Internal Tides in Northern Gulf of Mexico: Unraveling a Coastal Transport Mechanism

K. Huguenarda, D. Boguckib, C. Mitchellc, E. Coelhod, T. Özgökmene, B. Hausf, A. Reniersg, A. Valle-Levinsonh, M. Goughi

a-cTexas A & M-Corpus Christi Department of Physical and Environmental Sciences6300 Ocean Drive, Building HRI 122, Corpus Christi, Texas 78412, USA

aKimberly.arnott@tamucc.edu ( Corresponding Author)(361) 825-2036bDarek.bogucki@tamucc.educ akishida.boom@gmail.com

dUniversity of New OrleansNaval Research LaboratoryCode 7322, Building 1009, Room C128Stennis Space Center, MS 39529, USAemanuel.coelho.ctr.po@nrlssc.navy.mil

eUniversity of Miami Department of Meteorology and Physical OceanographyRosenstiel School of Marine and Atmospheric Science4600 Rickenbacker CausewayMiami, FL 33149-1098, USAtozgokmen@rsmas.miami.edu

f, g, iUniversity of Miami Division of Applied Marine PhysicsRosenstiel School of Marine and Atmospheric Sciences4600 Rickenbacker CausewayMiami, FL 33149 USA

fbhaus@rsmas.miami.edugareniers@rsmas.miami.eduimkgough@nps.edu

hUniversity of Florida Department of Civil and Coastal Engineering365 Weil HallGainesville, FL 32611 USAarnoldo@ufl.edu

Abstract

Following the 2010 Deepwater Horizon Oil Spill, an effort to accurately predict oil spill movement has been made to better mitigate emergency response. Previous research (Boehm et al., 2002; Noble et al., 2009) suggested that nonlinear internal tides can induce transport at the surface, a mechanism that is not captured in various surface drift trajectory models.

The objective of this research is to determine the surface transport typical by internal tides observed in the northern Gulf of Mexico and evaluate whether these estimates aretheir contribution is large enough to contribute to inaccurateaffect particle trajectory forecasts. Evidence supporting surface transport induced by internal tides was characterized through hydrographic, acoustic, and surface drifter observations collected during the summer 2012 Grand Lagrangian Deployment (GLAD) in the northern Gulf of Mexico. Near-surface water density collected below the ship values displayed two reductions in value over several hours, a and was the first indication of internal tides. Acoustic measurements also showed internal tides in the distribution of echo intensity and were demonstrated byillustrated ~3.5 m pycnocline displacements. Baroclinic velocities revealed that these internal tides were propagating onshore. An Empirical Orthogonal Function (EOF) analysis of both the baroclinic velocities and echo intensity featured a vertically sheared spatial structure, which compared favorably with the vertical structure of the first mode vertical and horizontal velocities via the Taylor Goldstein analysis. The mode 1 wave speed was estimated to be 0.5 m/s. The theoretical horizontal surface transport was estimated to range from approximately 8 km to 13 km. To determine if internal tides influenced drifter transport, the across-shelf drifter displacements of a drifter over the Alabama/Louisiana shelf were filtered to remove synoptic wind and low frequency influences. The cumulative transport from internal tides was calculated to be 2.7 km based on analyzed drifter trajectories, which was lower than the 8 km transport prediction. These results provided evidence that internal tide- induced surface transport could be important and also provide insight into observed drifter trajectories.

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1. Introduction

Internal tides are long internal waves which that are formed through a perturbation of the pycnocline from the interaction of tides with abrupt changes in bathymetry such as a the continental shelf break or a sill (Pichon and Correard, 2006). For large bathymetry variations, most of the majority of the barotropic tide is transformed into low mode internal tides, which can propagate over 1000 km away from the generation site (Ray and Mitchum, 1997). The critical threshold for which internal tides are effectively generated occurs when the characteristic ray angle from the horizontal of internal tides matches the slope of the topography (Thorpe, 2005). Internal tides frequently propagate horizontally, have tidal frequencies (Lamb, 2014), and wavelengths that are much longer than the pycnocline depth. Baroclinic tidal currents can be comparable to barotropic tidal currents. The vertical shear from of baroclinic currents can be significant large enough to lead to instability and mixing (Garrett and Kunze, 2007). Internal tides can evolve into short, high-frequency internal waves as they propagate toward the shore and are common in the coastal ocean. Large wave amplitudes combined with dispersion can result in the internal tide becoming nonlinear (Lamb, 2014), causing it to steepen and break, which can support the formation of nonlinear, short wavelength internal waves (Ramp et al, 2004; Zhao and Alford 2006). These short wavelength internal waves can maintain a fixed phase relationship with the internal tide, even after four tidal cycles (da Silva, 2011) and are a common feature on a the continental shelf (Jackson and Apel, 2014).

