Cross‐shore transport of larvae, pollutants, and sediment between the surf zone and the inner shelf is important for coastal water quality and ecosystems. Rip currents are known to be a dominant pathway for exchange, but the effects of horizontal temperature and salinity gradients are not well understood. Airborne visible and infrared imaging performed on the California coast shows warm and cool plumes driven by rip currents in the surf zone and extending onto the shelf, with temperature differences of approximately 1°C. The airborne imagery and modeled temperatures and tracers indicate that warm plumes exhibit more lateral spreading and transport material in a buoyant near‐surface layer, whereas cool plumes move offshore in a subsurface layer. The average cross‐shore extent of warm plumes at the surface is approximately one surfzone width larger than for cool plumes. Future work may explore the sensitivity of nearshore plumes to density patterns, wave forcing, and bathymetry.

The inner shelf, the transition zone between the surf zone and the mid shelf, is a dynamically complex region with the evolution of circulation and stratification driven by multiple physical processes. Cross-shelf exchange through the inner shelf has important implications for coastal water quality, ecological connectivity, and lateral movement of sediment and heat. The Inner-Shelf Dynamics Experiment (ISDE) was an intensive, coordinated, multi-institution field experiment from Sep.–Oct. 2017, conducted from the mid shelf, through the inner shelf and into the surf zone near Point Sal, CA. Satellite, airborne, shore- and ship-based remote sensing, in-water moorings and ship-based sampling, and numerical ocean circulation models forced by winds, waves and tides were used to investigate the dynamics governing the circulation and transport in the inner shelf and the role of coastline variability on regional circulation dynamics. Here, the following physical processes are highlighted: internal wave dynamics from the mid shelf to the inner shelf; flow separation and eddy shedding off Point Sal; offshore ejection of surfzone waters from rip currents; and wind-driven subtidal circulation dynamics. The extensive dataset from ISDE allows for unprecedented investigations into the role of physical processes in creating spatial heterogeneity, and nonlinear interactions between various inner-shelf physical processes. Overall, the highly spatially and temporally resolved oceanographic measurements and numerical simulations of ISDE provide a central framework for studies exploring this complex and fascinating region of the ocean.

This is the first of a 2‐part series concerning remote observation and wave‐by‐wave analysis of the onset of breaking in the surf zone. In the surf zone, breaking waves drive nearshore circulation, suspend sediment, and promote air–sea gas exchange. Nearshore wave model predictions often diverge from in situ measurements near the break point location because common parameterizations do not account for the rapid changes that occur near the onset of breaking. This work presents extensive methodology to combine data from a line‐scanning LIDAR and thermal infrared cameras to detect breaking, classify breaker type, and measure geometric wave parameters on a wave‐by‐wave basis, which can be used to improve breaker parameterizations. Over 2,600 non‐breaking and 1,600 breaking waves are analyzed from data collected at the USACE Field Research Facility in Duck, NC, including 413 spilling and 111 plunging waves for which the onset of breaking was observed. Wave height is estimated using a spatio‐temporal method for wave tracking that preserves the sea surface elevation maximum and overcomes field of view limitations. Methods for estimating instantaneous wave speed are refined by fitting a skewed Gaussian function to each wave profile before tracking the peaks. Wave slope is estimated from a linear fit to the upper 80% of the wave face, which provides a robust metric and strong correlation with geometric wave slope defined relative to mean sea level. Finally, breaking wave face foam coverage is analyzed to assess common model assumptions about roller length for wave energy dissipation parameterizations.

This is the second of a two‐part series concerning remote observation and wave‐by‐wave analysis of the onset of breaking for spilling and plunging waves in the surf zone. Nearshore phase‐averaged and phase‐resolving wave models parameterize and directly simulate wave breaking and require realistic critical values of key wave parameters, such as the depth‐limited breaking index γ, steepness, or phase speed to initialize wave breaking. Using LIDAR line‐scans and infrared imagery, we observe over 1,600 breaking waves at the US Army Corps of Engineers Field Research Facility (FRF) in Duck, NC, and examine these parameters on a wave‐by‐wave basis at the onset of breaking for 413 spilling and 111 plunging waves. We find that γ is maximum near the onset of breaking at values consistent with those previously observed at the FRF, but that γ for plunging waves (0.73 ≤ γ_P ≤ 0.81) is greater than γ for spilling waves (0.63 ≤ γ_S ≤ 0.71). Direct estimates of wave face slope are maximum at the onset of breaking, approximately 22° for spilling and 30° for plunging waves. Using the relationship between γ and wave face slope, we develop a threshold for the onset of breaking that is a linear function of the two parameters. Wave face slope and γ are further used together to quantify whether a spilling‐ or plunging‐type breaker is more likely. We test the Miche steepness limit on our depth‐limited breaking data and find it correctly predicts only 10% of the plunging breakers and none of the spilling breakers in the surf zone.

