Characterizing wave-induced mixing energy in OHMSETT wave basin 

for dispersant effectiveness testing

David W. Wang and Hemantha W. Wijesekera 

Oceanography Division, Naval Research Laboratory, Code 7332, 

Stennis Space Center, MS 39529

Acknowledgements 

This study was funded by the Bureau of Safety and Environmental Enforcement (BSEE), 

U.S. Department of the Interior, Washington D.C. under Contract E14PG00059, Project 1059.

Disclaimer

This final report has been reviewed by BSEE and approved for publication. Approval 

does not signify that the contents necessarily reflect the views or policies of BSEE, nor does 

mention of trade names or commercial products constitute endorsement or recommendation for 

use.
OHMSETT WAVE MIXING ENERGY 1

Table of Contents

Executive Summary ............................................................................ 2

Background ...................................................................................... 4

Experiment facility and Instrumentation .................................................... 7

Experiment procedure and Data processing ................................................10

Results and Discussion ........................................................................14

Conclusion ...................................................................................... 20

Recommendation .............................................................................. 21
OHMSETT WAVE MIXING ENERGY 2

Executive Summary

The goal of this study is to quantify and characterize the mixing energy under 

breaking wave actions in the Ohmsett facility. Mixing energy associated with surface 

wave breaking in the wave tank was evaluated by estimating turbulent kinetic energy 

(TKE) directly from measurements of microscale velocity shear. A total of 38 test runs 

were carried out to measure turbulent mixing levels for two types of wave conditions,

namely (1) long-duration wave action for the standard dispersant effectiveness tests and 

(2) short-duration wave actions prior to the presence of reflected waves from the tank 

boundary. The wave conditions for the dispersant effectiveness testing were based on 

wave maker setting of frequency 33.3 cycles per minute and stroke distance of 15.2 cm. 

Wave conditions for the rest of the test runs were based on wave maker settings of 35 and 

40 cycles per minute and 15.2 and 20.3 cm. Surface wave characteristics, TKE 

dissipation rates, background currents, and temperature and salinity in the tank were 

collected from multiple sensing packages mounted on the tank bridge-platform while

moving at a speed of 0.53 m/s. The major findings of this study are:

• The monochromatic waves generated by the wave maker modulated rapidly into

wave groups as they propagated downstream. The period of the modulated wave

group was 4 to 10 times larger than the period of the initial monochromatic wave

produced by the wave maker. Largest near-surface TKE dissipation rates were found

at or near the center of the modulated wave group. Our observations indicate that

wave breaking occurs when the wave steepness reaches the critical geometric limit

during the modulation process. During wave breaking events, the near-surface TKE 

dissipation rate reached to about of the order of 10-2 (hereafter O( )) W/kg which is 
OHMSETT WAVE MIXING ENERGY 3

two to three orders of magnitude larger than before and after the wave breaking. The 

strongest dissipation was observed within the near-surface layer of thickness 

equivalent to a significant wave height of about ~ 0.4 m.

• Vertical profiles of TKE dissipation rate,< ε > , were constructed for long- and shortduration wave actions. For wave breaking under short-duration wave actions without 

the effects from wave reflections, < ε > decreased from O(10-3 ) W/kg at 0.15 m to 

O(10-5

) W/kg at 0.4 m below the water level. However, < ε > decayed rapidly with 

depth under long-duration wave actions (i.e., dispersant effectiveness test), where

< ε > dropped from O(10-3

)W/kg at 0.15 m to O(10-6)W/kg at 0.4 m. The depth 

dependence of < ε > can be approximated by the power law, n z − < ε > ∝ , where z is 

the depth measured from the water surface, n = 5 for the long-duration dispersant

effectiveness test, and n = 3 for the short-duration test without impact from reflected

waves. At depths deeper than 0.4 m below the water level, the TKE dissipation rate

of long-duration wave actions was about 3x10-6 W/kg, which was one order of 

magnitude smaller than that of short-duration wave actions. 

• The enhancement of the TKE dissipation rate by wave breaking near or at the center 

of modulated-wave group is consistent with open ocean observations. The magnitude 

and vertical profile of the TKE dissipation rate under short-duration wave actions are 

comparable with open ocean observations. 
OHMSETT WAVE MIXING ENERGY 4

Background

Approximately 3 million gallons of oil are spilled into the waters of the United States 

every year (NRC 2005). The primary response methods consist of the deployment of mechanical 

on-water containment and recovery systems. However, mechanical recovery systems often 

become insufficient when the environmental conditions at the spill are outside the effective 

operation ranges of the equipment. There is a need to use on-water chemical dispersants to 

change the inherent chemical and physical properties of oil to enable it to mix with water more

easily. The purpose of dispersant is to break up the oil slick spill into numerous small droplets 

which become rapidly diluted into the water column and subsequently degraded by naturally 

occurring micro-organisms (NRC 2005). The use of dispersant enhances the amount of oil 

mixing into the water column. This can greatly reduce the potential contamination effect of 

surface slicks to habitats and bird, marine mammals and other organisms that live on or near the 

water surface or shorelines. However, by enhancing the mixing of oil into the water column, 

dispersant also increase the potential exposure of the water-column to the spill oil. The 

application of dispersant represents a critical decision making for reducing the risk to organisms 

at the water surface and near the shoreline while increasing the potential harm to organisms in 

the water column and at the sea floor. The use of dispersants must be considered carefully, to 

take into account the pros and cons of using them under various sea-state and weather conditions.