Nonlinear internal tides have been shown to induce cross-shelf transport (Boehm et al., 2002; Noble et al., 2009). Noble et al (2009) explored the strength of cross-shelf transport into nearshore waters from shoaling internal tides in San Pedro Bay, California. They found that nonlinear internal tides transport dissolved nutrients and suspended particles from the mid-shelf to nearshore regions. The scope of this investigation is focused on internal tides, which dynamically differ from their short wavelength, high frequency descendants.

1.1 Linear Internal Tide

The equations governing the linear internal tide in a rotating stratified, inviscid fluid (Baines, 1982) can be factored into horizontal and vertical dependence when presented in terms of the streamfunction φ (x , z ,t ):

φ ( x , z , t ) :=ϕ (z ) exp [ i ( kx−ωt ) ] . (1)

In general the assumption of linearity is applicable when the forcing is sufficiently small i.e. when the wave amplitude << than the relevant depth and signifies a baseline for discussing nonlinear effects when the forcing amplitude increases.

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Typically, the internal tide is observed as a long and hydrostatic mode 1 internal wave (Baines, 1982; Baines, 1995; Green et al, 2010) with the vertical variability captured by ϕ ( z )−¿the solution to the Taylor-Goldstein (TG) equation. With a 2D stream defined by

u=−∂ φ∂ z

(2)

and

w=∂ φ∂ x

, (3)

the associated TG describing ϕ ( z ) assumes the form:

d2 ϕdz2 +[ N2−ω2

ω2−f 2 ]k 2ϕ=0.(4)

The boundary conditions are ϕ (0 )=ϕ ( h )=0, N2=−gρ

∂ ρ∂ z is the buoyancy frequency, k is the

horizontal wavenumber, f is the Coriolis parameter, ω is the internal tide frequency and ϕ (z ) is the modal amplitude for internal wave modes in a waveguide of depth h. Equation 4 is an eigenvalue problem, where the eigenvalues, k, and eigenfunctions ϕ(z) represent various internal wave dynamic modes. The local value of ϕ (z ) is directly proportional to the vertical velocity and the gradient yields the perturbation horizontal velocity. These ideas will be applied to data collected in the northern Gulf of Mexico in 2012.

1.2 Motivation

Data from the Grand Lagrangian Deployment (GLAD- see http://carthe.org) in the Gulf of Mexico also revealed evidence of internal tides near DeSoto Canyon and the Alabama-Louisiana Shelf. This location gained historical significance because of the proximity of the Deepwater Horizon drilling rig. Its explosion in 2010 resulted in the release of ~4.4 million barrels of unprocessed crude oil into the ocean (Crone and Tolstoy, 2010). This event has generated research including an experiment in 2012 designed to understand surface currents in the Gulf. GLAD supported a consortium of 26 principal investigator scientists from 12 research institutions challenged with delivering high-level models of the complex surface and subsurface transport in the Gulf of Mexico. The researchers deployed over 300 drifters transmitting GPS coordinates that were tracked as they were transported through the Gulf. During this field campaign, unexpected observations revealed indication of internal tides. Two long reductions in density 2 m below the surface (collected at 0.2 Hz) onboard the R/V Walton Smith were observed over the Louisiana/Alabama shelf and indicated the presence of long internal waves

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with wavelengths comparable to internal tides (Figure 1). Correspondingly, a drifter was observed to move shoreward in close proximity to the density reductions (Figure 1).

These observations inspired two questions: Are internal tides inducing surface transport, similar to recent studies (i.e. Noble et al. 2009)? Could the transport be large enough to influence surface drifter movement, possibly leading to inaccurate drifter path predictions?

In answering these questions, the manuscript concludes the introduction by reviewing important features of study site. Section 2: Data Collection and Processing outlines the field campaign that provoked the objectives for this research and data processing techniques. Section 3 presents the evidence confirming the presence of internal tides near the shelf break and frames the importance of their existence in context of surface transport. Important findings and implications of this research are presented in the Discussion and Conclusions.

