DOI: 10.5061/dryad.pg4f4qs3b
title: Data from: Finescale measurements of Kelvin-Helmholtz instabilities at a Kuroshio seamount

description: Data supporting the results presented in 'Finescale measurements of
 Kelvin-Helmholtz instabilities at a Kuroshio seamount',
 Journal of Physical Oceanography DOI 10.1175/JPO-D-24-0235.1 Fine-scale
 properties of Kelvin–Helmholtz (KH)-like shear instabilities on the
 trailing edge of a nonlinear lee wave generated by the Kuroshio
 impinging on a seamount were measured using a towed CTD chain, shipboard
 ADCP, and echosounder. Lee-wave vertical velocity amplitudes vary
 in phase with the upstream semidiurnal along-stream current.
 The instabilities are analogous to atmospheric billows induced by
 a recirculation on the trailing edge of mountain lee waves. A
 total of 135 KH billows were identified in a 4-day-long time
 series roughly 300 m downstream of the center of the lee wave.
 The KH billows have heights H=52+-11 m, widths L=162+-72 m, and
 aspect ratios H/L=0.39+-0.18. Positive reduced shear squared
 S2-4N2 (where S is the vertical shear magnitude and N is the buoyancy
 frequency) in the shear-stratified billows suggests actively
 growing instabilities, with comparable contributions from across- and
 along-flow vertical shear. Billow cores are convectively unstable
 (N2&lt;0). Large turbulent kinetic energy dissipation rates O(10-5)
 W/kg are inferred from density overturns. Density, shear, and
 inferred turbulence properties vary with billow aspect ratios. As H/L
 increases, density gradients smear out. For 122 billows with
 H/L&lt;0.6, dissipation rates increase by one order of magnitude with
 increasing H/L. These observations of 1-m vertical and 5-m
 horizontal resolution billow structures and density overturn
 dissipation rates can provide a reference for future
 high-Reynolds-number direct numerical simulations.
description: # Data from: Finescale measurements of Kelvin-Helmholtz instabilities at a
 Kuroshio seamount Dataset DOI:
 [10.5061/dryad.pg4f4qs3b](https://doi.org/10.5061/dryad.pg4f4qs3b) ##
 Description of the data and file structure Data to accompany the article
 "Fine-Scale Measurements of Kelvin–Helmholtz Instabilities at a
 Kuroshio Seamount" (Journal of Physical Oceanography, DOI
 10.1175/JPO-D-24-0235.1) by Anda Vladoiu, Ren-Chieh Lien, Eric Kunze,
 Barry Ma, Sebastian Essink, Yiing Jang Yang, Ming-Huei Chang, Sen Jan,
 Jia-Lin Chen, Kai-Chieh Yang, and Yu-Yu Yeh. Contact Anda Vladoiu
 ([avladoiu@uw.edu](mailto:avladoiu@uw.edu)) for additional information.
 ### Files and variables #### File: supporting_data.zip The .zip archive
 contains .mat processed data files used in creating the figures in the
 article. Please see article for detailed data description and processing
 methods. Descriptions of each .mat file, corresponding to distinct
 figures, are below, with units in square brackets. Each file contains
 structures pertaining to variables plotted in each figure panel, named in
 alphabetical order. \# \# **FIG. 1.** (a) Spatial survey (red line) across
 a seamount between Taiwan to the northwest and Green Island to the
 southeast, with AVISO 0.125deg sea-surface-height-inferred geostrophic
 currents illustrating the Kuroshio (gray arrows). Background color
 illustrates bathymetry, and the white contour illustrates the 450-m
 isobath. (b) TCTD chain temperature transect across the seamount; gray
 contours are isopycnals; the black vertical dotted line is the time series
 station; the red vertical dotted line is the upstream 300-kHz ADCP
 mooring; black arrow illustrates Kuroshio mean direction; black contours
 mark isobaths every 50 m. (b ) Zoom-in on instabilities in the black
 rectangle in (b). file: Fig1.mat \# Structure "Fig1a" contains
 variables: "lat" = section latitude [degN] "lon" =
