ocean-shelf water exchange in the Celtic Sea is thought to be dominated by drainage in the bottom Ekman layer, non-linearity of the internal tide and prevailing winds driving a cross-shelf surface Ekman transport [Huthnance et al., 2009]. Here we propose that residual currents within the pycnocline, driven by non-linear mode two internal waves, are responsible for on-shelf advection of discrete lenses of high salinity water generated at the shelf edge by enhanced vertical internal tidal mixing. The salinity anomalies described here have similar characteristics to the salty intrusions observed over the Middle Atlantic Bight (MAB) for which a number of formation mechanisms have been hypothesized, including wind forcing, warm-core rings, and baroclinic pressure gradients [Lentz, 2003]. Owing to the contrasting dynamics of the Celtic Sea and MAB however our proposed formation mechanism is different.
 Observations were made over the 5–13 June 2010 in the Celtic Sea when thermally driven summer time stratification was well developed, at a location 100 km from the shelf break (Figures 1a and 1b). Despite wind speeds peaking at over 10 m s−1 on three separate occasions the thermocline was not broken down. A Seabird 911 plus CTD provided water column profiles around two mooring sites, IM1 and IM3, where bottom mounted 150 kHz ADCPs and thermistor chains were deployed. Scanfish, an undulating vehicle fitted with a SeaBird 911 plusCTD, towed at 7 knots behind the ship, provided sawtooth-like up and down casts between the surface and 90 m. A complete up and down cycle was completed over a distance of 1.3 km. In total, over 1000 km of Scanfish data was collected covering a (140 km)2 area (Figure 1b). Shear micro-structure measurements were made around the moorings using a Rockland Scientific VMP-500 micro-structure profiler.
 Tidal analysis shows barotropic currents to be dominated by a clockwise semi-diurnal tide with a semi-major axis amplitude of 0.35 m s−1. The major axis is inclined 45° counter-clockwise from due east, a direction orthogonal to the shelf-edge, and we define across-shelf currents as being along this axis. Residual currents were calculated by subtraction of the fitted barotropic tide (with M2, S2, N2, K1, O1 and M4 constituents).
3. Saline Pycnocline Lenses
 A 90 km long Scanfish section normal to the shelf edge (Figure 1c) reveals a train of discrete lenses of anomalously high salinity water occupying the entire depth of the pycnocline (25–30 m). The lens width increases from 3 to 5 km with distance on-shelf. The salinity maximum at the centre of each lens is 0.04–0.09 greater than the salinity in surrounding surface and bottom waters. Transects in an along-shelf direction reveal similar isolated 3–5 km wide anomalies confirming that these are discrete, approximately symmetric features rather than elongated along-shelf streaks. By identifying local maxima in the along-track pycnocline salinity anomaly, we estimate that approximately 160 lenses were observed in the 1000 km of Scanfish data collected (Figure 1b).
 The vertical structure of the lenses was captured by a series of 26 CTD casts taken over 7.6 days. The salinity maximum within the pycnocline is 35.41 ± 0.01 (mean ± 1 s.d) and lies along the 26.9 ± 0.1 isopycnal (at a depth of 30.7 ± 4.2 m). The lens is 29.3 ± 5.1 m thick and has a maximum salinity of 0.05 and 0.07 greater than surface and bottom waters respectively (Figure 2a). These casts were taken over a range of different tidal states, the first approximately three days before neaps, and the last four days post-neap. The temporal persistence of the anomaly indicates that it was a stable feature, at least over the period of observation. The range of maximum pycnocline salinity values captured in the CTD casts (35.40–35.42) matches the peak salinities observed by Scanfish within and between lenses as it passed closest to the mooring site (Figure 1d). This provides evidence that anomalies are propagating past a fixed point.
4. A Pulsed Shelf Edge Salt Source
 Water with a salinity of 35.4 found mid-shelf is anomalous and must originate from the shelf edge where typical salinities are 35.65. The pulsed nature of the lenses indicates that there is not a continuous flow of saline water into the pycnocline, rather, that there is a regular, pulsed source.