1.3 Gulf of Mexico Basin

The Gulf of Mexico is a semi-enclosed basin located along the south-ern central coast of the United States and the north eastern and eastern coast of Mexico. It is connected to the Atlantic Ocean and Caribbean Sea by the Florida Straits and the Yucatan Channel (Oey et al., 2005) respectively. The open ocean transport scenarios in the Gulf of Mexico include a large quasi-geostrophic Loop Current system which is typically represented in ocean models. In context of an oil spill, how oil would behave within this system is still a major issue. Moreover, near DeSoto Canyon and coastal regions, processes at multiple scales and depths become very important, further complicating the trajectory estimates of oil. The data included in the present paper ranges from the northern edge of the submarine DeSoto Canyon to the Louisiana/Alabama continental shelf in the northern Gulf of Mexico.

The stratification structure in this region generally demonstrates a thin layer of warm, less salty water above cooler, denser water during the summer, while winter brings a more uniform and well-mixed body of water. The continental shelf extends approximately 120 km offshore and connects to the canyon by a relatively moderate 9° slope (Harbison, 1968). DeSoto Canyon is an S-shaped erosional valley that is scattered with large salt domes. These domes that can extend hundreds of meters in height. This region is dominated by a diurnal tidal regime, and classified

by a Form Factor F=K1+O1

M2+S2 of 6 and features featuring a 0.43 m tidal range (Shell Beach

NOAA tidal station). Freshwater influences are significant in the coastal region because of several sources of riverine input. Freshwater enters the locale from the Atchafalaya and Mississippi River Deltas (Dinnel and Wiseman, 1986), in addition to the Mobile Bay River system to the east (Dzwonowski et al., 2011).

The Bermuda High Pressure system modulates the wind regime in the northern gulf, resulting in cold air temperatures in the fall, when the system weakens and moves northeast (DiMego et al., 1976). However, during the spring and summer, southeasterly breezes develop

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when the system Bermuda High strengthens and moves southwest. Dzwonkowski et al. (2011) showed that on the Alabama Shelf, wind stress often forced subtidal surface currents. The along-shelf wind correlated well with subtidal currents during all seasons. However, the cross-shelf winds are well correlated during fall/winter when the water column is weakly stratified, but not during the increasingly stratified summer months. A thermally driven daily sea breeze develops locally and features northward winds during the day that reverse at night. The ocean’s response during these episodes is a near-inertial oscillation (DiMarco et al., 2000). These oscillations materialize through surface intensified currents, manifested by sudden changes in surface wind stress (Jarosz et al., 2007). Potentially extending 100 km offshore, these events can remain for a week or and are most prevalent during the summer (Simpson et al., 2002). The associated currents can be an one order of magnitude larger than those induced by Ekman drift. Provided that relevant information describing the study area has been reviewed, the data collection and processing techniques are detailed in the following section.

2. Data Collection and Processing

In an effort to develop an understanding of the movement and life cycle of hydrocarbons released in the ocean, the Consortium for Advanced Research on Transport of Hydrocarbon in the Environment (CARTHE) organized a summer expedition in the Gulf of Mexico. The expedition was executed to gather data used to clarify large and small-scale ocean movementat different spatial scales of motion. The University of Miami’s vessel, the R/V Walton Smith, set out to deploy 300 drifters from July 17 to August 3rd 2012 in the proximity of the former Deepwater Horizon and Desoto Canyon during an experiment coined the Grand Lagrangian Deployment (GLAD). Travelling at speeds of approximately 4 m/s (much faster than mode1 internal wave speed), the ship collected near surface temperature and conductivity from a flow through system with its intake at 2-m below mean sea level.

The water was sampled with a SeaBird SBE-45 MicroThermosalinograph (TSG) at a rate of 0.2 Hz. Additionally, a SeaBird Conductivity Temperature Depth (CTD) profiler was deployed periodically at various locations along the continental shelf break and in DeSoto Canyon. Current velocities profiles were measured at 0.67 Hz using a hull-mounted 600 kHz Acoustic Doppler Current Profiler (ADCP) that was mounted at the base of the ship. This instrument was programmed with a 3 m blanking distance and collected 1 m bins to a depth of 20 m. The ADCP configuration yielded short and long term averaging ensembles, providing velocity profiles at 1 and 5 minute intervals.

2.1 ADCP Data Processing

The 5 min averaged data from the ADCP were filtered depurated using a criterion that accepted values with percent good > 90% and absolute value of the error velocity < 10 cm/s. The bottom 10% of the measurements was removed to account for side lobe effects when the ship was over shallow depths. The Current velocity values were interpolated onto a uniform grid

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consisting ofwith a 1 m depths depth resolution and 5 min time intervals. The north-south and east-west velocities were rotated 70° to reflect across-shelf (y’) and along-shelf (x’) directions (Fig. 1). Baroclinic velocities were estimated by subtracting the depth-mean of the across-shelf velocities, a technique which can be implemented when velocity observations extend throughout most of the water column (Aguirre et al., 2010; Ross et al., 2014).