 section longitude [degE] "Ug_lon" = geostrophic velocity
 longitude [degE] "Ug_lat" = geostrophic velocity latitude [degN]
 "Ug_u" = geostrophic zonal velocity [m/s] "Ug_v" =
 geostrophic meridional velocity [m/s] \# Structure "Fig1b"
 contains: structure "sigma1" = section first isopycnal contour
 ``` "Fig1b.sigma1.lat" = latitude [degN]
 "Fig1b.sigma1.lon" = longitude [degE] "Fig1b.sigma1.z"
 = depth [m] ``` structures "sigma2", ... "sigma8" are
 the same as "sigma1", for deeper isopycnal contours variables:
 "timeseries_lat" = timeseries latitude [degN]
 "timeseries_lon" = timeseries longitude [degE]
 "mooring_lat" = mooring latitude [degN] "mooring_lon"
 = mooring longitude [degE] "T_lon" = temperature longitude
 [degE] "T_lat" = temperature latitude [degN] "T_z" =
 temperature depth [m] "T" = temperature [degC] \# Structure
 "Fig1bp" contains variables: "T_x" = temperature
 distance [m] "T_z" = temperature depth [m] "T" =
 temperature [degC] "sigma_x" = density distance [m]
 "sigma_z" = density depth [m] "sigma" = density
 [kg/m^3] \# \# **FIG. 2.** Example (a),(c),(e) TCTD temperature and
 (b),(d),(f) echosounder backscatter time series at the black vertical
 dotted line in Fig. 1b; gray contours in (a), (c), and (e) are isopycnals
 every 0.2 kg/m^3^ ; each of the three times series corresponds to 1000-m
 distance inferred from mean along-stream velocity. file: Fig2.mat \#
 Structure "Fig2a" contains variables: "time" = time
 [matlab time] "z" = depth [m] "T" = temperature [degC]
 "sigma" = density [kg/m^3] \# Structure "Fig2b"
 contains variables: "time" = time [matlab time] "z" =
 depth [m] "backscatter" = backscatter [db] \# Structure
 "Fig2c" contains variables: "time" = time [matlab
 time] "z" = depth [m] "T" = temperature [degC]
 "sigma" = density [kg/m^3] \# Structure "Fig2d"
 contains variables: "time" = time [matlab time] "z" =
 depth [m] "backscatter" = backscatter [db] \# Structure
 "Fig2e" contains variables: "time" = time [matlab
 time] "z" = depth [m] "T" = temperature [degC]
 "sigma" = density [kg/m^3] \# Structure "Fig2f"
 contains variables: "time" = time [matlab time] "z" =
 depth [m] "backscatter" = backscatter [db] \# \# **FIG. 3.**
 Example profiles at the location marked by the dotted vertical white
 (gray) line in Figs. 13b (Fig. 14d). (a) Measured (black) and depth-sorted
 (gray) potential density profile. (b) Shear-unstable patch thickness
 L~KWB~ (blue), absolute value of Thorpe displacements |d~Th~| (gray),
 overturn Thorpe-scale L~Th~ (black), and 5-m binned Thorpe-scale l~Th~
 (red). (c) The N^2^ (gray), S^2^~KWB~/4 (light blue), N^2^~KWB~ (blue),
 patch-weighted N^2^~E~ (black), and 5-m weighted N^2^~E~ (red). (d)
 Reduced-shear (blue), overturn patch Thorpe scale (black) and 5-m patch
 Thorpe scale (red) dissipation rates, and vertical temperature gradient
 k~z~ spectrum inferred dissipation rate (green). (e) Vertical wavenumber
 k~z~ spectrum for vertical temperature gradient T~z~, raw (thin) and
 corrected for vertical interpolation (thick), with best fit (black dotted
 line). file: Fig3.mat \# Structure "Fig3a" contains variables:
 "sigma_theta_z" = potential density depth [m]
 "sigma_theta" = potential density [kg/m^3]
 "sigma_theta_s_z" = depth-sorted potential density depth [m]
 "sigma_theta_s" = depth-sorted potential density [kg/m^3] \#
 Structure "Fig3b" contains variables: "deltaTh_z" =
 Thorpe displacement depth [m] "deltaTh" = Thorpe displacement
 [m] "z" = depth [m] "L_KWB" = shear-unstable thickness
 [m] "L_Th" = overturn patch Thorpe scale [m] "l_Th" =
 5-m Thorpe scale [m] \# Structure "Fig3c" contains variables:
 "N2_z" = buoyancy frequency depth [m] "N2" = buoyancy
 frequency [s^-2] "z" = depth [m] "S2_4_KWB" = vertical
 shear magnitude divided by 4 [s^-2] "N2_KWB" = unstable patch
 buoyancy frequency [s^-2] "N2_E" = overturn-weighted buoyancy