Before any dispersant is approved for application to any spill in US waters, both the 

toxicity and effectiveness of the chemical dispersants must be evaluated. The effectiveness of 

chemical dispersants are often evaluated in laboratory standardized bench-scale tests (Kaku et 

al., 2005), such as the Swirling Flask Test (SFT) and Baffled Flask Test (BFT). The mixing 

process generated in the laboratory flask tests cannot account for the transport and dilution 
OHMSETT WAVE MIXING ENERGY 5

effects in the water column caused by turbulence induced by the action of surface waves as 

observed in the open ocean (Venosa et al., 2005; Boufadel et al., 2008). The methods of 

generating turbulence motions by shaking of laboratory flasks, by breaking surface waves, or by 

shear-driven near-surface motions are not identical, and therefore the mixing energy in a 

laboratory set up and in an oceanic environment require better quantification. Furthermore, the 

efficiency of mixing in both cases would not be similar. In support of an operational validation 

of the dispersant for oil dispersion effectiveness, a full-scale field evaluation test under various 

wave conditions is desirable and necessary. However, such a test is logistically difficult and 

expensive. The applicability of evaluation results are hampered by limited and uncontrolled 

wave conditions. The large outdoor Ohmsett wave tank facility (Figure 1) is designed and 

equipped to simulate realistic sea conditions by producing regular waves (up to 1 m height) and 

random waves that can’t be generated in smaller tanks (Li et al., 2008; Wickley-Olsen et al.,

2008). The evaluation of dispersant effectiveness can be carried out under controlled and 

reproducible wave conditions, and is cost effective and operationally feasible. The evaluation of 

dispersant effectiveness has been carried out in the past using the Ohmsett facility (S. L. Ross,

2005; Mullin & Trudel, 2006).

The mixing energy in the water column resulting from small-scale velocity-shear plays a 

key role in the breakup of an oil slick into tiny droplets and in dispersion of the spilled oil into 

the water column in the presence of a chemical dispersant (Venosa et al., 2006; Li et al., 2008). 

The magnitude of turbulent kinetic energy (TKE) near the surface is the key factor determining 

the effectiveness of the oil dispersant. Therefore, understanding how TKE dissipation rates of 

mechanically-generated surface waves relate to various wave conditions is necessary for 

correlating the wave tank measurements with oceanic observations (Belore et al., 2005).
OHMSETT WAVE MIXING ENERGY 6

The turbulent kinetic energy is dissipated by viscous friction. The resulting energy 

dissipation rate, ε for homogeneous isotropic turbulence is expressed as (Tennekes & Lumley,

1972)

2

7.5 



 





∂

∂ = xu

ε ν , (1)

where ( )

2 ∂u / ∂x is the variance of the velocity shear in 1/s; v is the kinematic molecular 

viscosity in m2/s; ε is in W/kg, and the angle brackets denote either time or space average. Thus, 

ε from turbulent velocity shear is directly linked to the intensity of the mixing energy (NRC 

2005). When the Reynolds number is sufficiently large, there exists an inertial subrange where 

production and dissipation scales are separable. The velocity shear variance can be estimated by 

resolving the spatial gradient of turbulent velocity fluctuations at scales ranging from O(mm) to 

O(m). Therefore the dissipation method (or shear spectral method) provides a direct estimate of 

the TKE dissipation rate. 

The goal of this project is to provide a scientifically validated method to determine 

mixing energy based on direct measurements of the TKE dissipation rate in the wave tank under 

wave conditions comparable to the oceanic environment. This report describes methodology and 

findings of direct measurements of TKE dissipation rates in the Ohmsett wave tank. Section 2 

provides a description of the experiment facility and instrumentation setup. Section 3 discusses 

measurement procedure and data processing. Results and discussion are presented in Section 4. 

Finally, a short summary and recommendations are given in Section 5.
OHMSETT WAVE MIXING ENERGY 7

Experiment facility and Instrumentation

We conducted two experiments at the Ohmsett tank facility during January 12-17, and 

during September 21-25, 2015. Each experiment consisted of multiple test runs covering a wide 

range of wave actions with varying frequencies and amplitudes produced by the wave maker

(Tables 1 and 2). The experiment conducted in January 2015 (Table 1) was a proof-of-concept 

for measuring microscale velocity shear and quantifying platform noise levels from sensors 

mounted on the bridge platform (Figure 1). In the following, we describe experiment setups, 

measurements, and results, while focusing on the experiment conducted in September 2015 

(Table 2).

Wave tank and Instrument platform

The outdoor tank at Ohmsett is 203 m long, 20 m wide, and 3.5 m deep (Figure 1a). The 

tank is equipped with a bottom-hinged flap-type wave maker with an adjustable paddle strokefrequency and distance (Asher, 2005; Guarino et al., 2010; Brown & Guarino, 2010). The wave 

maker is located at the south end of the tank, and a wave-damping beach system is installed at 

the north end to reduce wave reflection of incoming waves. During our experiments, the beach 

was raised from the tank floor to the water line to dampen incident wave energy. Details of the 

wave damping system are given in Guarino et al. (2010). The Ohmsett tank is equipped with 

three movable bridges with tow speeds up to 3.2 m/s.

The microstructure measurements were made from sensors mounted on an

instrumentation-platform (also referred as the NRL platform), which was constructed by 

combining a cylindrical pole (hereafter “pole”) attached to a 2.3 m long H-beam. The NRL 

platform was connected to the main tank-bridge to make underway measurements from the 

movable bridge. In this set up, only the H-beam was attached rigidly to the bridge (Figure 1b).
OHMSETT WAVE MIXING ENERGY 8

The pole was mounted on the beam in such a way that the pole could be moved vertically (up 

and down) along the beam to position the microstructure-sensors at different depths. Three 

microstructure sensing packages (MicroRider-1000, hereafter “MR”) and one acoustic Doppler 

velocimeter (ADV) were mounted on the pole (Figures 1b and c). A Conductivity-TemperatureDepth (CTD) package and another ADV were attached at fixed locations on the H-beam. An 

upward looking acoustic Doppler current profiler (ADCP) was mounted on a horizontal 

extension beam attached to the bottom of the H-beam (Figures 1c and d). The flow field around 

the instrument-platform can be distorted as waves pass the NRL-platform. Therefore the 

microstructure sensing packages were mounted on the pole so that the turbulent sensors, such as 

shear probes and fast thermistors were placed about 0.8 m from the center of the H-beam to 

avoid the distorted flow field (Figure 1c). The ADV was about 0.4 m from the center of the 

beam. Note that all the sensing elements were directed toward the wave maker.

Apart from measurements inside the tank, background wind speed, wind direction, and 

air temperature were also recorded from the weather station next to the tank at 8 m above the 

ground. Environmental conditions and wave maker settings for the two experiments are given in 

Tables 1 and 2, respectively. 