Acoustic backscatter (the normalized version of echo intensity) is often used to examine internal waves (Sandstrom et al., 1989; Valle-Levinson et al., 2004; Ross et al., 2014) and the sound scattered in the ocean is often presented in terms of sound scattering strength, I(z,t) (Urick, 1983).

I ( z , t )=10 log10(Echo Intensity ) (5)

The normalization of I(z,t) functions to account for bottom to surfacesound attenuation and spreading losses away from the source (Rippeth and Simpson, 1998):

EchoN=I ( z , t )−⟨ I (z )⟩ (6)

EchoN was calculated by subtracting the temporal mean of the sound scattering strength from the instantaneous sound scattering strength. The vertical gradient of EchoN can clearly delineates internal wave activity unambiguously (e.g. Ross et al., 2014).

An Empirical Orthogonal Function (EOF) analysis was performed on the baroclinic velocity and EchoN to compare the spatial structures with the vertical structure of z obtained from the Taylor Goldstein analysis (Small et al., 1999). EOFs are a statistical technique that decomposes the temporal variance of a spatially varying signal into orthogonal modes, termed here “EOF-mode” to distinguish from internal wave mode. Essentially, this method consists of finding the eigenvalues and eigenvectors of the covariance of the matrix of velocity data. The eigenvalue represents the percentage of the variance accounted for each EOF-mode, while the eigenvector represents the vertical structure of baroclinic velocity or of (EchoN) for each EOF-mode (in this particular application). The corresponding weighted amplitudes describe the temporal variable of each EOF-mode.

2.2 Transport Predictions

The goal of this investigation is to estimate the surface transport displacement from internal tide observations and compare it with that obtained from drifter trajectories to determine if internal tides are significantly influencing the transportmotion. The surface transportdisplacement, LTransport, associated with a long horizontally propagating, internal tide is

estimated to the first order in a

H 1 as (Eq. 10- see Appendix):

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LTransport=12

aH 1

L (7)

where a is the amplitude, H1 is the upper layer thickness (distance of modal amplitude from surface) and L is the length of the internal tide.

In order to utilize use Equation 7, a, H1 and L must be obtained from CT, CTD, and ADCP observations. The wavelength of the internal tides, L, was determined from the GPS coordinates of most seaward reduction in surface temperature. The amplitude was estimated from various acoustic measurements. Lastly, H1 was determined from the Taylor Goldstein equation. The mean density profile (N2 ) used in Eq. 4 (Fig. 3a) was estimated from the average of 22 CTD casts collected on July 24th and 25th, 2012 near the shelf break of Desoto Canyon. Given that the resolution of the density data began recording at 3 m depth, the mean profile was extrapolated to the surface, assuming the 1 m value equaled the minimum density in the density reductions of the near surface ship observations (Fig. 1). The mean density profile was averaged into 5 m bins and then interpolated onto a 1 m grid, assuming the gradient of density was zero near the surface for stability. These steps were taken because of the sensitivity of the vertical gradient of density to the analysis (Smyth et al., 2010). The density profiles were truncated at 30 m to reflect the depth during the first internal tide observation. These profiles were used to find the phase speed and modal structure of the internal wave first mode – see Appendix. Then, H1

was determined from the distance from the surface to the depth (zmax) where the eigenfunction zattained a maximum (i .e . ϕ (zmax)’= 0).

2.3 Drifter Data Processing

The drifters were a modified CODE style (Davis, 1985) designed to track the upper 1-m of the water column. Each drifter carried a Spot-GPS unit that provided updates of its position by satellite every 5 minutes with a nominal position resolution of 5 m. The surface drifter data were supplied post-processed by the Naval Research Laboratory. The quality-controlled data set was interpolated onto a 15-minute grid and corrected for anomalies in position and velocity. Given that the cross-shelf movement was of interest, the north-south and east-west displacements for every 15 min were rotated, similarly to velocity, to reflect across- and along-shelf directions. Only one drifter was transported onto the Alabama-Louisiana shelf from Desoto Canyon and was selected to investigate if internal tides were influencing surface transport.

2.4 Wind, Stokes Drift and Buoyancy Data Processing

Complicating this analysis is the fact that there are a variety of other mechanisms that can impact horizontal surface displacement,: namely : wind drift, Stokes drift, tides, and buoyancy-induced currents. To isolate these other mechanisms, hourly wind data were acquired from NOAA buoy Luke offshore platform. Wind data were converted into north-south and east-west components to explore the relationship between wind and drifter displacements. From the same platform, various spectral wave parameters were obtained to estimate a Stokes drift velocity.