 frequency [s^-2] "N2_E_tilde" = 5-m weighted buoyancy frequency
 [s^-2] \# Structure "Fig3d" contains variables:
 "eps_Tz_z" = depth [m] "eps_Tz" = vertical temperature
 gradient epsilon [W/kg] "z" = depth [m] "eps_KWB" =
 reduced shear dissipation rate epsilon [W/kg] "eps_Th" =
 overturn Thorpe scale epsilon [W/kg] "eps_Th_tilde" = 5-m Thorpe
 scale epsilon [W/kg] \# Structure "Fig3e" contains variables:
 "kz" = vertical wavenumber [cpm] "Phi" = raw vertical
 temperature gradient spectrum [degC^2/m^2 /cpm] "Phi_corr" =
 interpolation corrected vertical temperature gradient spectrum [degC^2/m^2
 /cpm] "fit" = spectrum least-squares fit [degC^2/m^2 /cpm] \# \#
 **FIG. 4.** (a) Four dissipation rate microstructure profiles (solid
 curves) from Yeh et al. (2024, their Figs. 3 and 4); the profiles cross
 KH-like billows identified in echosounder backscatter and are located
 immediately downstream of the seamount close to the TCTD time series
 station (Yeh survey T05-black, T07-orange, T03-red, T09-purple).
 Dissipation rates (squares and circles) were estimated from VMP CTD
 profiles interpolated on a 1-m vertical-resolution depth grid, using the
 same method as for the TCTD. TCTD time series dissipation rate histogram
 (teal) for bins with at least 10 points is shown for reference. (b)
 Probability density functions for microstructure dissipation rate (black),
 overturn Thorpe scale dissipation rate (black), 5-m patch Thorpe scale
 dissipation rate (red), and TCTD time series dissipation rate (teal); only
 depths where there are Thorpe-scale estimates are included for
 microstructure profiles. (c) Scatterplot of microstructure and
 Thorpe-scale dissipation rates, with depth in color. file: Fig4.mat \#
 Structure "Fig4a" contains variables: "z_VMP" = depth
 [m] "eps_VMP_black" = microstructure dissipation rate epsilon
 [W/kg] "eps_VMP_yellow" = microstructure dissipation rate
 epsilon [W/kg] "eps_VMP_red" = microstructure dissipation rate
 epsilon [W/kg] "eps_VMP_purple" = microstructure dissipation
 rate epsilon [W/kg] "eps_Th_VMPctd_black" = VMP CTD overturn
 Thorpe scale dissipation rate epsilon [W/kg]
 "eps_Th_tilde_VMPctd_black" = VMP CTD 5-m Thorpe scale
 dissipation rate epsilon [W/kg] "eps_Th_VMPctd_yellow" = VMP CTD
 overturn Thorpe scale dissipation rate epsilon [W/kg]
 "eps_Th_tilde_VMPctd_yellow" = VMP CTD 5-m Thorpe scale
 dissipation rate epsilon [W/kg] "eps_Th_VMPctd_red" = VMP CTD
 overturn Thorpe scale dissipation rate epsilon [W/kg]
 "eps_Th_tilde_VMPctd_red" = VMP CTD 5-m Thorpe scale dissipation
 rate epsilon [W/kg] "eps_Th_VMPctd_purple" = VMP CTD overturn
 Thorpe scale dissipation rate epsilon [W/kg]
 "eps_Th_tilde_VMPctd_purple" = VMP CTD 5-m Thorpe scale
 dissipation rate epsilon [W/kg] "eps_Th_TCTD" = towed CTD chain
 5-m Thorpe scale dissipation rate epsilon [W/kg] "eps_Th_TCTD_z"
 = towed CTD chain depth [m] "eps_Th_TCTD_histogram" = towed CTD
 chain 5-m Thorpe scale dissipation rate histogram [counts] \# Structure
 "Fig4b" contains histograms line objects. \# Structure
 "Fig4c" contains variables: "eps_VMP" = microstructure
 dissipation rate epsilon [W/kg] "eps_Th_VMPctd" = VMP CTD 5-m
 Thorpe scale dissipation rate epsilon [W/kg] "z" = depth [m] \#
 \# **FIG. 5.** Example section of measured (a) echosounder backscatter,
 (b) TCTD temperature, (c) along-stream velocity anomaly with (c ) vertical
 profile of section-mean along-stream velocity , (d) across-stream velocity
 (positive out of the page), and (e) vertical velocity, for a typical
 lee-wave transect. In all panels, black contours are isopycnals, the black
 dotted vertical line marks the location of the time series station, and
 the red dotted vertical line marks the location of the upstream ADCP
 mooring. Distance is positive downstream of the highest seamount peak.
