Challenger Deep internal wave turbulence events

Marine life has been detected in the ocean's trenches at great depths down to nearly 11 km. Such life is subject to particular environmental conditions of large static pressure exceeding 1000 atmosphere. While current flows are expected to be slow, waters cannot be stagnant with limited exchange of fresh nutrients needed to support life. For sufficient nutrient supply, the physics process of turbulent exchange is required. However, the environmental conditions hamper research in such waters. To study potential turbulent water motions, a string equipped with specially designed high-resolution temperature sensors was moored near the deepest point on Earth in the Challenger Deep, Mariana Trench for nearly three years. A preliminary analysis of a six-day period when the mooring was still demonstrates hundreds of meters slanted convection due to internal waves breaking from above. The associated turbulence dissipation rate with peak values hundred times above the background value is considered sufficient to maintain deep-trench life. Turbulence associates with one-ten thousandth of a degree temperature anomalies of about one hour duration.


Introduction
Like in the atmosphere, where breathing would be impossible without turbulent motions, marine life larger than microbial requires turbulent rather than laminar flows for sufficient supply of nutrients and energy, also in the oceans 'hadal' zone of deep trenches (Jamieson, 2015;Gallo et al., 2015;Nunoura et al., 2015). While marine species have been observed at such great depths, establishment and quantification of turbulence processes has been very limited.
Mainly due to the logistical problems imposed by the large hydrostatic pressure which normal oceanographic equipment does not withstand, little is known about the physical oceanography of deep trenches and nothing about the physics that govern the turbulent processes. Turbulence overturn shapes calculated from limited shipborne Conductivity Temperature Depth CTD data from the Puerto Rico Trench averaged over a suitable depth range of 600 m suggest dominant shear-convective turbulence (van Haren, 2015a). Such shearconvective turbulent mixing process is quite different in magnitude from the mainly sheardriven turbulence found in deep passages through ridges and between islands (e.g., Polzin et al. 1996;Lukas et al., 2001;Alford et al., 2011). However, in both cases turbulence is intermittent and has overturn sizes reaching 200 m.
The only moored and hourly sampled measurements so far near the deepest point on Earth, the bottom of the Challenger Deep--Mariana Trench, showed typical current amplitudes of 0.02 m s -1 with a dominant semidiurnal tidal periodicity (Taira et al., 2014). Although these authors did not show internal wave band spectra they mentioned sub-peaks at diurnal and inertial frequencies. These data already suggested that trench-waters are not stagnant. Turbulence could not be calculated from these moored observations. In deep lake Baikal, observations (Ravens et al., 2000) from shipborne microstructure profiler indicated very weakly density stratified waters with mean buoyancy frequency N = 1.410 -4 s -1 , a value which is found around z = -7000 m in the Challenger Deep (van Haren et al., 2017), mean dissipation rates  = O(10 -10 ) m 2 s -3 and mean vertical turbulent diffusivities Kz = 1-910 -3 m 2 s -1 .
In this paper, we report on a six-day detail of high-resolution temperature data from sensors that were moored in the Challenger Deep. The data show internal wave initiated turbulent convection with largest values occurring in a slanted spur-like fashion rather than shear-induced overturning. Near the trench-floor, all dynamics is contained in 0.0001ºC temperature changes: A considerable technical challenge to resolve.

Methods
For a study on internal wave turbulence in hadal zones of the ocean 295 high-resolution temperature T-sensors were custom-made rated to 1400 Bar. Between November 2016 and November 2019 the stand-alone sensors were moored at 11 19.59 N, 142 11.25 E, about 10,910 m water depth in the Challenger Deep, Mariana Trench, close to the deepest point on Earth (van Haren et al. 2017). The 7 km long mooring consisted of a single pack of floatation providing 2.9 kN net buoyancy at its top 4 km below the ocean surface, more than 6 km of slightly buoyant Dyneema rope as a strength member, and two acoustic releases at 6 m above the anchor-weight. Two sections of instrumentation were in the mooring line: One around 2 km below the top consisting of two current meters and a 200 m long array of standard NIOZ4 Tsensors, and one between 595 and 7 m above the trench floor consisting of the 1400 Bar rated For reference, three shipborne SeaBird 911 Conductivity Temperature Depth CTD-profiles were obtained at about 1 km from the mooring site. One profile came to 50 m from the trenchfloor (van Haren et al., 2017). The CTD-data are used to establish a temperature-density relationship for quantification of turbulence parameter values from the moored T-sensor data, and for a pressure and drift-correction to the background stratification of the T-sensor data. All analyses were performed after transferring temperature into dynamically correct Conservative (~potential) Temperature () using the Gibbs-Sea-Water-software described in (IOC, SCOR, IAPSO, 2010).
The moored T-sensor data are used to calculate turbulence dissipation rate εT = c1 2 d 2 N 3 and vertical eddy diffusivity KzT = m1c1 2 d 2 N using the method of reordering potentially unstable vertical density profiles in statically stable ones, as proposed by Thorpe (1977). Here, d denotes the displacements between unordered (measured) and reordered profiles. N denotes the buoyancy frequency computed from the reordered profiles. Rms-values of displacements are not determined over individual overturns, as in Dillon (1982), but over 200 and 588 m vertical intervals that exceed the largest overturn intervals. We use standard constant values of c1 = 0.8 for the Ozmidov/overturn scale factor (Dillon, 1982) and m1 = 0.2 for the mixing efficiency (Osborn, 1980;Oakey, 1982;Ravens et al., 2000), which were mean values in an at least one order of magnitude wide distribution of different turbulence type values established from microstructure profiler data. This is the most commonly used parameterization for oceanographic data after sufficient averaging to achieve statistical stationarity, see further