 The generation of an M2internal tidal wave at the shelf edge as the pycnocline is depressed during off-shelf barotropic tidal flow leads to the formation of steep, higher frequency non-linear waves, which form on-shelf propagating packets [Pingree and New, 1995]. The associated strong current shear leads to increased localized turbulence and vertical mixing [Rippeth and Inall, 2002] that is responsible for the cool band of surface water along the shelf edge (Figure 1b). Given that these 1–2 km wavelength waves typically form in packets of 2–8 [New and Pingree, 1990], the local horizontal scale of each mixing event is approximately 2–16 km. We propose therefore that increased diapycnal mixing at the shelf edge, associated with breaking internal wave packets, generated at a semi-diurnal frequency, is the mechanism by which high salinity water enters the pycnocline.
 As discussed by Sundermeyer et al. , an isolated mixing event, vertically distorting isopycnals, produces a patch of weakly stratified water that will tend to collapse laterally driven by the resulting horizontal pressure gradients. Evidence of well mixed patches may be found in individual CTD casts that show the pycnocline to have a stepped structure, with 5–10 m layers of weaker stratification associated with the salinity maxima (not shown). Depending on the length and time scales of mixing, vortical modes may form, where the mixed patch starts to rotate, eventually falling into geostrophic balance [McWilliams, 1988]. The length scale to which horizontal expansion continues before being arrested by rotation will be set by the internal Rossby radius, Lro = c/f.The phase speed for long, non-dispersive internal wavesc = [(g′H1H2)/(H1 + H2)]0.5is calculated from an idealized 2-layer water column with surface and lower layer depths ofH1 = 30 m and H2 = 105 m having mean densities ρ1 = 1026.22 kg m−3 and ρ2 = 1027.26 kg m−3 respectively (Figure 2a). For the Coriolis frequency, f, at a latitude of 49.4°N, Lro = 4.3 km. The 3–5 km wide saline lenses are therefore consistent with estimates of the internal Rossby radius suggesting that they are in near-geostrophic balance and formed by smaller scale mixing events (<5 km).
5. On-Shelf Advection and Diffusion
 The high-salinity lenses are not restricted to the shelf edge and a net residual on-shelf flow, within the pycnocline, is required to achieve this. We will firstly estimate the advection speed by calculating the approximate rate of salt loss from a lens assumed to be propagating on-shelf over a known distance. ADCP currents will then be examined to independently support this estimate.
 Consider a lens to be a cylinder with radius r = 2.5 km and height h = 25 m, whose salinity decreases from S1 = 35.42 to S2 = 35.36 over a distance of x = 50 km (Figure 1d). Assuming that this salt loss is caused primarily by vertical diffusion the rate of change of salt integrated over the volume of the cylinder is
and are the vertical eddy diffusivities at the top (σθ = 26.4) and base (σθ = 27.2) of the pycnocline respectively. Depth, z(m), is positive upwards. From vertical micro-structure measurements made near continuously between 6–8 June, the mean vertical diffusivities along the 26.4 and 27.2 potential density contours were 9.1 × 10−5 and 6.7 × 10−6 m2 s−1 respectively. From CTD casts, ∂S/∂zs = −0.004 S m−1and ∂S/∂zb = 0.005 S m−1 are the vertical salinity gradients at the top and base of the lens. Rearranging equation 1 to find the time taken (Δt) for the salinity of the lens to decrease from S1 to S2, the average speed, u, required for the lens to be advected x km in this time is
Using the above values, Δt = 44 days and u = 0.013 m s−1. Substituting and with a single value of 3.9 × 10−5 m2 s−1, the mean Kz within the top and base of the pycnocline during the measurement period gives an estimate of 0.012 m s−1. This Kzvalues agrees with the range of daily mean vertical diffusivities calculated on-shelf bySharples et al.  of 2 − 7 × 10−5 m2 s−1.
 Estimates of the horizontal diffusivity (Kh) at the scale of the lens can be made following Okubo . Based on length scales of 2 to 6 km calculated from the mean pycnocline salinity (Figure 1d), Kh = 0.6 − 2.3 m2 s−1. Assuming that the horizontal salinity gradient, ∣∂S/∂x∣ = 1 × 10−5 S m−1, is constant in all directions and taking Kh = 1 m2 s−1, the additional rate of salt loss horizontally from the lens ( S m3 s−1) may be included in our calculations. In doing so the estimated advection speed slightly increases to 0.018–0.020 m s−1.