 file: Fig5.mat \# Structure "Fig5a" contains variables:
 "x" = distance [m] "z" = depth [m]
 "backscatter" = backscatter [db] "sigma_x" = potential
 density distance [m] "sigma_z" = potential density depth [m]
 "sigma" = potential density [kg/m^3] \# Structure
 "Fig5b" contains variables: "x" = distance [m]
 "z" = depth [m] "temperature" = temperature [degC]
 "sigma_x" = potential density distance [m] "sigma_z" =
 potential density depth [m] "sigma" = potential density [kg/m^3]
 \# Structure "Fig5c" contains variables: "x" =
 distance [m] "z" = depth [m] "ualong_anom" =
 along-stream velocity anomaly [m/s] "sigma_x" = potential
 density distance [m] "sigma_z" = potential density depth [m]
 "sigma" = potential density [kg/m^3] \# Structure
 "Fig5cp" contains variables: "z" = depth [m]
 "ualong_mean" = mean along-stream velocity [m/s] \# Structure
 "Fig5d" contains variables: "x" = distance [m]
 "z" = depth [m] "uacross" = across-stream velocity
 [m/s] "sigma_x" = potential density distance [m]
 "sigma_z" = potential density depth [m] "sigma" =
 potential density [kg/m^3] \# Structure "Fig5e" contains
 variables: "x" = distance [m] "z" = depth [m]
 "w" = vertical velocity [m/s] "sigma_x" = potential
 density distance [m] "sigma_z" = potential density depth [m]
 "sigma" = potential density [kg/m^3] \# \# **FIG. 6.** Example
 section of observed (a) stratification , (b) vertical shear magnitude, (c)
 reduced-shear, and (d) Thorpe-scale inferred turbulent kinetic energy
 dissipation rate, for a typical lee-wave transect. In all panels, black
 contours are isopycnals. Distance is positive downstream of the highest
 seamount peak. file: Fig6.mat \# Structure "Fig6a" contains
 variables: "x" = distance [m] "z" = depth [m]
 "N2" = log10 buoyancy frequency squared [s^-2]
 "sigma_x" = potential density distance [m] "sigma_z" =
 potential density depth [m] "sigma" = potential density [kg/m^3]
 \# Structure "Fig6b" contains variables: "x" =
 distance [m] "z" = depth [m] "S2_4" = log10 vertical
 shear magnitude divided by 4 [s^-2] "sigma_x" = potential
 density distance [m] "sigma_z" = potential density depth [m]
 "sigma" = potential density [kg/m^3] \# Structure
 "Fig6c" contains variables: "x" = distance [m]
 "z" = depth [m] "reducedshear" = reduced shear [s^-2]
 "sigma_x" = potential density distance [m] "sigma_z" =
 potential density depth [m] "sigma" = potential density [kg/m^3]
 \# Structure "Fig6d" contains variables: "x" =
 distance [m] "z" = depth [m] "eps_Th" = log10 overturn
 Thorpe scale dissipation rate epsilon [W/kg] "sigma_x" =
 potential density distance [m] "sigma_z" = potential density
 depth [m] "sigma" = potential density [kg/m^3] \# \# **FIG. 7.**
 The 15-section median (a) vertical velocity, (b) stratification , (c)
 vertical shear, (d) reduced-shear, and (e) Thorpe-scale turbulent kinetic
 energy dissipation rate . In all panels, black contours are the 15-section
 mean isopycnals. Only bins with at least three points are shown. file:
 Fig7.mat \# Structure "Fig7a" contains variables: "x"
 = distance [m] "z" = depth [m] "w" = vertical velocity
 [m/s] "sigma_x" = potential density distance [m]
 "sigma_z" = potential density depth [m] "sigma" =
 potential density [kg/m^3] \# Structure "Fig7b" contains
 variables: "x" = distance [m] "z" = depth [m]
 "N2" = log10 buoyancy frequency squared [s^-2]
 "sigma_x" = potential density distance [m] "sigma_z" =
 potential density depth [m] "sigma" = potential density [kg/m^3]
 \# Structure "Fig7c" contains variables: "x" =
 distance [m] "z" = depth [m] "S2_4" = log10 vertical