Turbulent shear probe

The turbulence shear probe is part of a self-contained turbulence microstructure sensing

package (MicroRider-1000) developed by Rockland Scientific Inc. (e.g., Goodman et al. 2006; 

Wolk et al. 2009). It is about 10 cm in diameter, 1 m long, and weighs 5.5 kg in air. The nose 

cone of the instrument (Figure 3) holds the following sensors: two shear probes (SPM-38), two 

fast-response thermistors (FP07) and high resolution pressure, acceleration and tilt sensors. The 

instrument is powered by 9 – 18 VDC and data are recorded internally on a memory card. 
OHMSETT WAVE MIXING ENERGY 9

Sampling frequencies for individual channels can be between 8 Hz and 4096 Hz. Apart from 

TKE dissipation rates, the MicroRider-1000 is capable of measuring turbulent temperature 

variance (TTV) dissipation rate. Dissipation rate of TTV is also a mixing energy estimator when 

stratification is important. The sampling rate of shear probes and fast thermistors is 512 Hz, and 

the rest of sensors sample at 64 Hz. For the January experiment, only one MR was deployed. For 

the September experiment, we mounted three MRs at depth intervals of about 0.23 and 0.25 m 

(Figures 1 and 2). As mentioned above, the three MRs were mounted on the movable pole on the 

NRL instrument platform that was adjusted vertically to obtain dissipation estimates between 

0.16 m and 0.75 m depths (Figure 2).

Acoustic Doppler velocimeters (ADV)

Two acoustic Doppler velocimeters (ADV), owned by Ohmsett, were also used to 

measure the turbulence velocities under wave actions. The ADV samples the flow field in three 

perpendicular directions (along tank, cross tank, and vertical) at a rate of 32 Hz. The accuracy of 

the measurement is about 1 mm/s. One ADV was placed 0.25 m below the three MRs on the 

movable pole and a second ADV was placed on the beam at depth 1.5 m below the water 

surface. 

Acoustic Doppler current profiler (ADCP)

The ADCP mounted on the bottom of the NRL platform was a 1200-kHz broadband 

Workhorse Sentinels (RD Instruments). Furthermore, two 600-kHz ADCPs were placed on the 

bottom of the tank floor (35m and 163 m, respectively, to the wave maker) (Figure 1). The 

ADCPs recorded profiles of currents and bubble echo intensity during both experiments.
OHMSETT WAVE MIXING ENERGY 10

Measurement procedure and Data processing

Measurement procedure

We conducted TKE dissipation measurements for both short- and long-duration wave 

actions. Tests under short-duration wave actions focused on TKE dissipation measurements prior 

to the presence of reflected waves from the tank boundary. Tests under long-duration wave 

actions represented the standard dispersant effectiveness testing (S.L. Ross, 2001). 

During short-duration testing, the bridge and instrument-platform were first positioned at 

a distance of 170 m from the wave maker before starting the wave maker. Once waves were

generated, the bridge-instrument platform moved toward the wave maker from its initial position 

to a location 35 m from the wave maker at a steady towing speed of 0.53 m/s, while encountering 

wave breaking events and collecting concurrent measurements of microscale velocity shear, 

currents, and temperature and salinity in the tank. Depending on the wave periods generated by 

different paddle-frequency settings (Table 2), the waves reflected from the beach end reached the 

moving bridge and instrument platform within 240 – 290 sec after the start of wave actions.

The protocol of the standard dispersant effectiveness tests at Ohmsett requires a 5-min 

wave generation for the development of wave conditions prior to the release of oil and dispersant 

into the tank. The duration of the dispersant effectiveness test can last 30 min or longer (Fingas 

& Decola, 2006; S.L. Ross, 2001). Strong interactions among incoming and reflected waves

were observed during the long-duration wave actions. TKE production and dissipation rates

under these long-duration wave actions were affected by reflected waves. 

For a given test run, microscale velocity shears were measured at three different depths

with vertical spacing of about 0.23 and 0.25 m (Figure 1c and Table 2). Each test run lasted

about 250 sec. We repeated this measurement procedure to construct vertical profiles of TKE 
OHMSETT WAVE MIXING ENERGY 11

dissipation rates by adjusting the vertical position of the pole at increments of 2 cm to 5 cm to 

construct vertical profile of TKE dissipation rate between 0.16 m and 0.75 m below the water 

level. The wave maker settings for wave actions of monochromatic as well as random waves

based on the Pierson–Moskowitz (PM) spectra are given in Tables 1 and 2. 

TKE dissipation from shear probe measurements 

For homogeneous isotropic turbulence, the TKE dissipation rate is computed from the 

variance of the turbulent velocity gradients (1). In practice, the velocity shear variance,

< ∂ ∂ >2 ( u / x) , is estimated directly by integrating the shear spectrum from a specified 

wavenumber band ranging from a low-wavenumber representing inertial subrange motions to the 

dissipation wavenumber (or the Kolmogorov wavenumber, 3 1/ 4 (ε /ν ) ). However, when turbulent 

motions are highly energetic, such as during surface wave-breaking events, the shear probes used 

in microstructure sensing packages do not fully resolve the shear spectrum at higher 

wavenumbers, thus underestimating the TKE dissipation rate. When the turbulent dissipation is 

weak, and the background noise is large or comparable with the velocity shear signal, shear 

probes observations are contaminated by the background noise (such as vibrations resulting from 

the measuring platform). Therefore, the area under the measured velocity shear spectra 

represents only part of the total variance of shear. To estimate the dissipation rate, the measured 

shear spectra are fit to the Nesmith universal spectrum (Oakey, 1982; Wolk et al., 2009) or the

theoretical spectral shape in the inertial-subrange 

 4/3 2/3 1/3

1 φ(k) = Aα(2π ) ε k , (2)

where A1=24/55 for the transverse spectrum, and α=1.5 is the universal constant. Note that the 

wavenumber k is in cycles per meter (hereafter cpm). The dissipation rate can be estimated by 

fitting the theoretical form of φ (k) (2) to the observed shear spectrum, (k) φ M , in the inertial 
OHMSETT WAVE MIXING ENERGY 12

subrange wavenumber band from ka to kb. By combining (2) and the observed transverse 

wavenumber spectrum, (k) φ M , we determined the TKE dissipation rate as (e.g.,Tennekes &

Lumley, 1972; Bluteau et al., 2016):