Sea state is a key variable in ocean and coastal dynamics. The sea state is either sparsely measured by wave buoys and satellites or modelled over large scales. Only a few attempts have been devoted to sea state measurements covering a large domain; in particular its estimation from optical images. With optical technologies becoming omnipresent, optical images offer incomparable spatial resolution from diverse sensors such as shore-based cameras, airborne drones (unmanned aerial vehicles/UAVs), or satellites. Here, we present a standalone methodology to derive the water surface elevation anomaly induced by wind-generated ocean waves from optical imagery. The methodology was tested on drone and satellite images and compared against ground truth. The results show a clear dependence on the relative azimuth view angle in relation to the wave crest. A simple correction is proposed to overcome this bias. Overall, the presented methodology offers a practical way of estimating ocean waves for a wide range of applications.

Quantifying energy dissipation due to wave breaking remains an essential but elusive goal for studying and modeling air‐sea fluxes of heat, gas, and momentum. Previous observations have shown that lifetimes of bubble plumes and surface foam are directly related to the dissipated energy. Specifically, the foam decay time can be used to estimate the timescale of the subsurface bubble plume and the energy dissipated in the breaking process. A mitigating factor is that the foam decay time can be significantly affected by the surfactant concentration. Here we present an experimental investigation of a new technique that exploits the thermal signature of cooling foam to infer wave breaking dynamics. The experiments were conducted in a laboratory wave tank using artificial seawater with and without the addition of a surfactant. We show that the time from the start of the breaking process to the onset of cooling scales with the bubble plume decay time and the dissipated energy, and is not significantly affected by the presence of additional surfactants. We confirm observations from the field of the spatial variability of the temperature of foam generated by an individual breaking event, which has implications for inferring the spatial variability of bubble plume depth.

We develop a remote wave gauging technique to estimate wave height and period from imagery of waves in the surf zone. In this proof-of-concept study, we apply the same framework to three datasets: the first, a set of close-range monochrome infrared (IR) images of individual nearshore waves at Duck, NC, USA; the second, a set of visible (i.e. RGB) band orthomosaics of a larger nearshore area near Santa Cruz, CA, USA; and the third, a set of oblique (unrectified) images from the same site. The network is trained using coincident images and in situ wave measurements. The optical wave gauge (OWG) consists of a deep convolutional neural network (CNN) to extract features from imagery — called a ‘base model’, with additional layers to distill the feature information into lower dimensional spaces, and a final layer of dense neurons to predict continuously varying quantities. Four base models are compared. The OWG is trained for both individual wave height and period, and statistical quantities like significant wave height and peak wave period. The best performing OWG on the IR dataset achieved RMS errors of 0.14 m and 0.41 s for height and period, respectively, capturing up to 98% of the variance in these quantities. The best performing OWG on the visible band rectified dataset achieved RMS errors of 0.08 m and 0.79 s, respectively, for height and period. The same values for the oblique RGB imagery were 0.11 m and 0.81 s for height and period, respectively. Overall, wave height and period accuracy is sensitive to choice of base model; OWGs built upon MobilenetV2 tend to perform worst and those built on Inception-ResnetV2 have the smallest RMS error. The presence or otherwise of residual layers in the model makes little systematic difference to the final OWG accuracy. Smaller batch sizes used in model training tend to result in more accurate OWGs. An out-of-calibration validation, using images associated with wave heights or periods outside the range of values represented in the training data, showed that the ability for OWGs to predict the bottom 5% of low wave heights and the top 5% of high wave heights was reasonably good, but the same was not generally true of wave period. The same framework, not optimized for either dataset, predicts both quantities with high accuracy when trained on imagery, despite the differences in electromagnetic band, perspective, and scale. The OWG estimates wave properties from an image in less than 100 ms on a modestly sized CPU, allowing for the possibility of continuous real-time wave estimates.