 shear magnitude divided by 4 [s^-2] "sigma_x" = potential
 density distance [m] "sigma_z" = potential density depth [m]
 "sigma" = potential density [kg/m^3] \# Structure
 "Fig7d" contains variables: "x" = distance [m]
 "z" = depth [m] "reducedshear" = reduced shear [s^-2]
 "sigma_x" = potential density distance [m] "sigma_z" =
 potential density depth [m] "sigma" = potential density [kg/m^3]
 \# Structure "Fig7e" contains variables: "x" =
 distance [m] "z" = depth [m] "eps_Th" = log10 overturn
 Thorpe scale dissipation rate epsilon [W/kg] "sigma_x" =
 potential density distance [m] "sigma_z" = potential density
 depth [m] "sigma" = potential density [kg/m^3] \# \# **FIG. 8.**
 (a) Section-median along-stream velocity 500 m upstream of the seamount
 peak (blue) and angle of the upper 150-m mean current (red). (b) Lee-wave
 center position relative to the seamount peak (blue) and lee-wave width
 (red), inferred from depth-mean SADCP vertical velocity (solid) and
 isopycnal local maximum depth (dashed–dotted). (c) Bandpassed along-stream
 semidiurnal and diurnal plus semidiurnal tidal velocity below 100-m depth
 (blue) from the upstream mooring during the transects. SADCP vertical
 velocity averaged over upper 75th percentiles of the leewave upwelling and
 downwelling between 50- and 250-m depth for each transect (red). (d)
 Median (circles) and mean (curve) Thorpe-scale dissipation rates between
 50- and 250-m depth within 1 km downstream of the lee-wave center for each
 transect. file: Fig8.mat \# Structure "Fig8a" contains
 variables: "time" = matlab time [days] "ualong_upstr"
 = upstream along-stream velocity [m/s] "theta_U" = Kuroshio
 direction [deg] \# Structure "Fig8b" contains variables:
 "time" = matlab time [days] "xleewave_w" = lee wave
 center position from vertical velocity [m] "xleewave_sigma" =
 lee wave center position from isopycnal [m] "Dxleewave_w" = lee
 wave width from vertical velocity [m] "Dxleewave_sigma" = lee
 wave width from isopycnal [m] \# Structure "Fig8c" contains
 variables: "time" = matlab time [days] "D2" = upstream
 semidiurnal tidal velocity [m/s] "D1D2" = upstream diurnal plus
 semidiurnal tidal velocity [m/s] "w_time" = matlab time [days]
 "w" = vertical velocity [m/s] \# Structure "Fig8d"
 contains variables: "time" = matlab time [days]
 "eps_Th_mean" = mean overturn Thorpe scale dissipation rate
 epsilon [W/kg] "eps_Th_median" = median overturn Thorpe scale
 dissipation rate epsilon [W/kg] \# \# **FIG. 9.** Estimation method for
 two billow heights H, widths L, and braid angles (solid red vertical,
 horizontal, and diagonal lines, respectively) based on TCTD absolute
 vertical temperature gradient profile time series converted to distance
 using mean along-stream velocity. Billow outer contours are illustrated in
 dashed–dotted red and core contours in dashed red. Potential density
 contours (black) are every 0.1 kg/m^3^ . file: Fig9.mat \# Structure
 "Fig9" contains variables: "x" = distance [m]
 "z" = depth [m] "Tz" = absolute vertical temperature
 gradient [degC/m] "sigma" = potential density [kg/m^3]
 "billow1_core_x" = billow1 core distance [m]
 "billow1_core_z" = billow1 core depth [m] "billow1_x"
 = billow1 distance [m] "billow1_z" = billow1 depth [m]
 "billow1_H_z" = billow1 height depth [m] "billow1_H_x"
 = billow1 height distance [m] "billow1_L_z" = billow1 width
 depth [m] "billow1_L_x" = billow1 width distance [m]
 "billow1_braid_z" = billow1 width depth [m]
 "billow1_braid_x" = billow1 braid distance [m]
 "billow2_L_x" = billow2 distance [m] "billow2_L_z" =