 4/3 4/3 4/3 3/ 2

1 [(4 / 3) /( (2 ) ( )] b a ε = E Aa π k − k , (3)

where ( ) . ∫ =

b

a

k

k

M E φ k dk

During the experiments, the two shear probes in each MR were mounted orthogonal to 

each other to measure the cross-stream and vertical velocities gradients while the sensor platform 

was moving along the tank or the along-stream direction. We computed transverse spectra of 

velocity shear for the two orthogonal components (cross-stream and vertical), and then averaged 

both together to construct a representative spectrum for a given data segment, (k) φ M , where k is 

the wavenumber in the direction of the mean flow (i.e., along the tank-axis). The measurements 

from the moving platform enable the conversion of the velocity-shear frequency spectrum into a 

wavenumber spectrum using Taylor’s frozen turbulence hypothesis. For a sampling rate of 512 

Hz and a platform speed of 0.53 m/s, velocity fluctuations can be resolved at 1 mm spatial scales. 

Velocity-shear frequency spectra, ( f ) f M , were calculated for 1-sec segments of velocity-shear 

measurements. The frequency spectra ( f ) f M were converted to the wavenumber spectrum,

where (k) U ( f ) f M = Bf M , k=f/UB, UB is the towing speed of the bridge in m/s, and f is the 

frequency in Hz. Examples of velocity shear spectra for 1-sec data segments from Test 15 (Table 

2) for three different dissipation levels are illustrated in Figure 4 along with the Nasmyth 

empirical spectrum. The TKE dissipation rate (3) was evaluated first by averaging spectral 

estimates from two shear probes, and then by integrating the averaged shear spectrum between 
OHMSETT WAVE MIXING ENERGY 13

ka=10 cpm and kb=35 cpm. Estimated TKE dissipation rates based on (3) for the spectra shown 

in Figure 4 are 2.99x10-6 W/kg, 1.37x10-4 W/kg, and 7.35x10-2 W/kg, respectively.

TKE dissipation from ADV measurements

We collected three-dimensional turbulent velocity fluctuations in the along-stream 

(along-tank), cross-stream (cross-tank), and vertical directions from the ADVs mounted on the 

platform. The sampling rate of 32 Hz was sufficient to resolve the inertial-subrange velocity 

fluctuations at a bridge speed of 0.53 m/s. As discussed above, the inertial-subrange velocity 

spectral level can be used to evaluate the TKE dissipation rate by fitting a theoretical turbulent 

longitudinal velocity spectrum,

 2/3 2/3 5/3

2 ( ) (2 )

− − k = A k u φ α π ε , (4)

where A2=18/55. The velocity frequency spectrum, ( f ) fuM was computed for each 10-second 

segment of ADV data, and then the wavenumber spectrum, (k) φuM was constructed by 

following Taylor’s frozen hypothesis, where (k) U ( f ) fuM = BfuM . Examples of (k) φuM from the 

two ADVs at 0.9 m and 1.5 m depths during Test 15 are shown in Figures 5a and b, respectively

(Table 4). The spectral peaks in Figure 5a represents the wave orbital velocity motions of the 

monochromatic waves generated by the wave maker with a frequency setting of 35 cycles per 

minute. Note that peak wavenumbers (Figure 5) of the velocity spectra from the ADVs on the 

NRL platform were a slightly higher than those corresponding to the paddle frequency due to the 

Doppler shift by the platform’s moving speed UB . At higher wavenumbers, a -5/3 spectral slope

can be clearly identified despite the presence of a spectral peak at wavenumber 7.5 cpm, which 

could be caused by vibration of the bridge during towing. By fitting the velocity spectra, (k) φuM , 

to the spectral model (4) between k=3.5 cpm and 5.5 cpm, TKE dissipation rates were estimated. 
OHMSETT WAVE MIXING ENERGY 14

Resulting dissipation rates for the spectra shown Figures 5a and b, are about 2x10-4 W/kg and 

3x10-5 W/kg, respectively. 

Wave parameters 

During the experiments, surface wave elevations were obtained from measurements by

pressure sensors in the MRs at a sampling rate of 512 Hz and by the downward-looking sonicaltimeters mounted on the bridge platform at a sampling rate of 10 Hz. Surface wave elevations 

estimated from the altimeters and the pressure sensors were very similar. For a better 

synchronization with velocity shear measurements from the MRs, we used surface elevations 

derived from the pressure sensor in MR121 (Figure 1c). Wave actions in the tank were

characterized by the significant wave height, 1/ 2 HS = 4σ , where σ is the variance of wave 

elevation of a specified time segment. In addition, the local wave amplitude, a, and frequency, fp,

were derived from wave elevations by using the wavelet analysis method (Huang et al., 2007;

Wang & Wijesekera, 2017). The local frequency, fp , was corrected for the Doppler shift by the 

moving platform. We then computed the local steepness, a / g

2 δ = ω , where p ω = 2pf and g is the 

gravitational constant. 

Results and Discussion

During these experiments, TKE dissipation measurements were carried out under wave 

actions with frequent occurrences of wave breaking. Figure 6a shows a snap shot of whitecap 

formations from wave breakings. The occurrences of whitecaps were evenly distributed in the 

along-tank direction but with considerable patchiness. Figure 6b shows a wave breaking event

near the instrument-platform. Depth-averaged velocity between 0.4 m and 0.6 m (Figure 7) was

obtained from the bottom mounted ADCP placed at 163 m from the wave maker (Figure 1). The 
OHMSETT WAVE MIXING ENERGY 15

5-min averaged, along- and cross-tank velocities fluctuated with a magnitude of 5 cm/s or less

during the experiment. The backscatter echo-intensity from the ADCP increased when the wave 

maker was running and the background flow was relatively large (Figure 7b). The deepening of 

high echo-intensity (Figure 7b) suggests stirring and movement of particles in the tank by 

currents and turbulent motions, and entrainment of bubbles generated by wave breaking. Time 

series of temperature and salinity were also collected from the CTD mounted near the bottom of 

the tank (Figure 8). CTD observations showed no changes in salinity during the testing period 

during September 25-26, but the temperature followed a diurnal cycle with a temperature 

difference of about 1o

C. A small increase in temperature (~0.05oC) was found when the wave 

maker was active (Figure 7b). 