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Following the method of Tamura et al. (2012), the magnitude of the Stokes drift velocity was calculated from the directional wave spectrum. Water level data from NOAA tidal station at Pilottown, LA was obtained to identify the tidal regime and the phase of the tide when drifter displacements occurred. Lastly, to investigate the influence of the Mississippi River and Mobile Bay river system on surface transport, surface salinity and temperature measurements were collected at USGS Northeast Bay Gardene Station (every 15 minutes) near the Mississippi delta and at NOAA Mobile State Docks Station (every 6 minutes). Surface horizontal density gradient

values were calculated, ∂ ρ∂ x , relative to the ship’s surface density observations. To achieve this,

we interpolated the ship density data onto both 6 and 15 minute grids to calculate the horizontal gradient. Next, the evidence is presented that supporting supports the hypothesis that internal waves are influencing drifter trajectories in the Northern Gulf of Mexico is presented.

3. Results

The focus of this analysis was to determine if whether internal tides generated at the northern shelf break of DeSoto Canyon are influencinginfluence surface drifter transportdisplacements. Near surface density measurements, collected on July 24th, 2012, revealed the first sign of internal tides. Density measurements collected approximately 2 m below the surface depicted reduction characteristic of a mode 1 long internal wave (Fig. 1). Two density reductions (Δρ ~ 3 kg/m3), delineated by two blue arrows in Figure 1, were observed as the ship traveled southward at 4 m/s southward.

A map (Fig. 2a) displays tThe ship trajectory covered the continental shelf (grey path in Fig. 2a) corresponding to the ship location over the shelf, while the red path denotes observations in overand a portion over Desoto Canyon (red path in Fig. 2a). The results described herein are from the observations over the shelf. A moving average was used to remove the diurnal (24 hrs) trend (low-frequency variability) from the instantaneous temperature values collected 2 m below the surface (Fig. 2b). The vertical gradient of EchoN (Fig. 2c) was used to trace the location of the pycnocline. Pycnocline departures oscillations indicated very long internal waves of depression, linked to two large reductions (ΔT > -0.5 °C) in temperature after times 24.2 and 24.4 (highlighted with yellow blocks arrows in Fig. 2b). The across-shelf distance travelled by the ship during internal tide observations was 44 km (landward) and 39 km (seaward). These lengths were corrected (as presented in the following section) for the Doppler shift between the boat and internal tide using the internal tide speed, c. They represent the approximate lengths of internal tides, which are consistent with a long wave when compared to the water depth.

During pycnocline departures oscillations at times 24.3 and 24.45, the corresponding baroclinic velocity (Fig. 2d) featured shoreward flow in the upper layer and seaward flow beneath. This demonstrated a velocity distribution consistent with a mode 1 long internal wave. The baroclinic velocity and vertical gradient of EchoN provided the internal wave amplitude (a ~ 3 m to 4 m). The observations are compared next with predictions using internal tide theory.

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3.1 Taylor Goldstein and Empirical Orthogonal Function Analyses

The results from the TG and EOF analyses are depicted in Figure 3. The climatological stratification of the area in July 2012 featured the pycnocline from 6 m to 9 m, depicted by elevated (N2 = 0.003 s-2) squared buoyancy frequency values (Fig. 3a). Based on the solution of the TG problem (Eq. 4), the profile of modal amplitude, ϕ(z), which represented the vertical structure of the vertical velocity, showed the greatest value near 9 m. Therefore, the gradient of the modal amplitude, ϕ’(z), in that location would be minimum, meaning that for a small amplitude internal tide the horizontal velocities at this depth should also be minimum. The horizontal velocity minimum associated with the internal wave follows the pycnocline location (following Eq. 1 through Eq. 4).

The observed baroclinic velocity minimum in Figure 2d after times 24.2 and 24.4, which reflected indicated the combined wave amplitude and upper layer height (a + H1), was located at 9 m. We attribute the differences to the sensitivity of the TG equation solution sensitivity to the location of the strong near surface density gradient (Fig 3a). Our analysis estimates the upper layer thickness, H1, to range from 5 m to 6 m combined with wave amplitude ranging from 3 m to 4 m. The ratio of the approximate internal wave amplitude and upper layer height (a/H1 = 3/5 and 4/6 = 0.6 and 0.66) indicated that the internal tides were neither linear nor nonlinear (0.1 < a/H1 < 1), but somewhere between.