 billow2 depth [m] "billow2_braid_z" = billow1 width depth [m]
 "billow2_braid_x" = billow1 braid distance [m]
 "billow2_core_x" = billow1 core distance [m]
 "billow2_core_z" = billow1 core depth [m] "billow2_z"
 = billow1 depth [m] "billow2_x" = billow1 distance [m]
 "billow2_H_z" = billow1 height depth [m] "billow2_H_x"
 = billow1 height distance [m] \# \# **FIG. 10.** Billow (a) aspect ratio
 H/L, (c) width L, (e) height H, (b) billow-median depth z, (d) SADCP
 vertical velocity w, and (f) Thorpe-scale dissipation rate, as functions
 of SADCP along-stream velocity. file: Fig10.mat \# Structure
 "Fig10a" contains variables: "HL" = aspect ratio H/L
 "ualong" = along-stream velocity [m/s] \# Structure
 "Fig10b" contains variables: "z" = depth [m]
 "ualong" = along-stream velocity [m/s] \# Structure
 "Fig10c" contains variables: "L" = width [m]
 "ualong" = along-stream velocity [m/s] \# Structure
 "Fig10d" contains variables: "w" = vertical velocity
 [m/s] "ualong" = along-stream velocity [m/s] \# Structure
 "Fig10e" contains variables: "H" = height [m]
 "ualong" = along-stream velocity [m/s] \# Structure
 "Fig10f" contains variables: "eps_Th" = overturn
 Thorpe-scale dissipation rate epsilon [W/kg] "ualong" =
 along-stream velocity [m/s] \# \# **FIG. 11.** (a),(e),(i) TCTD buoyancy
 frequency squared , (b),(f),(j) reduced shear squared, (c),(g),(k)
 Thorpe-scale overturn patch inferred dissipation rates, and (d),(h),(l)
 and 5-m patch dissipation rate. Example billows with different aspect
 ratios (height/width H/L) representative of the 25th, 50th, and 75th
 percentiles, respectively: H/L=0.23 in (a)–(d), H/L=0.36 in (e)–(h), and
 H/L=0.63 in (i)–(l). Downstream coordinate x and depth z are both
 normalized by width L. Fig11.mat \# Structure "Fig11a" contains
 variables: "x" = distance [m] "z" = depth [m]
 "N2" = log10 buoyancy frequency squared [s^-2] \# Structure
 "Fig11b" contains variables: "x" = distance [m]
 "z" = depth [m] "reducedshear" = reduced shear [s^-2]
 \# Structure "Fig11c" contains variables: "x" =
 distance [m] "z" = depth [m] "eps_Th" = log10 overturn
 Thorpe-scale dissipation rate epsilon [W/kg] \# Structure
 "Fig11d" contains variables: "x" = distance [m]
 "z" = depth [m] "eps_Th_tilde" = log10 5-m
 Thorpe-scale dissipation rate epsilon [W/kg] \# Structure
 "Fig11e" contains variables: "x" = distance [m]
 "z" = depth [m] "N2" = log10 buoyancy frequency
 squared [s^-2] \# Structure "Fig11f" contains variables:
 "x" = distance [m] "z" = depth [m]
 "reducedshear" = reduced shear [s^-2] \# Structure
 "Fig11g" contains variables: "x" = distance [m]
 "z" = depth [m] "eps_Th" = log10 overturn Thorpe-scale
 dissipation rate epsilon [W/kg] \# Structure "Fig11h" contains
 variables: "x" = distance [m] "z" = depth [m]
 "eps_Th_tilde" = log10 5-m Thorpe-scale dissipation rate epsilon
 [W/kg] \# Structure "Fig11i" contains variables: "x" =
 distance [m] "z" = depth [m] "N2" = log10 buoyancy
 frequency squared [s^-2] \# Structure "Fig11j" contains
 variables: "x" = distance [m] "z" = depth [m]
 "reducedshear" = reduced shear [s^-2] \# Structure
 "Fig11k" contains variables: "x" = distance [m]
 "z" = depth [m] "eps_Th" = log10 overturn Thorpe-scale
 dissipation rate epsilon [W/kg] \# Structure "Fig11l" contains
 variables: "x" = distance [m] "z" = depth [m]
 "eps_Th_tilde" = log10 5-m Thorpe-scale dissipation rate epsilon
 [W/kg] \# \# **FIG. 12.** (a),(e),(i) TCTD buoyancy frequency squared,
 (b),(f),(j) reduced-shear, (c),(g),(k) Thorpe-scale overturn patch
 inferred dissipation rates , and (d),(h),(l) 5-m patch dissipation rates.