TKE dissipation measurements under short-duration wave actions

Two examples of observations of short-duration wave actions made from the MRs are 

shown in Figures 9 and 10, representing, respectively, paddle stroke frequency (cycles per 

minute)/distance (cm) of 35/8 (Test 15, Table 2), and 40/6 (Test 5, Table 2). Both tests 

produced similar results (Figures 9 and 10). In the following, we discuss results from Test 15 in 

more detail. The 200-sec short segment of measurements, shown in Figure 9, was not affected by 

the reflected waves from the beach end of the tank. The MRs first encountered the incoming 

waves from the wave maker at about 10 sec into the measurements (Figure 9a). Surface wave 

elevations showed highly modulated wave groups as depicted by the wave amplitude (Figure 9a).

The modulated wave groups are caused by the Benjamin-Feir instability mechanism (BFM), 

which is the interaction between a strong carrier harmonic wave and waves at adjacent side-band 

frequencies. The BFM leads to modulation of the initially monochromatic wave train, and as a 

result some waves can become very large at the expense of others and ultimately break 
OHMSETT WAVE MIXING ENERGY 16

(Benjamin & Feir, 1967; Babanin et al. 2007). Figure 9b illustrates time evolution of wave

steepness, δ, and microscale velocity-shear squared Sh2

, which is used as an indicator of the 

TKE dissipation rate. The velocity shear, Sh, was obtained by filtering velocity shear 

measurements of the MR140 between frequencies of 5.3 Hz and 18.6 Hz and the corresponding

wavenumbers are 10 cpm and 35 cpm, respectively, for UB=0.53 m/s. The time series of TKE 

dissipation rates were estimated from 1-sec segments of velocity shear data at 0.19m, 0.44m and 

0.67m below the water level (Figure 9c).

Both δ and Sh2 peak near or at the center of the wave group (Figure 9b). Modulation 

instability increased wave steepness to the geometry limits (Tulin & Waseda, 1999; Babanin et 

al., 2007; Tian et al., 2012), and eventually led to wave breaking while injecting turbulence into 

the water column. The periodicity of wave breaking at or near the center of the modulated group 

is similar to observations from the open ocean described by Donelan et al. (1972) and Gemmrich 

& Farmer (2004). Near-surface TKE dissipation at 0.19 m below the water surface varied in a 

periodic manner in most occasions. The TKE dissipation rate varied between 10-6 W/kg and 10-2

W/kg and the strongest dissipations were found during breaking events. The enhancement of

dissipation rate was highly correlated with the increasing wave steepness (Figure 9). However, 

the relationships among wave breaking, wave steepness, and the resulting TKE dissipation rates 

at depths deeper than one wave height (0.53 m) are less correlated and dissipation rates remained 

at O(10-6

) to O(10-4) W/kg. Similar results were also observed in TKE measurements for slightly 

different wave maker settings (Figure 10). .

TKE dissipation measurements under long-duration wave actions

Figure 11 shows a 200-sec of wave and TKE dissipation measurements under wave 

actions after a 5-minute wave development, representing wave conditions for dispersant 
OHMSETT WAVE MIXING ENERGY 17

effectiveness test (S.L. Ross, 2001). The wave fields under the long-duration wave actions were

affected by reflective wave energy. As a result, time series of surface wave elevations show 

strong wave modulation and formation of wave groups (Figures. 11a and b). Near-surface TKE 

dissipation rate at 0.21 m below the surface was strongest at or near the center of wave groups

(Figure 11c). Wave breakings inject turbulent energy and increase the instantaneous dissipation 

rate from 10-6 W/kg to 10-2 W/kg. Variations in TKE dissipations at deeper depths (0.46 and 0.69 

m) are less significant under breaking waves. These results are similar to the measurements 

under short-duration wave actions (Figures 8 and 9). 

Results of TKE dissipation measurements are presented by time-averaging TKE 

dissipation rate, <ε> over a selected 80-sec segment for each test run. Here the 80-sec segment 

from the moving bridge at UB=0.53 m/s covers about a 42-m length of the tank. Averaged TKE 

dissipation rates under short-duration and long-duration wave actions are tabulated in Table 3 

and 4, respectively.

Vertical profiles of TKE dissipation 

Vertical profiles of TKE dissipation were constructed by time averaging dissipation 

estimates at depths from 0.15 m to 0.75 m. Figure 12 shows vertical profiles of TKE dissipation 

for both experiments. The vertical profiles of TKE dissipation rate for long-duration wave 

actions, < ε L > are from the observations made during the second experiment conducted in 

September 2015 (Table 5). The vertical profiles of TKE dissipation rate for short-duration wave 

actions, < ε S > were obtained by combining both January and September experiments. At depths

less than 0.2 m, the near-surface < ε L > is O(10-4 )W/kg, which is comparable with < ε S > .

However, the vertical structure of < ε L > and < ε S > are significantly different at depths below 

0.3 m. < ε L > decreases with depth more rapidly than < ε S > . At depths below 0.4 m, < ε L >
OHMSETT WAVE MIXING ENERGY 18

became one order of magnitude smaller than < ε S > . These observations suggest that the injected 

turbulence generated by breaking waves under long-duration wave actions has less impact on the 

vertical distribution of TKE dissipation as compared to that of short-duration wave actions. The 

difference in the depth-dependent vertical structure of TKE dissipation is likely caused by the 

wave flow fields influenced by strong interactions between incident and reflected waves during 

long-duration wave actions. Further study is needed. 

In general, < ε L > and < ε S > decrease with depth (Figure 12) following a power law 

relation and can be approximately represented by

 3 10 , 0.1m z 0.4 m 8 5 < >= × ≤ ≤ − − z L ε , and (5)

 5 10 , 0.1m z 0.5 m. 6 3 < >= × ≤ ≤ − − z S ε (6)

At depths below 0.4 m, both < ε L > and < ε S > do not change significantly with depth. < ε L >

remains about 3x10-6 W/kg, which is one order of magnitude smaller than < ε S > that is about 

4x10-5 W/kg.