Horizontal velocities above the pycnocline were directed onshore (with the largest values near the surface) and values beneath were directed offshore, as shown by the vertical profile of horizontal velocity (Fig. 3c). This profile was consistent with the vertical structure of the baroclinic velocity during internal tide observations. To explore this further, an EOF analysis was performed on the baroclinic velocity and normalized echo anomaly to compare the observations with the TG first modal amplitude structure. The EOF spatial structure of the first modes of baroclinic velocity (grey) and EchoN (black) are presented in Figure 4e, and represented 83% and 70% of the variance, respectively. Results showed vertically sheared profiles consistent with vertical profile of horizontal velocities from TG analysis (Fig. 3d). The weighted amplitude of the baroclinic velocity (Fig. 3e), which describes how EOF-mode 1 changes in time, was compared to the near surface temperature measurements (Fig. 3f). This was done to link baroclinic velocities to isotherm departures and showed consistency during internal tide observations at times 24.3 and 24.45.

The first mode wave speed, c, estimated from TG analysis was 0.5 m/s. The corrected lengths of the internal tides observed in Figure 2 were 38 km (landward) and 33 km (seaward). These values were obtained, assuming the waves were travelling at approximately 0.5 m/s across-shelf as the boat travelled in an opposing direction, were 38 km (landward) and 33 km (seaward). Due to the uncertainties associated with the estimates of H1 and a, we use the linear wave mode 1 speed as the true wave speed, acknowledging that the real wave speed was somewhat larger when considering the contribution of nonlinearities. Using these new Doppler

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shift corrected lengths and c, the period of response, T, for the internal tides was 21 hrs and 18 hrs.

To provide evidence that the internal tides were indeed, ducted (i.e. propagating nearly horizontally), the ray slope (Lamb and Kim, 2012) was estimated using:

r=√ ω2−f 2

N 2−ω2

(8)

where ω is the wave frequency (2π/T) and f is the Coriolis parameter (3.3 x 10-5 s-1). Using the periods of response mentioned above and N2 in the pycnocline, the angles at which the internal tides were propagating with the horizontal were 8° (landward) and 9.7° (seaward). Internal tide generation occurs where the seabed slope is the same as the internal tide wave characteristic slope (Sharples et al., 2001)., This indicating indicates that the internal tides were likely generated at the 9° shelf slope of Desoto Canyon (Harbison, 1968). Our results presented earlier have provided evidence of two weakly nonlinear (i.e. 0.01 < a/H1 < 1) internal tides, propagating onshore, with lengths spanning 33 km and 38 km. To estimate the transport horizontal displacement at the surface, a, H1, and L were used in Equation 7 to yield Ltransport Ldisplacement = 8 km and 13 km, with the details outlined in Table 1. This predicted transport was compared next with drifter transports from a drifter that was deployed near the Alabama/Louisiana shelf.

3.2 Comparison of Projected Surface Transport with Drifter Observations

During the GLAD experiment, over 300 drifters were deployed at various locations over DeSoto Canyon. Inertial oscillations were prevalent amongst the drifters, but the mean movement varied widely. In the deep water of northern DeSoto Canyon, a group of drifters moved principally east-west along the shelf break, whereas a cluster of drifters, located near the southeastern edge of the Canyon, swiftly diverted southward. Drifters located seaward of the intersection of the northern and southern edge of the Canyon diverged in time; roughly half of the drifters moved south while the rest traversed to the north. These drifter clusters were likely influenced by either a single eddy or pairs of counter-rotating eddies that dominate the surface currents over DeSoto Canyon (Wang et al., 2003).

A drifter was deployed in the shelf break onto of the Louisiana/Alabama shelf and was transported landward onto the shelf. Figure 4a displays a map of the drifter trajectory from July 22 (near when it was deployed) to July 25, after which the drifter was transportedmoved to the west toward the Mississippi Delta. The north-south and east-west drifter displacements over 15 min periods were calculated and transformed to reflect represent across-shelf movement. Provided that across-shelf movement from internal tides was of interest, the across-shelf displacements were smoothed using a moving average spanning 48 hrs over an 8 day period. The filtered movement was then subtracted from the instantaneous values to reflect the removal the low frequency forcing (i.e. synoptic wind) below 48 hrs from drifter movements. Three tidal

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pulses were selected to be investigated, two representing movement during flood (red and yellow areas in Fig. 4b) and one ebb (blue area) during July 23 and 24th. The total across-shelf displacements were calculated during each tidal phase, yielding 5.7 km (flood), 6 km (ebb), 8.4 km (flood). Given the IW observations occurred on July 24th, the flood event during the 24th was subtracted from the previous flood phase to estimate transport induced by internal tides (LT = 2.7 km).