 Median properties of composite billows for aspect ratios 0.10.5 in (i)–(l) (29 billows). Downstream coordinate x and depth z
 are both normalized by width L.  file: Fig12.mat \# Structure
 "Fig12a" contains variables: "x" = distance [m]
 "z" = depth [m] "N2" = log10 buoyancy frequency
 squared [s^-2] \# Structure "Fig12b" contains variables:
 "x" = distance [m] "z" = depth [m]
 "reducedshear" = reduced shear [s^-2] \# Structure
 "Fig12c" contains variables: "x" = distance [m]
 "z" = depth [m] "eps_Th" = log10 overturn Thorpe-scale
 dissipation rate epsilon [W/kg] \# Structure "Fig12d" contains
 variables: "x" = distance [m] "z" = depth [m]
 "eps_Th_tilde" = log10 5-m Thorpe-scale dissipation rate epsilon
 [W/kg] \# Structure "Fig12e" contains variables: "x" =
 distance [m] "z" = depth [m] "N2" = log10 buoyancy
 frequency squared [s^-2] \# Structure "Fig12f" contains
 variables: "x" = distance [m] "z" = depth [m]
 "reducedshear" = reduced shear [s^-2] \# Structure
 "Fig12g" contains variables: "x" = distance [m]
 "z" = depth [m] "eps_Th" = log10 overturn Thorpe-scale
 dissipation rate epsilon [W/kg] \# Structure "Fig12h" contains
 variables: "x" = distance [m] "z" = depth [m]
 "eps_Th_tilde" = log10 5-m Thorpe-scale dissipation rate epsilon
 [W/kg] \# Structure "Fig12i" contains variables: "x" =
 distance [m] "z" = depth [m] "N2" = log10 buoyancy
 frequency squared [s^-2] \# Structure "Fig12j" contains
 variables: "x" = distance [m] "z" = depth [m]
 "reducedshear" = reduced shear [s^-2] \# Structure
 "Fig12k" contains variables: "x" = distance [m]
 "z" = depth [m] "eps_Th" = log10 overturn Thorpe-scale
 dissipation rate epsilon [W/kg] \# Structure "Fig12l" contains
 variables: "x" = distance [m] "z" = depth [m]
 "eps_Th_tilde" = log10 5-m Thorpe-scale dissipation rate epsilon
 [W/kg] \# \# **FIG. 13.** Example 2-h billow-train time series: (a)
 echosounder backscatter, (b) TCTD temperature, (c) buoyancy
 stratification, (d) reduced shear squared, (e) reduced shear turbulent
 kinetic energy dissipation rate, (f) overturn patch Thorpe-scale turbulent
 kinetic energy dissipation rate, and (g) 5-m patch Thorpe-scale turbulent
 kinetic energy dissipation rate . In all panels, thin black contours are
 isopycnals every 0.2 kg/m^3^. file: Fig13.mat \# Structure
 "Fig13a" contains variables: "time" = matlab time
 [days] "z" = depth [m] "sigma" = potential density
 [kg/m^3] "backscatter" = backscatter [db] \# Structure
 "Fig13b" contains variables: "time" = matlab time
 [days] "z" = depth [m] "sigma" = potential density
 [kg/m^3] "T" = temperature [degC] \# Structure
 "Fig13c" contains variables: "time" = matlab time
 [days] "z" = depth [m] "sigma" = potential density
 [kg/m^3] "N2" = log10 buoyancy frequency squared [s^-2] \#
 Structure "Fig13d" contains variables: "time" = matlab
 time [days] "z" = depth [m] "sigma" = potential
 density [kg/m^3] "reducedshear" = reduced shear [s^-2] \#
 Structure "Fig13e" contains variables: "time" = matlab
 time [days] "z" = depth [m] "sigma" = potential
 density [kg/m^3] "eps_KWB" = log10 reduced-shear dissipation
 rate epsilon [W/kg] \# Structure "Fig13f" contains variables:
 "time" = matlab time [days] "z" = depth [m]
 "sigma" = potential density [kg/m^3] "eps_Th" = log10
 overturn Thorpe-scale dissipation rate epsilon [W/kg] \# Structure
 "Fig13g" contains variables: "time" = matlab time