 These indirect estimates are supported by observations. Residual currents within the pycnocline, smoothed with a 12.4 hour window, for the seven days preceding the Scanfish transect are shown in Figure 3. At both IM1 and IM3 the magnitude of flow over a tidal cycle is 0.01–0.06 m s−1. The direction of flow between the two sites however is very different illustrating the meandering nature of residual currents over the shelf. At IM1 flow is primarily north-northwestward whereas at IM3 it is more variable and swings 270° from an initially southward to a west-northwestward direction. The time mean flows at IM1 and IM3 are 0.022 m s−1 NNW and 0.006 m s−1 WNW respectively but, given the short record and wide range in direction at IM3 they cannot be considered reliable measures of the long term net residual. Although still not a direct measure of the lenses' propagation speed these observations are supportive of the estimated 0.012–0.020 m s−1on-shelf transport.
6. Non-linear Internal Wave Transport
 Having estimated a feasible propagation speed for the lenses, it remains to identify the mechanisms driving the residual flow. We propose that the on-shelf flux of water within the pycnocline is principally driven by non-linear mode 2 internal waves.
 Non-linearity of the internal tide in the Celtic Sea is well recognized and is characterized by a deeply penetrating trough, more rounded wave crests and large amplitude, high-frequency non-linear waves propagating on-shelf in the trough [Pingree and New, 1995]. This asymmetry is readily observed in the thermistor chain record, as are packets of high-frequency solitons (not shown). Current variability of the internal tide is well represented by the first baroclinic mode [Pingree et al., 1986], and transport attributed to non-linearities is estimated to be of the order 1 m2 s−1 [Huthnance, 1995]. Here we show, based on analysis of the theoretical and empirical modes of current variability, that the second baroclinic mode is more likely than the first to be driving on-shelf advection of slope water within the pycnocline.
 The theoretical baroclinic modes, given a mean buoyancy profile N, are eigenvectors of the wave equation, ∂2w/∂z2 + [(N2 − σ2/σ2 − f2)]k2w = 0, where f is the inertial frequency, k the horizontal wave number, w the vertical perturbation at depth z, and σ the wave frequency. Figure 2b shows the horizontal velocity structures associated with mode 1 and 2 internal waves when σ = 12.4−1hours. Dominance of the first baroclinic mode and the importance of the second is confirmed by empirical orthogonal function (EOF) analysis performed independently on the residual across and along-shelf velocities at IM3. Structures comparable to baroclinic modes 1 and 2 are captured by the first three EOFs which together account for 95% of the variance in both the across and along-shelf directions (Figures 2c–2e).
 The first EOF (Figure 2c), containing the greatest percentage of the variance, is most comparable to the first baroclinic mode. The water column above and below 25 m oscillates in different directions, at a dominant inertial frequency. On-shelf transport in surface waters driven by non-linearities would favor more saline surface waters and fresher bottom waters, as we observe in the mean salinity profile (Figure 2a).
 The second two EOFs (Figures 2d and 2e), together explaining >26% of the variance, have mode 2 type structures and oscillate predominantly at the M2tidal frequency. Currents within the pycnocline (20–40 m) are stronger and for the third EOF in the opposite direction to those in surface and bottom waters. Both structures peak between 25 and 30 m, close to the location of the salinity maximum (30.7 m). Just as non-linear mode 1 waves sustain on average an on-shelf upper layer transport, so non-linear mode 2 current variability generates on-shelf advection within the pycnocline, and off-shelf transport in the layers above and below. Importantly, the zero crossing point for the first EOF is near the centre of the pycnocline and the mean depth of the salinity maximum. Consequently, despite the dominance of mode 1 throughout the water column as a whole, it is EOF modes 2 and 3 that make the more significant contribution to variability and residual flow within the pycnocline.