Uncooled thermal infrared (TIR) imagers, commonly used on aircraft and small unmanned aircraft systems (UAS, "drones"), can provide high‐resolution surface temperature maps, but their accuracy is dependent on reliable calibration sources. A novel method for correcting surface temperature observations made by uncooled TIR imagers uses observations over melting snow, which provides a constant 0°C reference temperature. This bias correction method is applied to remotely sensed surface temperature observations of forests and snow over two mountain study sites: Laret, Davos, Switzerland (27 March 2017) in the Alps, and Sagehen Creek, California, USA (21 April 2017) in the Sierra Nevada. Surface temperature retrieval errors that arise from temperature‐induced instrument bias, differences in image resolution, retrieval of mixed pixels, and variable view angles were evaluated for these forest snow scenes. Applying the melting snow‐based bias correction decreased the root‐mean‐square error by about 1°C for retrieving snow, water, and forest canopy temperatures from airborne TIR observations. The influence of mixed pixels on surface temperature retrievals over forest snow scenes was found to depend on image resolution and the spatial distribution of forest stands. Airborne observations over the forests at Sagehen showed that near the edges of TIR images, at more than 20° from nadir, the snow surface within forest gaps smaller than 10 m was obscured by the surrounding trees. These off‐nadir views, with fewer mixed pixels, could allow more accurate airborne and satellite‐based observations of canopy surface temperatures.

Sea Surface Temperature (SST) modifies the turbulent mixing, drag, and pressure gradients within the marine atmospheric boundary layer that accelerate near‐surface flow from cool to warm SST and decelerate the flow from warm to cool SST. This phenomenon is well documented on scales of 100–1,000 km (the oceanic mesoscale); however, the nature of this air–sea coupling at scales on the order of 1–10 km (the submesoscale) remains unknown. The Advanced Spaceborne Thermal Emission and Reflection Radiometer can be used to study submesoscale phenomena because the high‐resolution infrared and near‐infrared images can used to estimate both SST and wind speed. Observations of dramatic temperature and wind gradients along the Gulf Stream landward edge are used to examine the surface wind response to submesoscale fronts in SST. Our analysis indicates that SST‐induced wind speed perturbations are observed at the scales of order 1–10 km, significantly smaller than previously suggested.

Highlights

- Aerial IR sensing shows surface temperatures vary by 10–20°C across 1 km.
- Midwave and longwave satellite IR bands can separate snow and forest temperatures.
- At night, retrieved snow surface temperatures match observations within ±1°C.
- During the day, reflected sunlight must be subtracted from midwave IR.
- MODIS can provide two temperatures and fractional snow coverage per pixel.

Gravity currents represent a broad class of geophysical flows including turbidity currents, powder avalanches, pyroclastic flows, sea breeze fronts, haboobs, and river plumes. A defining feature in many gravity currents is the formation of three-dimensional lobes and clefts along the front and researchers have sought to understand these ubiquitous geophysical structures for decades. The prevailing explanation is based largely on early laboratory and numerical model experiments at much smaller scales, which concluded that lobes and clefts are generated due to hydrostatic instability exclusively in currents propagating over a nonslip boundary. Recent studies suggest that frontal dynamics change as the flow scale increases, but no measurements have been made that sufficiently resolve the flow structure in full-scale geophysical flows. Here we use thermal infrared and acoustic imaging of a river plume to reveal the three-dimensional structure of lobes and clefts formed in a geophysical gravity current front. The observed lobes and clefts are generated at the front in the absence of a nonslip boundary, contradicting the prevailing explanation. The observed flow structure is consistent with an alternative formation mechanism, which predicts that the lobe scale is inherited from subsurface vortex structures.

Tides and river slope are fundamental characteristics of estuaries, but they are usually undersampled due to deficiencies in the spatial coverage of water level measurements. This study aims to address this issue by investigating the use of airborne lidar measurements to study tidal statistics and river slope in the Columbia River estuary. Eight plane transects over a 12-h period yield at least eight independent measurements of water level at 2.5-km increments over a 65-km stretch of the estuary. These data are fit to a sinusoidal curve and the results are compared to seven in situ gauges. In situ– and lidar-based tide curves agree to within a root-mean-square error of 0.21 m, and the lidar-based river slope estimate of 1.8 × 10⁻⁵ agrees well with the in situ–based estimate of 1.4 × 10⁻⁵ (4 mm km⁻¹ difference). Lidar-based amplitude and phase estimates are within 10% and 8°, respectively, of their in situ counterparts throughout most of the estuary. Error analysis suggests that increased measurement accuracy and more transects are required to reduce the errors in estimates of tidal amplitude and phase. However, the results validate the use of airborne remote sensing to measure tides and suggest this approach can be used to systematically study water levels at a spatial density not possible with in situ gauges.