Comparison with open ocean observations

Near-surface TKE dissipation rates in the ocean are on the order of 10-4 to 10-2 W/kg for

winds reaching 20 m/s and wave heights exceeding 7 m (Thomson et al. 2016). Similar 

dissipation rates were also found during moderate wind conditions (e.g., Gemmrich, 2010; 

Schwendeman et al., 2014; Sutherland & Melville, 2015). Germmrich and Farmer (2004) 

measured TKE dissipation rates associated with individual breaking events at winds up to 14 

m/s. They showed that the background TKE dissipation at 1-m depth prior to the breaking event 

was about 5x10-6 W/kg and that the dissipation at the same depth during breaking was as large as 
OHMSETT WAVE MIXING ENERGY 19

8x10-3 W/kg. Furthermore, they reported that wave breaking occurred near the crest of the largest 

wave in the wave group. These observations are consistent with the magnitude and pattern of 

dissipation rate enhancement during wave breakings in our tank experiments, even though the 

length and time scales of waves in the tank are much smaller than wave conditions in the open 

ocean. More recently, Callaghan et al. (2016) suggested that space and time averaged TKE 

dissipation rates in actively breaking waves are largely independent of length and time scales of 

breaking waves. They postulated that more energetic breaking waves increase air entrainment 

but not significantly increase the averaged turbulent intensity. Vertical profiles of near-surface 

TKE dissipation in the open ocean tend to follow the power law, z

-m, where m varies from 1 to 2 

(e.g. Sutherland & Melville, 2015; Thomson et al., 2016), and is close to the vertical structure of

< ε S > with wave breaking without the influence of reflected waves (6). 

TKE dissipation by ADV measurements

During these experiments, TKE dissipation rate was also computed from velocity 

measurements by the two ADVs. The ADV on the movable pole measured currents at 0.92 to 

0.97 m depths. The second ADV was at a fixed depth of 1.5 m. The results are shown in Table 

4. The TKE dissipation rates from the ADVs are in the range of O(10-4) to O(10-5) W/kg that is 

relatively higher than those from MRs considering that the ADVs are at deeper depths. We 

suspect this could be caused by contamination of velocity data at high frequencies due to the 

vibration from the moving platform as shown in Figure 5. Veron (2009) measured dissipations 

by an ADV at 0.53 m depth and reported dissipation in the range of O(10-3) to O(10-4)W/kg. 

Further study is needed for the validity of using ADV measurements for TKE dissipation at 

Ohmesett.

 
OHMSETT WAVE MIXING ENERGY 20

Conclusions

A total of 38 test runs were carried out to evaluate turbulent mixing levels for two types of 

wave conditions, namely (1) long-duration wave action for the standard dispersant effectiveness 

tests, and (2) short-duration wave actions prior to the presence of reflected waves from the tank 

boundary. The monochromatic waves, generated by the wave maker, modulated rapidly into 

wave groups as they propagated downstream. Periods of the modulated wave groups were 4 to 

10 times the initial periods of the monochromatic waves. Largest near-surface TKE dissipation 

rates were found at or near the center of the modulated wave groups, where the wave steepness 

was large. The observations suggest that the modulation instability increased wave steepness to 

its critical geometric limit, thus initiating wave breaking. During wave breaking events, the nearsurface TKE dissipation was on the order of 10-2 W/ kg, which was two to three orders of 

magnitude larger than before and after the wave breaking. The strongest turbulent mixing was 

limited to a near-surface layer of about 0.4 m (~ equivalent to a significant wave height).

Vertical profiles of TKE dissipation rate were constructed by time-averaging dissipation 

estimates. The vertical profiles of long-duration wave actions,< ε L > , and short-duration wave 

actions, < ε S > , are comparable at depths less than 0.2 m. However, the vertical structure of 

< ε L > and < ε S > were significantly different at deeper depths. < ε L > decreased with depth 

more rapidly than that of < ε S > . At depths below 0.4 m, < ε L > became one order magnitude 

smaller than < ε S > . The depth dependence of < ε > can be approximated by the power law,

n z − < ε > ∝ , where z is the depth from the water surface, n = 5 for long-duration dispersant 

effectiveness tests, and n = 3for short-duration tests without impact from reflected waves. 
OHMSETT WAVE MIXING ENERGY 21

The enhancement of TKE dissipation by wave breaking occurring near or at the center of 

wave groups is consistent with the open ocean observations. The magnitude and vertical profile 

of TKE dissipation rate under breaking waves of short-duration wave actions are comparable 

with open ocean observations. 

Recommendations

1. We find significant differences in the vertical structure of TKE dissipation rate for wave 

breaking under short-duration monochromatic wave actions and long-duration more 

complex wave conditions caused by reflected waves. The vertical structure of TKE 

dissipation rate under short-duration wave actions is closer to results from field 

observations. We recognize that the dispersant effectiveness test at Ohmsett requires a 

long-duration of wave actions (30 min or longer, S. L. Ross 2001). Therefore, the impacts 

of reflective waves on wave breaking, breaking mechanisms, and the resulting energy 

dissipation under long-duration wave actions should be further examined. The energydamping setup in the tank partially absorbs the incident wave energy, and the wave 

conditions under the effect of reflected waves could result in stronger modulations, and 

more wave breakings. We recommend that vertical profile measurements of TKE 

dissipation should be conducted at a fixed time interval to characterize the temporal and 

spatial evolution of TKE dissipation under longer duration wave actions.

2. A redesign of the energy damping beach to reduce impacts of wave reflections during 

long-duration tests should be considered. 
OHMSETT WAVE MIXING ENERGY 22

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OHMSETT WAVE MIXING ENERGY 27

Table 1

Summary of setups and environmental conditions for the first mixing energy experiment

conducted in January 2015.

Test Time

(UTC)

wave maker

UB

Environmental 

condition

Remarks

# Fs Ds u 

(m/s)

θu

(°)

Tair

(°F)

1 Jan 14

19:49

0 0 0.53 2.0 47 32 Tank water salinity is 

22.5psu and water 

temperature is 31.1F 

at 4’ depth

2 20:01 20 7.6 0.53 2.8 58 32 No breaking waves 

3 20:21 20 7.6 0.53 3.0 97 32 No breaking waves 

4 21:38 40 15.2 0.53 2.8 75 32

5 Jan 15

14:33

40 15.2 0 2.9 300 29 No MR data

6 14:58 40 15.2 0.53 2.3 302 30 No MR data

7 15:24 40 15.2 0.13 2.9 306 30 No MR data

8 15:53 40 7.6 0.53 3.1 286 31 No MR data

9 16:16 35 20.3 0.53 3.2 298 32

10 16:41 40 15.2 0.53 3.3 305 32

11 18:20 40 15.2 0.13 3.0 279 33

12 18:49 40 7.6 0.53 3.1 261 35 Weak breaking 

waves 

13 19:10 33.3 15.2 0.53 2.7 277 37 5-min wave buildup 

before the test. 