 This is illustrated in Figure 4where the mean across and along-shelf currents between 20 and 40 m have been reconstructed. EOFs 2 and 3 combine to give a period of sustained on-shelf flow between 12:00 on 8 June and 10:00 on 10 June matching the observed time-mean flow of 0.017 m s−1 over this period (Figure 4a). The contribution from the first EOF, that has a predominately mode 1 baroclinic structure, is an order of magnitude smaller (<0.001 m s−1). A period of sustained along-shelf flow averaging 0.023 m s−1 is also observed between 12:00 on 10 June and 13 June (Figure 4b). The second and third EOFs contribute a mean 0.026 m s−1 current. The difference is accounted for by a weak (−0.003 m s−1) southward mode 1 residual. The magnitude of these currents, sustained for two or more days and seemingly driven by baroclinic mode 2 type structures, fits well with the previously estimated advection speeds. Further evidence supporting the importance of mode 2 waves may be found in the thermistor chain data where the thermocline thickness oscillates with amplitudes of 1–9 m at inertial to M2 tidal frequencies (not shown).
7. Discussion and Conclusions
 The magnitude of tidally averaged residual flows observed within the pycnocline (0.01–0.06 m s−1) and the estimated advection speed (0.012–0.020 m s−1) compare well. Crucially however, the length of the ADCP record prevents residuals from being calculated over timescales comparable to the expected lifetime of the lenses. We are able to demonstrate that on- and off-shelf flows of the necessary magnitude are sustained for a number of days, but are unable to quantify the net residual over monthly timescales, although the observed salinity field is strong evidence that a net on-shelf flow is maintained.
 The salt flux based estimate of propagation speed should be treated as a minimum bound. Firstly, we assumed that the lenses originated from the nearest shelf edge point to the transect and were advected along it. The wide range of flow directions observed however demonstrate that the path of each individual lens is unlikely to be so direct. Also, estimates of Kzwere made over a neap tide; greater diffusivities and faster advection speeds would be expected during springs. A number of processes are likely to contribute to a meandering on-shelf flow and patchy generation of saline lenses. Firstly, the shelf edge is not smooth; rough and variably sloping topography mean that increased mixing does not take place in one long band along the shelf edge. Secondly, along-slope as well as across-slope flow is responsible for the generation of high frequency wave packets and diapycnal mixing [Holt and Thorpe, 1997]. In this way, internal waves propagate on-, off- and along-shelf dependent upon their generation mechanism.
 The estimated propagation speed is dependent upon the diffusivity, which may vary by two orders of magnitude. Minimum values observed were within the range of molecular diffusivity (4–7 × 10−7 m2 s−1). Maximum values at the top and bottom of the pycnocline were 8.1 × 10−4 m2 s−1 and 8.5 × 10−5 m2 s−1 respectively. Using these maxima, the estimated propagation speed of 0.12 m s−1remains realistic (50 km in 4-5 days). These speeds are observed, but maintained for hours rather than days (Figure 4). Given the patchy and wide ranging nature of diffusivity values it was appropriate to base an estimate of the propagation speed of each lens on the average diffusivity that it experiences.
 The strength of the pycnocline may be an important controlling factor in the persistence of these features. A three-layer water column with a broad pycnocline, as seen here, as opposed to a tighter two-layer structure, would better support higher mode internal waves and thus advection by mode 2 baroclinic currents. Additionally, within a wide pycnocline, where the diapycnal diffusivity is generally low, straining from oscillatory mode 1 current shear is insufficient to cause significant horizontal dispersion of the lenses [Young et al., 1982].
 The importance of this new mechanism that can transport slope water hundreds of kilometers onto the continental shelf is yet to be explored from a biogeochemical perspective. Increased mixing at the shelf edge drives a vertical flux of inorganic nitrate into the base of the pycnocline [Sharples et al., 2007]. Although this nitrate is used rapidly, the organic matter produced may be transported on-shelf within the lenses and ultimately be recycled.
 This work was funded by UK NERC grants, FASTNEt (NE/I030224/1) and Inertial Mixing (NE/F002432/1). ADCP and micro-structure profiler data were provided by Chris Old and Yueng-Djern Lenn (Bangor University, Wales). Thanks to Jeff Polton for helpful discussion. AVHRR SST data were supplied courtesy of NEODAAS, Plymouth.
 The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.