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Jamie MacMahan

Abstract

Short-term observations of sea surface elevations η along the 10-m isobath and long-term observations inside and outside of a large bay (Monterey Bay, CA) were obtained to describe the nodal structure of the modes 0–3 seiches within the bay and the low-frequency (<346 cpd) seiche forcing mechanism. The measured nodal pattern validates previous numerical estimates associated with a northern amplitude bias, though variability exists across the modal frequency band, particularly for modes 0 and 1. Low-frequency oceanic η white noise within seiche frequency bands (24–69 cpd) provides a continuous resonant forcing of the bay seiche with a η 2 (variance) amplification of 16–40 for the different modes. The temporal variation of the oceanic η white noise is significantly correlated (R 2 = 0.86) at the 95% confidence interval with the bay seiche η that varies seasonally. The oceanic η white noise is hypothesized as being from low-frequency, free, infragravity waves that are forced by short waves.

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Jamie MacMahan

Abstract

Drag coefficients C d obtained through direct eddy covariance estimates of the wind stress were observed at four different sandy beaches with dissipative surfzones along the coastline of Monterey Bay, California. The measured surfzone C d (~2 × 10−3) is twice as large as open-ocean estimates and consistent with recent estimates of C d over the surfzone and shoaling region. Owing to the heterogeneous nature of the near shore consisting of nonbreaking shoaling waves and breaking surfzone waves, the surfzone wind stress source region is estimated from the footprint probability distribution derived for stable and unstable atmospheric conditions. An empirical model developed for estimating the C d for open-ocean foam coverage dependent on wind speed is modified for foam coverage owing to depth-limited wave breaking within the surfzone. A modified empirical C d model for surfzone foam predicts similar values as the measured C d and provides an alternative mechanism to describe roughness.

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Matthew S. Spydell, Falk Feddersen, and Jamie Macmahan

Abstract

Oceanographic relative dispersion Dr2 (based on drifter separations r) has been extensively studied, mostly finding either Richardson–Obukhov (Dr2~t3) or enstrophy cascade [Dr2~exp(t)] scaling. Relative perturbation dispersion Dr2 (based on perturbation separation rr 0, where r 0 is the initial separation) has a Batchelor scaling (Dr2~t2) for times less than the r 0-dependent Batchelor time. Batchelor scaling has received little oceanographic attention. GPS-equipped surface drifters were repeatedly deployed on the Inner Shelf off of Pt. Sal, California, in water depths ≤ 40 m. From 12 releases of ≈18 drifters per release, perturbation and regular relative dispersion over ≈4 h are calculated for 250 ≤ r 0 ≤ 1500 m for each release and the entire experiment. The perturbation dispersion Dr2 is consistent with Batchelor scaling for the first 1000–3000 s with larger r 0 yielding stronger dispersion and larger Batchelor times. At longer times, Dr2 and scale-dependent diffusivities begin to suggest Richardson–Obukhov scaling. This applies to both experiment averaged and individual releases. For individual releases, nonlinear internal waves can modulate dispersion. Batchelor scaling is not evident in Dr2 as the correlations between initial and later separations are significant at short time scaling as ~t. Thus, previous studies investigating Dr2(t) are potentially aliased by initial separation effects not present in the perturbation dispersion Dr2(t). As the underlying turbulent velocity wavenumber spectra is inferred from the dispersion power law time dependence, analysis of both Dr2 and Dr2 is critical.

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Matthew S. Spydell, Falk Feddersen, and Jamie Macmahan