Airborne data measured during the recent RIVET II field experiment has revealed that horizontally distributed thermal fingers regularly occur at the Mouth of Columbia River (MCR) during strong ebb tidal flows. The high-resolution, non-hydrostatic coastal model, NHWAVE, predicts salinity anomalies on the water surface which are believed to be associated with the thermal fingers. Model results indicate that large amplitude recirculation are generated in the water column between an oblique internal hydraulic jump and the North Jetty. Simulation results indicate that the billows of higher density fluid have sufficiently large amplitudes to interrupt the water surface, causing the prominent features of stripes on the surface. The current field is modulated by the frontal structures, as indicated by the vorticity field calculated from both the numerical model and data measured by an interferometric synthetic aperture radar.

Thermal infrared (IR) imagery is combined with in situ flow measurements to examine the impact of subsurface stratification on boil activity in the tidally influenced Snohomish River. Boils at the river’s surface are an expression of bottom-generated turbulence, appearing as a disruption of the cool-skin surface layer in the IR imagery. Boil activity has previously been linked to the amount of aeration occurring in river systems. A synthesis of data across an ebb tide showed that when a tidal salinity intrusion retreated, turbulent kinetic energy and dissipation rapidly increased by 700% and 575%, respectively. Additionally, the mean boil area fraction in the IR field of view increased by almost 500% across the entire ebb tide time series, with approximately half of this change occurring during the period when the stratification ceased. Using an empirical method for estimating aeration, the change in areal fraction associated with the loss of density stratification is predicted to generate a more than 300% increase in the air-water gas flux.

The deep ocean, continental shelf, and surf zone are defined by their unique physical processes and dynamics. The nearshore region from about 50 m water depth to the outer edge of the surf zone (SZ) is known as the inner shelf. This region is characterized by overlapping and interacting surface and bottom boundary layers. At the offshore side of the inner shelf, instabilities from wind-driven currents and fronts create cross-shelf meanders and eddies. In addition, energetic nonlinear internal waves (NLIWs) are ubiquitous on the inner shelf.

To understand and predict the exchange of water properties (heat, gases, sediment, pollutants, biota) across the inner shelf over a range of temporal and spatial scales, the Office of Naval Research Inner Shelf Dynamics Departmental Research Initiative (Inner Shelf DRI) is coordinating field observations (in situ and remote sensing) coupled to numerical modeling efforts on a 50-km section of coast off Vandenberg Air Force Base, California, located in the vicinity of Point Sal. The overall goal is to develop and improve the predictive capability of a range of numerical models to simulate the 3D circulation, density, and surface wave field across the inner shelf associated with a broad array of physical processes and complex bathymetry.

Highlights

We measured infrared emissivity of seawater and sea foam in a laboratory experiment.

We developed a method to estimate emissivity for incidence angles up to 85°.

Foam emissivity is higher than water for all wavelengths and angles > 65°.

The difference between foam and water emissivity increases with incidence angle.

Thermal infrared (IR) imagery is used to quantify the high spatial and temporal variability of dissipation due to wave breaking in the surf zone. The foam produced in an actively breaking crest, or wave roller, has a distinct signature in IR imagery. A retrieval algorithm is developed to detect breaking waves and extract wave roller length using measurements taken during the Surf Zone Optics 2010 experiment at Duck, NC. The remotely derived roller length and an in situ estimate of wave slope are used to estimate dissipation due to wave breaking by means of the wave-resolving model by Duncan (1981). The wave energy dissipation rate estimates show a pattern of increased breaking during low tide over a sand bar, consistent with in situ turbulent kinetic energy dissipation rate estimates from fixed and drifting instruments over the bar. When integrated over the surf zone width, these dissipation rate estimates account for 40–69% of the incoming wave energy flux. The Duncan (1981) estimates agree with those from a dissipation parameterization by Janssen and Battjes (2007), a wave energy dissipation model commonly applied within nearshore circulation models.