Other mechanisms are known to influence surface transport. Despite thatAlthough the drifter displacements were filtered to remove synoptic wind and low frequency forcing, time series of wind (Fig. 4c), water levels (Fig. 4d), Stokes drift velocities (black) and horizontal density gradients (grey- Northeast Bay Gardene and Mobile State Docks NOAA stations) were plotted (Fig. 4e).Wind velocities showed moderate (> 5 m/s) onshore winds that persisted until time 23.5, after which the diurnal cycle of sea breeze during the day and offshore winds at night developed. The water levels revealed that the onshore/offshore drifter pulses were, in fact, linked to the tides. The Stokes drift velocity was calculated from wave spectra data from NOAA offshore directional wave buoy on the shelf break at 160 m depth and displayed increased drift velocities from July 24th to the 25th. However, the largest values were ~5 mm/s and suggested that Stokes drift had a minimal role in surface transport over the outer continental shelf. The surface horizontal density gradient at both Mississippi Delta and Mobile Bay locations, calculated relative to the ship density measurements, yielded low frequency variability that gradually increased to a maximum near day 24. Spectra (not shown) of the horizontal density gradients showed that the Mobile Bay horizontal density gradients were dominated at 0.5 cycles per day (cpd) and Mississippi Delta at 2.5 cpd. The Mobile Bay horizontal density gradients were controlled at frequencies lower than the tides and the Mississippi Bay system was dominated near the semidiurnal frequency. Therefore, internal tide induced surface transport may act in-concert or modify currents from density fronts.

4. Discussion and Conclusions

The Data collected in situ data hashave shown evidence of internal tide activity over the shelf, located shoreward of DeSoto Canyon. Reductions in temperature measurements 2 m below the surface indicated weakly nonlinear, internal tides, outlined by pycnocline departures observed in normalized echo anomaly data. The baroclinic velocities provided further evidence of internal tides and demonstrated shoreward across-shelf velocities in the upper layer and seaward velocities beneath. These long waves were located in the upper region of the water column and displayed amplitudes of approximately 3 m to 4 m amplitudes. The observed amplitudes were relatively large considering the 5 to 6 m thickness of the upper layer of 5 m to 6 m. The TG analysis determined the mode 1 speed (0.5 m/s) of the internal tide. The spatial structure of the vertical and horizontal velocities (via TG) compared favorably with the spatial structure of the first EOF modes of baroclinic velocity and normalized echo anomaly. Additionally, the weighted amplitude of the EOF-mode1 of baroclinic velocity was consistent with the temperature reductions from the near surface ship observations. This provided evidence

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linking isotherm departures to baroclinic velocities. Using c to account for the Doppler shift in wavelength estimates, the corrected wave lengths were 33 km and 38 km. The predicted surface transport associated with the internal tides ranged from 8 km to 13 km.

The filtered across-shelf drifter displacements of the drifter that crossed the shelf break onto the Alabama/Louisiana shelf showed pulses of flow that was were connected with theto tides. However, the cumulative displacement during the flood phase on July 24th was 2.7 km larger than observed during the subsequent flood phase on the 23rd. This was assumed to represent the transport inducted by the shoreward propagating internal tide observations collected onboard the ship on July 24th. Wind, Stokes drift, and buoyancy were compared with the drifter displacements to see it they could be contributing to the variability. Stokes drift was negligible and while the buoyant currents could not be counted out, their trend did not explain the cumulative displacement variability observed between successive floods. Lastly, the drifter displacements were filtered to remove synoptic influences; however the diurnal sea breeze cycle did develop toward the end of the 24th. Comparing the northward wind during the flood displacements on from the 23rd and to the 24th revealed stronger wind forcing on the 23rd. However a smaller cumulative displacement suggested that onshore wind was not responsible for the enhanced cumulative displacement during flood on the 24th. The observed transport (2.7 km), assumed to be induced by internal tides, was lower than the predicted transport (8 km). This could arise from a variety of reasons. The theory used in the transport predictions assumes linearity, (i.e. a << H1). However, the observations revealed that 0.01 < a/H1 < 1 and, which indicated that the internal tides were weakly nonlinear. This could explain the difference in transport estimates between predicted and observed.