Abstract

Differential kinematic flow properties (DKP), such as vertical vorticity, have been estimated from surface drifters. However, previous DKP error estimates were a posteriori and did not include correlated errors across drifters. To accurately estimate submesoscale (≤1 km) DKPs from drifters, errors must be better understood. Here, the a priori vorticity standard error is derived that depends upon the number of drifters in the cluster, the drifter cluster major and minor axes lengths, the instrument velocity error, and the cross-drifter error correlation. Two stationary GPS experiments, with zero vorticity, were performed at separations of O(101–103) m to understand vorticity error and test the derivation using 1 Hz position differences and Doppler shift velocities. Vorticity errors of ±5f (where f is the local Coriolis parameter)were found for ≈40 m separations. The frequency-dependent velocity variances and GPS-to-GPS correlations are quantified. Vorticity estimated with a “blended” velocity has reduced error. The stationary vorticity error can be well predicted given velocity error, correlation, and minor axis length. Vorticity error analysis is applied to submesoscale-sampling in situ GPS drifters near Point Sal, California. The derivation predicts when large high-frequency vorticity fluctuations (indicating noise) occur. Previously, cluster area or ellipticity were used as criteria to distinguish error. We show that the drifter cluster minor axis (narrowness) is a key time-dependent factor affecting vorticity error, and even for velocity errors <0.004 m s−1, the vorticity error exceeds ±5f when cluster minor axis <50 m. These results will aid submesoscale drifter deployment planning.

Open access
Jamie MacMahan, Ross Vennell, Rick Beatson, Jenna Brown, and Ad Reniers

Abstract

Applying a two-dimensional (2D) divergence-free (DF) interpolation to a one-person deployable unmanned underwater vehicle’s (UUV) noisy moving-vessel acoustic Doppler current profiler (MV-ADCP) measurements improves the results and increases the utility of the UUV in tidal environments. For a 3.5-h MV-ACDP simulation that spatially and temporally varies with the M 2 tide, the 2D DF-estimated velocity magnitude and orientation improves by approximately 85%. Next the 2D DF method was applied to velocity data obtained from two UUVs that repeatedly performed seven 1-h survey tracks in Bear Cut Inlet, Miami, Florida. The DF method provides a more realistic and consistent representation of the ADCP measured flow field, improving magnitude and orientation estimates by approximately 25%. The improvement increases for lower flow velocities, when the ADCP measurements have low environmental signal-to-noise ratio. However, near slack tide when flow reversal occurs, the DF estimates are invalid because the flows are not steady state within the survey circuit.

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Jamie MacMahan, Ed Thornton, Jessica Koscinski, and Qing Wang

Abstract

Surfzone sensible heat flux (H S,SZ) obtained through direct eddy-covariance estimates was measured at four different sandy beach sites along Monterey Bay, California. The H S,SZ source region is estimated from a footprint probability distribution function (pdf) model and is only considered when at least 70% of the footprint pdf occupies the surfzone. The measured H S,SZ is 2 times the modeled interfacial sensible heat (H S,int) using COARE3.5. A formulation for estimating sensible heat flux from spray droplets (H S,spray) generated during depth-limited wave breaking is developed. The sea-spray generation function for droplet radii ranging over 0.1 < r o < 1000 μm is based on self-similar spectra of spray droplets measured from the surfzone forced by the average depth-limited breaking wave dissipation across the surfzone. However, it is shown that the size of the spume droplets that contribute to H S,spray is limited owing to the relatively short residence time in air as the droplets fall to the sea surface during wave breaking. The addition of the surfzone-modeled H S,spray to the COARE3.5 H S,int gives values similar to the observed surfzone H S,SZ, highlighting the importance of depth-limited wave-breaking processes to sensible heat flux. Measured H S,SZ values are an order of magnitude larger than simultaneous open ocean observations.

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Jenna A. Brown, Jamie H. MacMahan, Ad J. H. M. Reniers, and Ed B. Thornton

Abstract

Cross-shore exchange between the surf zone and the inner shelf is investigated using Lagrangian and Eulerian field measurements of rip current flows on a rip-channeled beach in Sand City, California. Surface drifters released on the inner shelf during weak wind conditions moved seaward due to rip current pulses and then returned shoreward in an arcing pattern, reentering the surf zone over shoals. The cross-shore velocities of the seaward- and shoreward-moving drifters were approximately equal in magnitude and decreased as a function of distance offshore. The drifters carried seaward by the rip current had maximum cross-shore velocities as they exited the surf zone and then decelerated as they moved offshore. The drifters moving shoreward accelerated as they approached the surfzone boundary with maximum cross-shore velocities as they reentered the surf zone over shoals. It was found that Stokes drift was not solely responsible for the onshore transport across the surfzone boundary. The cross-shore diffusivity on the inner shelf was greatest during observations of locally contained cross-shore exchange. These field observations provide evidence that the cross-shore exchange between the surf zone and inner shelf on a rip-channeled beach is due to wave-driven rip current circulations and results in surface material being contained within the nearshore region.