14 19:34 40 15.2 0.53 4.6 275 36

15 19:50 35 20.3 0.53 5.2 295 36

16 20:35 40 15.2 0.53 4.6 282 35

17 20:35 35 20.3 0.53 3.6 286 35

18 Jan 16

13:34

PM spectrum 

16 m/s wind

-- 5.0 260 33 Aborted due to wave 

generator issue

19 13:49 40 15.2 0.53 4.3 261 33 Tank water salinity is 

21.7 psu and water 

temperature is 36 F.

20 14:11 40 15.2 0.53 5.3 263 34

21 14:14 40 15.2 0.53 6.4 264 36

Note. Wave maker setting Fs and Ds are, respectively, the paddle frequency (cycles per minute) 

and stroke distance (cm). UB is the bridge towing speed (m/s) during the experiment. The 

weather station next to the tank provides environmental conditions of wind speed u (m/s), wind 

direction θu (°) and air temperature,Tair(°F).
OHMSETT WAVE MIXING ENERGY 28

Table 2

Summary of setups and environmental conditions for the second mixing energy experiment 

conducted in September 2015

Test Time

(UTC)

 wave 

maker

Environmental 

conditions

Remarks

# Fs Ds UB u θu Tair

1 Sept 23

19:24

0 0 0.53 1.4 70 77 Tank water salinity is 34.5 psu 

and water temperature is 71.6 

F at 4’ depth

2 19:35 40 15.2 0 2.0 70 77

3 20:05 40 15.2 0.53 2.7 82 76

4 20:19 35 20.3 0 2.4 85 76

5 Sept 24

13:25

40 15.2 0.53 2.3 38 72 Tank water salinity is 34.6 psu 

and water temperature is 70.5 

F at 4’ depth

6 14:15 35 20.3 0.53 3.3 42 73

7 14:35 33.3 15.2 0.53 3.1 31 74 5-min wave action before 

starting the TKE measurements 

(dispersant test condition) 

8 15:09 40 15.2 0.53 Missing data from bridge 

9 15:23 35 20.3 0.53 2.6 51 75

10 15:40 33.3 15.2 0.53 2.7 49 76 5-min wave action

11 16:59 40 15.2 0.53 2.4 83 78

12 17:14 35 20.3 0.53 2.2 85 77

13 18:05 33.3 15.2 0.53 2.7 111 79 5-min wave action 

14 18:19 40 15.2 0.53 2.6 95 80

15 18:34 35 20.3 0.53 1.8 75 79

16 18:54 PM spectrum 

8 m/s

0.53 2.7 96 80

17 19:07 PM spectrum 

10.6 m/s

0.53 2.9 93 79

Note. Wave maker setting Fs and Ds are, respectively, the paddle frequency (cycles per minute) 

and stroke distance (cm). UB is the bridge towing speed (m/s) during the experiment. The 

weather station next to the tank provides environmental conditions of wind speed u (m/s), wind 

direction θu (°) and air temperature, Tair(°F).
OHMSETT WAVE MIXING ENERGY 29

Table 3

Summary of turbulent mixing measurements of the first mixing energy experiment

 Test wave maker wave TKE dissipation

# Fs Ds Hs

m

z

m

<ε>x104

W/kg

19 40 15.2 0.47 0.15 31.81

10 40 15.2 0.43 0.22 2.41

20 40 15.2 0.43 0.30 1.30

14 40 15.2 0.42 0.38 0.41

16 40 15.2 0.41 0.53 0.55

9 35 20.3 0.58 0.22 5.15

15 35 20.3 0.54 0.38 1.29

17 35 20.3 0.59 0.53 0.31

2 20 7.6 0.18 0.22 0.00072

3 20 7.6 0.16 0.22 0.00041

12 40 7.6 0.25 0.22 0.04

13 33.3 15.2 0.50 0.22 1.34

Note. Hs is the significant wave height. <ε> is the ensemble average TKE dissipation over the 80-

sec TKE dissipation measurements. z is the MicroRider depth to the water line.
OHMSETT WAVE MIXING ENERGY 30

Table 4 

Summary of turbulent mixing measurements of the second mixing energy experiment.

Test wave 

maker

TKE dissipation rate <ε>

MR ID

TKE dissipation rate <ε>

ADV ID

MR 140 MR121 MR088 ADV 9659 ADV 9677

# Fs Ds Hs

m

z

m

<ε> 

x104

z

m

<ε> 

x104

z

m

<ε> 

x104

z

m

<ε> 

x104

z

m

<ε> 

x104

3 40 15.2 0.41 0.16 9.10 0.41 1.00 0.64 0.55

5 40 15.2 0.41 0.16 8.31 0.41 1.16 0.64 0.45

14 40 15.2 0.31 0.19 0.80 0.44 0.07 0.67 0.02 0.90 0.29 1.50 0.27

8 40 15.2 0.39 0.21 1.91 0.46 0.34 0.69 0.38 0.92 0.71 1.50 0.24

11 40 15.2 0.40 0.26 1.33 0.51 0.43 0.74 0.10 0.97 0.41 1.50 0.15

6 35 20.3 0.58 0.16 25.74 0.41 0.06 0.64 0.03

15 35 20.3 0.53 0.19 20.02 0.44 0.95 0.67 0.82 0.90 2.63 1.50 0.37

9 35 20.3 0.46 0.21 11.72 0.46 0.95 0.69 0.30 0.92 2.14 1.50 0.68

12 35 20.3 0.48 0.26 4.71 0.51 1.01 0.74 0.35 0.97 2.11 1.50 0.48

7 33.3 15.2 0.49 0.16 4.4 0.41 0.03 0.64 0.03

10 33.3 15.2 0.41 0.21 2.0 0.46 0.05 0.69 0.02 0.92 0.74 1.50 0.05

13 33.3 15.2 0.47 0.26 0.11 0.51 0.02 0.74 0.02 0.97 3.53 1.50 0.24

16 PM spectra

8 m/s

0.19 0.001 0.44 0.001 0.67 0.005

17 PM spectra

10.6 m/s

0.19 0.004 0.44 0.002 0.67 0.006

Note. Hs is the significant wave height. <ε> is the ensemble average TKE dissipation of 80-sec 

measurement segments. z is the MicroRider depth to the water surface.
OHMSETT WAVE MIXING ENERGY 31