Bathymetry is a major factor in determining nearshore and surf zone wave transformation and currents, yet is often poorly known. This can lead to inaccuracy in numerical model predictions. Here bathymetry is estimated as an uncertain parameter in a data assimilation system, using the ensemble Kalman filter (EnKF). The system is tested by assimilating several remote sensing data products, which were collected in September 2010 as part of a field experiment at the U.S. Army Corps of Engineers Field Research Facility (FRF) in Duck, NC. The results show that by assimilating remote sensing data alone, nearshore bathymetry can be estimated with good accuracy, and nearshore forecasts (e.g., the prediction of a rip current) can be improved. This suggests an application where a nearshore forecasting model could be implemented using only remote sensing data, without the explicit need for in situ data collection.

The infrared signature of breaking waves at large incidence angles was investigated using laboratory experiments and a radiometric model. Infrared imagery of the water surface at incidence angles greater than 70° shows multipath reflections for both spilling and plunging waves generated using a programmable wave maker. For the spilling breakers, the multipath signature was initially distinct from the breaking wave front roller signature but then merged to create a single large bright distributed target. For the plunging breakers, the roller and multipath signatures overlapped from the inception of breaking. The radiance of the multipath reflection was higher than the surrounding water for simulated cold sky conditions and lower for a simulated warm sky. A specular double-reflection model successfully predicted the presence of multipath reflection but the magnitude was sensitive to small uncertainties in geometry, wave slope, and input temperatures. The results show that multipath reflection from breaking waves is characteristic of large incidence angle infrared measurements and increases the area and magnitude of the infrared signature of breaking waves compared to the background.

We investigate the relationship between turbulence statistics and coherent structures (CS) in an unstratified reach of the Snohomish River estuary using in situ velocity measurements and surface infrared (IR) imaging. Sequential IR images are used to estimate surface flow characteristics via a particle-image-velocimetry (PIV) technique, and are conditionally sampled to delineate the surface statistics of bottom-generated CS, or boils. In the water column, we find that turbulent kinetic energy (TKE) production exceeds dissipation near the bed but is less than dissipation in the midwater column and that TKE flux divergence closes a significant portion of the measured imbalance. The surface boundary leads to divergence in upwelling CS, and leads to the redistribution of vertical TKE to the horizontal. Very near the surface, statistical anisotropy is observed at length scales larger than the depth H (3%u20135 m), while boil-scale motions of O(1)m are nearly isotropic and exhibit a –5/3 turbulent cascade to smaller scales. Conditional sampling suggests that TKE dissipation in boils is approximately 2 times greater on average than dissipation in ambient flow. Similarly, surface boils are marked by significantly greater velocity variance, upwelling, divergence, and TKE flux divergence than ambient flow regions. Coherent structures and their surface manifestation, therefore, play an important role in the vertical transport of TKE and the water column distribution of dissipation, and are an important component of the TKE budget.

Incised channels on tidal flats create a complex flow network conveying water on and off the flat during the tidal cycle. In situ and remotely sensed field observations of water drainage and temperature in a secondary channel on a muddy tidal flat in Willapa Bay, Washington (USA) are presented and a novel technique, employing infrared imagery, is used to estimate surface velocities when the water depth in the channel becomes too shallow for ADCP measurements, i.e., less than 10 cm. Two distinct dynamic regimes are apparent in the resulting observations: ebb-tidal flow and the post-ebb discharge period. Ebb tide velocities result from the surface slope associated with the receding tidal elevation whereas the post-ebb discharge continues throughout the low tide period and obeys uniform open-channel flow dynamics. Volume transport calculations and a model of post-ebb runoff temperatures support the hypothesis that remnant water on the flats is the source of the post-ebb discharge.