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John A. Colosi, Nirnimesh Kumar, Sutara H. Suanda, Tucker M. Freismuth, and Jamie H. MacMahan

Abstract

Moored observations of temperature and current were collected on the inner continental shelf off Point Sal, California, between 9 June and 8 August 2015. The measurements consist of 10 moorings in total: 4 moorings each on the 50- and 30-m isobaths covering a 10-km along-shelf distance and an across-shelf section of moorings on the 50-, 40-, 30-, and 20-m isobaths covering a 5-km distance. Energetic, highly variable, and strongly dissipating transient wave events termed internal tide bores and internal solitary waves (ISWs) dominate the records. Simple models of the bore and ISW space–time behavior are implemented as a temperature match filter to detect events and estimate wave packet parameters as a function of time and mooring position. Wave-derived quantities include 1) group speed and direction; 2) time of arrival, time duration, vertical displacement amplitude, and waves per day; and 3) energy density, energy flux, and propagation loss. In total, over 1000 bore events and over 9000 ISW events were detected providing well-sampled statistical distributions. Statistics of the waves are rather insensitive to position along shelf but change markedly in the across-shelf direction. Two compelling results are 1) that the probability density functions for bore and ISW energy flux are nearly exponential, suggesting the importance of interference and 2) that wave propagation loss is proportional to energy flux, thus giving an exponential decay of energy flux toward shore with an e-folding scale of 2–2.4 km and average dissipation rates for bores and ISWs of 144 and 1.5 W m−1, respectively.

Open access
Kyle C. Landon, Greg W. Wilson, H. Tuba Özkan-Haller, and Jamie H. MacMahan

Abstract

Velocity measurements from drifter GPS records are used in an ensemble-based data assimilation technique to extract the river bathymetry. The method is tested on a deep meandering reach and a shallow braided reach of the Kootenai River in Idaho. The Regional Ocean Modeling System (ROMS) is used to model numerous statistically varied bathymetries to create an ensemble of hydrodynamic states. These states, the drifter observations, and the uncertainty of each are combined to form a cost function that is minimized to produce an estimated velocity field and bathymetry. The goals of this study are to assess whether ROMS can accurately reproduce the Kootenai River flow to an extent that depth estimation is feasible, to investigate if drifter paths are sensitive enough to bottom topography to make depth estimation possible, and to establish practical limitations of the present methodology. At both test sites, the depth estimation method produced a bathymetry that was more accurate than the prior estimate.

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Matt K. Gough, Thomas M. Freismuth, Jamie H. MacMahan, John A. Colosi, Sutara H. Suanda, and Nirnimesh Kumar

Abstract

Cross-shore heat flux (CHF) spatiotemporal variability in the subtidal (ST), diurnal (DU), and semidiurnal (SD) bands is described for 35 days (summer 2015) from collocated vertical measures of temperature and currents obtained by moorings deployed from 50- to 7-m water depths near Pt. Sal, California. The CHF is largest in the ST and SD bands, with nearly zero contribution in the DU band. The sum of CHF and surface heat flux (SHF) account for 31% and 17% of the total change in heat storage on the midshelf and inner shelf, respectively. The ST CHF for the midshelf and inner shelf is mostly negative and is correlated with upwelling-favorable winds. A mostly positive SD CHF on the midshelf and inner shelf decreases linearly in the shoreward direction, is correlated with wind relaxations, and is attributed to warm-water internal tidal bores (WITBs) that are observed to propagate to the edge of the surf zone. A negative SD CHF is correlated with upwelling-favorable winds on the midshelf at 15–25-h time lags, and is believed to be associated with cold-water internal tidal bores. The WITBs have characteristics of progressive waves on the midshelf and transition to partially standing waves on the inner shelf potentially reducing the SD CHF contribution on the inner shelf. Heat accumulation over the midshelf and inner shelf is primarily driven by WITBs and SHF, which is largely balanced by cumulative cooling by ST processes over the midshelf and cumulative cooling by alongshore heat flux (AHF) over the inner shelf.

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