Table 5

Vertical profile of TKE dissipation rate

Depth TKE 

dissipation rate

95% confidence interval <ε>

z (m) <ε> x104

W/kg 

Upper ε 

x104 

W/kg

Lower ε

x104 

W/kg

0.16 4.42 10.60 1.84

0.21 2.03 4.49 0.92

0.26 0.11 0.158 0.072

0.41 0.032 0.044 0.024

0.46 0.045 0.065 0.032

0.51 0.022 0.028 0.018

0.64 0.031 0.042 0.023

0.69 0.024 0.030 0.019

0.74 0.021 0.025 0.017

Note. Ensemble average <ε>, upper and lower limits of 95% confidence interval of 80-sec TKE 

measurement segments under long-duration wave actions generated according to wave maker

setting of paddle stroke frequency of 33.3 cycles per minute and distance of 15.2 cm. 
OHMSETT WAVE MIXING ENERGY 32

(c) (d)

Figure 1. (a) Ohmsett aerial photo, (b) schematic diagram of the wave tank, the NRL 

instrument platform, and locations of three MRs (red) and two ADVs (blue), three 

ADCPs (yellow), CTD (brown) and Altimeter (green). (c) Configuration of the 

instrument platform and sensors, and (d) photo of the platform and mounted sensors 

before the deployment.
OHMSETT WAVE MIXING ENERGY 33

(a) (b) 

Figure 2. (a) installation of the instrument platform to the main bridge, and (b) 

adjustment of platform vertical position during the experiments. 
OHMSETT WAVE MIXING ENERGY 34

(a) (b)

Figure 3. (a) The three MRs and the mounting bracket of the NRL platform for the second 

experiment. (b) A close-up look of MR nose cone showing two shear probes and two 

thermistors. 
OHMSETT WAVE MIXING ENERGY 35

Figure 4. Velocity shear wavenumber spectra for TKE dissipation rate of 2.99x10-6, 

1.37x10-4 and 7.35x10-2 W/kg. The velocity shear data are from the MR140 at 0.19 m 

depth below water surface during Test 15 (Table 2). The gray curves represent the 

universal Nysmith spectra for dissipation rates from 10-1 to 10-6 W/kg. 
OHMSETT WAVE MIXING ENERGY 36

Figure 5. Longitudinal velocity wavenumber spectra from Test 15 by (a) ADV9659 and 

(b) ADV9677 with TKE dissipation rates 2x10-4 and 3.1x10-5 W/kg, respectively. The 

red dashed lines represent the k

-5/3 fitting for the inertial subrange based on the spectral 

energy between 3.5 to 5.5 cpm as indicated by the two red circles, respectively. 
OHMSETT WAVE MIXING ENERGY 37

(a) (b)

Figure 6. Photos of whitecaps from wave breakings during the experiments. (a) periodic 

occurrence of whitecaps in along-tank direction (wave is travelling from photo’s bottom 

to top ) and (b) whitecap of an individual wave breaking near the NRL platform (wave is 

traveling away from the platform)
OHMSETT WAVE MIXING ENERGY 38

Figure 7. Time series of velocity measurements from the ADCP on the floor (163 m to 

the wave maker) during the second experiment. (a) 5-min averaged along-tank (blue) and 

cross-tank (red) velocities between 0.4 to 0.6 m depth (b) vertical profiles of echo 

intensity. 
OHMSETT WAVE MIXING ENERGY 39

Figure 8. Time series of (a) water temperature and (b) salinity measurements from the 

CTD during the second experiment. 
OHMSETT WAVE MIXING ENERGY 40

Figure 9. TKE dissipation measurements of Test 15. A 200-sec segment of (a) surface 

wave elevation(blue) and amplitude of modulated wave group (red dashed line), (b) 

band-passed velocity-shear squared, Sh2

/1000 (red), and wave steepness, δ,(blue) and 

(c) TKE energy dissipation rate of 1-sec velocity shear measurement segments from the 

MRs at depths z= 0.19m (red), 0.44m (blue) and 0.67 m (black). 
OHMSETT WAVE MIXING ENERGY 41

Figure 10. TKE dissipation measurements of Test 5. A 200-sec segment of (a) surface 

wave elevation(blue) and amplitude of modulated wave group (red), (b) band-passed 

velocity- shear squared, Sh2/1000, (red) and local wave steepness, δ, (blue) and (c) TKE 

energy dissipation rate of 1-sec velocity shear measurement segments from the three MRs 

at depth z= 0.16 (red), 0.41 (blue) and 0.64 m (black), respectively. 
OHMSETT WAVE MIXING ENERGY 42

Figure 11. TKE dissipation measurements of Test 10. A 200-sec segment of (a) surface 

wave elevation(blue) and amplitude of modulated wave group (red), (b) band-passed 

velocity shear squared, Sh2

/500, (red) and local wave steepness, δ, (blue) , and (c) TKE 

dissipation rate of 1-sec velocity shear measurement segments from MRs at depth z= 0.21 

(red), 0.46 (blue) and 0.69 m (black). 
OHMSETT WAVE MIXING ENERGY 43

Figure 12. Vertical profile of TKE dissipation under wave actions. <εL> from longduration wave actions from the second experiment are represented by solid red circles. 

<εS> from the short-duration wave actions tests of the first and second experiment are 

represented, respectively, by blue triangles and circles. Horizontal solid lines represent 

95% confidence intervals. The thick black dashed line represents an empirically-fitted 

power law function, z-5, for near-surface <εL>. The dotted blue line represents the z

-3 fit 

for <εS> and z is measurement depth to the water surface of the tank.