These findings support the hypothesis that internal tides generated at the shelf break of DeSoto Canyon are contributing to surface transport in the northern Gulf. The purpose of this investigation was to draw attention to yet another mechanism that may be important when considering surface transport. Why are the implications of internal tide generated surface transport important? There are millions of dollars currently invested in accurately forecasting oil spill movement in the Gulf of Mexico. Internal waves are not well captured by various forecasting schemes, including coupled numerical model systems and Lagrangian Coherent Structure core analyses. Therefore, any associated surface transport would not be included. The observed and estimated internal tide induced surface transport ranged from 2.7 km to 13 km, suggesting these transports are large enough to play a role in contributing to inaccurate drifter predictions from various model approaches. In order to improve surface transport predictions, internal wave induced transport should be addressed.

This research has provided two important conclusions:

1. Internal tides have been observed on the Louisiana/ Alabama continental shelf. The internal tide-induced surface transport likely accounted for 2.7 km of the total transport during flood phases of the tide.

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[2.] Models used to predict drifter trajectories need to accurately represent internal waves accurately.

Appendix

To calculate the horizontal transport for a neutrally buoyant, flow following particles by a passing long internal wave, we assume that in a general case of long nonlinear tide with wave amplitude the isopycnal displacementη ( x , z ,t ) associated the wave can also be factored as:

η ( x , z ,t )=a ϕ ( z ) f ( x−ct ), (9)

This assumption is in line with linear internal tide formalism – Eq. 1 (Baines, 1982). Here also the eigenfunction ϕ ( z ) is obtained as a solution to TG problem:

ϕ ' '+[ ω2

ω2−f 2 ] N2

(c )2ϕ=0

(10)

With boundary conditions ϕ (0 )=ϕ ( h )=0.The waveshape function f ( ζ ), is assumed to be

supported on a closed interval: −L

2¿ L

2 with f ( ζ ), vanishing outside that interval.

Since the particle displacement is the same in Eulerian or wave following coordinate frame, we proceed to calculate the depth dependent particle displacement Δs(z ) in the wave following coordinate frame. The exact value of Δs(z ) for a general long internal wave described by Equation 10 is given in Bogucki et. al 1997 (Eq. 23) and yields:

Δ s ( z )=∫−∞

∞ a ϕ' ( z ) f (ζ )1+aϕ ' ( z ) f (ζ)

dζ .(11)

In the first-order approximation for a mode 1 wave, with ϕ ' ( z=H 1 )=0 , the wave shape function f ( ζ ) is well approximated by a triangle of height 1. The expression for the induced water

displacement to the first order in a

H 1 becomes:

Δ s ( z )=a ϕ ' ( z ) ∫−L/2

L/2

f (ζ )dζ +O( aH 1 )

2

=12

aH1

L+O( aH1 )

2 (12)

14

where H1 is the depth where eigenfunction ϕ ' (z )reaches maximum, hence the wave induced horizontal current attains minimal value – Eq. (10).

Acknowledgements

This research paper was made possible , in part or in full, by a grant from BP/The Gulf of Mexico Research Initiative.

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Figure Captions

Figure 1. Study area map including: Ribbon plot depicting near surface density values as a function of position collected on a ship on July 24th, 2012 (blue arrows denote surface reductions) and one drifters trajectory. Data station locations: Northwest Bay Gardene and Mobile State Docks (salinity), Mobile Bay Buoy (surface current velocities), Pilottown (tides), and Luke offshore platform (wind and waves).

Figure 2. a) Map of ship path on July 24th, 2012. Grey denotes shelf measurements which corresponds with b, c, d times up to 24.6 (denoted by red dashed line). After which, red path

17

denotes location of observations. b) time series of near surface temperature with diurnal trend removed and highlightings two reductions, c) normalized echo intensity anomaly and d) baroclinic velocities.

Figure 3. a) Squared buoyancy frequency, N2 and density from climatological density profile, b) vertical structure of mode 1 amplitude from Taylor Goldstein Equation solution, c) vertical structure of horizontal velocity, d) EOF first mode spatial structure for baroclinic velocities (grey) and normalized echo intensity anomaly (black),e) temperature fluctuations with diurnal mean removed, f) baroclinic velocity weighted amplitude for EOF-mode 1.

Figure 4. a) map showing drifter trajectory from July 22 to July 25th 2012, b) filtered across-shelf drifter displacements, c) wind velocity vector plot (scaled by 0.5) direction represents where wind is headed and red line denotes scale, c) water levels at Pilottown, LA e) Sstokes drift velocity (black) and horizontal surface density gradient (grey): solid (AL) and dashed (LA).

Table 1. Internal tide surface transport parameters.

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