 [days] "z" = depth [m] "sigma" = potential density
 [kg/m^3] "eps_Th_tilde" = log10 5-m Thorpe-scale dissipation
 rate epsilon [W/kg] \# \# **FIG. 14.** (a) Buoyancy stratification and
 vertical shear magnitude; (b) unstable shear growth rate and total energy
 available for turbulence production; (c) overturn patch Thorpe-scale
 inferred dissipation rates (black) and 5-m patch dissipation rates (red),
 reduced-shear inferred dissipation rate (blue), and vertical temperature
 gradient spectrum inferred dissipation rate (green); and (d) instability
 length scales and billow aspect ratios (gray circles). file: Fig14.mat \#
 Structure "Fig14a" contains variables: "time" = matlab
 time [days] "N2_E_median" = median overturn-weighted buoyancy
 frequency squared [s^-2] "N2_E_mean" = mean overturn-weighted
 buoyancy frequency squared [s^-2] "N2_KWB_median" = median
 unstable shear patch buoyancy frequency squared [s^-2]
 "N2_KWB_mean" = mean unstable shear patch buoyancy frequency
 squared [s^-2] "N2_E_tilde_median" = median 5m-weighted buoyancy
 frequency squared [s^-2] "N2_E_tilde_mean" = mean 5m-weighted
 buoyancy frequency squared [s^-2] "S2_4_KWB_median" = median
 unstable shear patch vertical shear magnitude divided by 4 [s^-2]
 "S2_4_KWB_mean" = mean unstable shear patch vertical shear
 magnitude divided by 4 [s^-2] \# Structure "Fig14b" contains
 variables: "time" = matlab time [days] "sigmaKH_median” =
 median unstable shear growth rate [s^-1] "sigmaKH_mean” = mean
 unstable shear growth rate [s^-1] "deltaE_median” = median energy
 available for turbulent production [m^2 s^-2] "deltaE_mean” = mean
 energy available for turbulent production [m^2 s^-2] \# Structure
 "Fig14c" contains variables: "time" = matlab time
 [days] "epsilon_Th_tilde_median” = median 5-m Thorpe scale
 dissipation rate epsilon [W/kg] "epsilon_Th_tilde_mean” = mean 5-m
 Thorpe scale dissipation rate epsilon [W/kg] "epsilon_KWB_median” =
 median reduced shear dissipation rate epsilon [W/kg]
 "epsilon_KWB_mean” = mean reduced shear dissipation rate epsilon
 [W/kg] "epsilon_Th_median” = median overturn patch Thorpe scale
 dissipation rate epsilon [W/kg] "epsilon_Th_mean” = median overturn
 patch Thorpe scale dissipation rate epsilon [W/kg] "epsilon_Tz” =
 vertical temperature gradient dissipation rate epsilon [W/kg] \# Structure
 "Fig14d" contains variables: "time" = matlab time
 [days] “l_Th_median” = median 5-m Thorpe scale [m] “l_Th_mean” = mean 5-m
 Thorpe scale [m] “L_Th_median” = median overturn patch Thorpe scale [m]
 “L_Th_mean” = mean overturn patch Thorpe scale [m] “L_KWB_median” = median
 unstable shear patch thickness [m] “L_KWB_mean” = mean unstable shear
 patch thickness [m] “HL_time” = aspect ratio matlab time [days] “HL” =
 aspect ratio \# \# **FIG. 15.** (a) Billow-median Thorpe-scale inferred
 dissipation rate as a function of positive billow-median reduced-shear.
 (b) Billow-median ratio of Thorpe scale to unstable shear-layer thickness
 as a function of gradient Froude number. In both panels, color indicates
 billow aspect ratio H/L. file: Fig15.mat \# Structure "Fig15a"
 contains variables: “reducedshear” = reduced shear [s^-2] “eps_Th” =
 overturn patch Thorpe scale dissipation rate epsilon [W/kg] “HLratio” =
 aspect ratio \# Structure "Fig15b" contains variables: “Fr” =
 Froude number “LThLKWBratio” = Thorpe scale and unstable shear scale ratio
 “HLratio” = aspect ratio ##