Estuarine fronts are well known to influence transport of waterborne constituents such as phytoplankton and sediment, yet due to their ephemeral nature, capturing the physical driving mechanisms and their influence on stratification and mixing is difficult. We investigate a repetitive estuarine frontal feature in the Snohomish River Estuary that results from complex bathymetric shoal/channel interactions. In particular, we highlight a trapping mechanism by which mid-density water trapped over intertidal mudflats converges with dense water in the main channel forming a sharp front. The frontal density interface is maintained via convergent transverse circulation driven by the competition of lateral baroclinic and centrifugal forcing. The frontal presence and propagation give rise to spatial and temporal variations in stratification and vertical mixing. Importantly, this front leads to enhanced stratification and suppressed vertical mixing at the end of the large flood tide, in contrast to what is found in many estuarine systems. The observed mechanism fits within the broader context of frontogenesis mechanisms in which varying bathymetry drives lateral convergence and baroclinic forcing. We expect similar trapping-generated fronts may occur in a wide variety of estuaries with shoal/channel morphology and/or braided channels and will similarly influence stratification, mixing, and transport.

Thermal infrared (IR)-based particle image velocimetry (PIV) is used to measure the evolution of velocity, turbulent kinetic energy (TKE), and the TKE dissipation rate at the water surface in the tidally influenced Snohomish River. Patterns of temperature variability in the IR imagery arise from disruption of the cool-skin layer and are used to estimate the 2-D velocity field. Comparisons of IR-based PIV mean velocity made with a colocated acoustic velocimeter demonstrate high correlation. IR-based PIV provides detailed measurements of previously inaccessible surface velocities and turbulence statistics.

We investigate the generation of a mixing layer in the separated flow behind an estuarine sill (height H ~4 m) in the Snohomish River, Washington as part of a larger investigation of coherent structures using remote and in situ sensing. During increasing ebb flows the depth and stratification decrease and a region of sheared flow characterized by elevated production of turbulent kinetic energy develops. Profiles of velocity and acoustic backscatter exhibit coherent fluctuations of order 0.1 Hz and are used to define the boundaries of the mixing layer. Variations in the mixing layer width and its embedded coherent structures are caused by changes to both the normalized sill height H/d and to a bulk Richardson number Ri_h defined using the depth of flow over the sill. Entrainment E_T and the mixing layer expansion angle increase as stratification and the bulk Richardson number decrease; this relationship is parameterized as E_T = 0.07Ri_h^-0.5 and is valid for approximately 0.1 < Ri_h < 2.8.

Available comparisons with literature for inertially dominated conditions (Ri_h < 0.1) are consistent with our data and validate our approach, though lateral gradients may introduce an upwards bias of approximately 20%. As the ratio H/d increases over the ebb, the free surface boundary pushes the mixing layer trajectory downward, reduces its expansion angle, and produces asymmetry in the acoustic backscatter (coherent structures). Three-dimensional divergence, as imaged by infrared video and transecting data, becomes more prominent for H/d > 0.8 due to blocking of flow by the sill.

Images of river surface features that reflect the bathymetry and flow in the river have been obtained using remote sensing at microwave, visible, and infrared frequencies. The experiments were conducted at Jetty Island near the mouth of the Snohomish River at Everett, Washington, where complex tidal flow occurs over a varied bathymetry, which was measured as part of these experiments. An X band (9.36 GHz) Doppler radar was operated from the river bank and produced images of normalized radar cross sections and radial surface velocities every 20 min over many tidal cycles. The visible and infrared instruments were flown in an airplane. All of these techniques showed surface evidence of frontal features, flow over a sill, and flow conditioned by a deep hole. These features were modeled numerically, and the model results correspond well to the remote observations. In situ measurements made near the hole showed that changes in measured velocities correlate well with the occurrence of the features in the images. In addition to tidal phase, the occurrence of these features in the imagery depends on tidal range. The surface roughness observed in the imagery appears to be generated by the bathymetry and flow themselves rather than by the modulation of wind waves.

Surface disruptions by boils during strong tidal flows over a rocky sill were observed in thermal infrared imagery collected at the Snohomish River estuary in Washington State. Locations of boil disruptions and boil diameters at the surface were quantified and are used to test an idealized model of vertical boil propagation. The model is developed as a two-dimensional approximation of a three-dimensional vortex loop, and boil vorticity is derived from the flow shear over the sill. Predictions of boil disruption locations were determined from the modeled vertical velocity, the sill depth, and the over-sill velocity. Predictions by the vertical velocity model agree well with measured locations (rms difference 3.0 m) and improve by using measured velocity and shear (rms difference 1.8 m). In comparison, a boil-surfacing model derived from laboratory turbulent mixed-layer wakes agrees with the measurements only when stratification is insignificant.