Observations
The 7-km long mooring line was extending above the surrounding ocean floor at about 5500 m depth and subject to currents that may have been different from those in the trench.
Occasionally, this caused mooring motions of a few tens of meters vertically. Because the deep waters in the trench are almost homogeneous with dΘ/dz = 510 -7 °C m -1 being about 200 times smaller in value and opposite in sign compared to the local adiabatic lapse rate, mooring motions created artificial large internal wave motions. As such artificial internal wave motions are spatially uniform over the vertical, their existence in the data has no effect on turbulent overturning calculations. Nevertheless, to minimize artificial effects and corrections during the post-processing, a six-day section of data is analysed here when the mooring motions were negligible with <0.1 m vertical deflections.

Six-day overview
The high-resolution temperature data reveal omnipresent internal wave activity in the Challenger Deep (Fig. 1). Around z = -6.1 km, isotherm amplitudes are several tens of meters ( Fig. 1a). A dominant periodicity does not occur suggesting strong intermittency as is typical for open-ocean internal waves (LeBlond and Mysak, 1978). Every 1.5 to 2.5 days, intensification of amplitudes seems to occur. The 2.5 day periodicity is associated with the local planetary inertial frequency f = 0.39 cpd, short for cycles per day, the lowest internal wave frequency at which internal gravity waves can freely propagate. Turbulent overturning is not directly visible in this graph, although the variable distancing between isotherms suggests internal wave straining and small-scale nonlinear overturning activity: Turbulence is weak but non-negligible (Fig. 1c). The larger turbulence values deeper in the trench associate with the considerably weaker stratification than found around z = -6.1 km and with continued internal wave activity from above facilitating the deep turbulent overturning. While overall correlation between the data around z = -6.1 and -10.6 km is non-significant, visual comparison of Fig. 1a and 1b demonstrates some correspondence between the larger scale periodic motions. Downdraught in isotherms of both data sets is seen around days 329.3 and 331.8. Fig. 1. Heavily smoothed, about 400 degrees of freedom, vertically averaged temperature variance spectra. The spectra are scaled with the power law σ -5/3 , which reflects the turbulence inertial sub-range. In green, data around z = -6.1 km, in black around z = -10.6 km. Inertial frequency f, semidiurnal Earth rotation 2, and the mean N and maximum Nmax buoyancy frequencies are indicated. Extensions min < f and max > N are also indicated. They reflect the internal wave band under weakly stratified conditions accounting for the horizontal Coriolis parameter (see text). The purple dashed line has slope 0 (log-log plot) and represents dominant shear-induced turbulence. The red dashed line has slope +2/3 (log-log plot) and can indicate dominant convective turbulence. The black-dashed line slopes at +5/3 and indicates instrumental white noise.

Figure 2. Frequency (σ) plot of data in
The weaker temperature stratification in the deep is reflected in more than two orders of magnitude smaller temperature variance and a smaller internal wave band compared to data from around z = -6.1 km (Fig. 2). The log-log spectral plot is scaled with the frequency (σ) slope of σ -5/3 , which reflects the slope of the turbulent inertial subrange and a mean dominance of shear-driven turbulence or a passive scalar (Tennekes and Lumley, 1972;Warhaft, 2000).
Around z = -6.1 km, still great ocean depths of the hadal zone, the inertial subrange is observed for σ > Nmax, the maximum 2-m-scale buoyancy frequency in thin layers over the six-day period.
Instrumental white noise levels are reached around 150 cpd. Within the internal wave band f  σ  N, the spectrum is weakly increasing and near-horizontal. Upper open-ocean internal wave spectra slope like σ -1 (van Haren and Gostiaux, 2009), i.e. +2/3 in the plot of Fig. 2. That slope is here mainly observed in the data around z = -10.6 km for the super-buoyancy range 1.5 < σ < 10 cpd, where local N = 0.8 cpd and Nmax = 5.5 cpd. This frequency band is still partially super-buoyancy when we account for: 1) the horizontal Coriolis force leading to an extended inertia-gravity wave band [σmin<f, σmax>N] (LeBlond and Mysak, 1978;Gerkema et al., 2008), and 2) the small-2-m-scale internal wave motions σ < Nmax. The spectral slope in this partially super-buoyancy range significantly departs from the slope of the inertial subrange and may also indicate a dominant buoyancy-driven convective turbulence or active scalar (Cimatoribus and van Haren, 2014). For σ > 10 cpd, the inertial subrange slope is found over a relatively small frequency band, with the notion that instrumental white noise levels are reached around 25 cpd.

Detail internal wave turbulence
A 14 h magnification plot (Fig. 3)

Discussion and concluding remarks
The computed turbulence values compare with open-ocean values (e.g., Gregg, 1989;Polzin et al., 1997). The small spurs are also slanted to the vertical at a wide variety of angles.
Such slanted convection is known to occur in an environment with a background sheared current-flow, or, mainly in very weakly stratified waters, due to the effects of the horizontal component of the Coriolis force (Straneo et al., 2002;Sheremet, 2004). While the former can have a wide range of slopes, the latter have a preferential direction of the Earth rotational vector.
At the latitude of the mooring, the Earth vector has a local slope of tan(11.3) = 0.2 to the horizontal. This slope is comparable to some of the observed convection spur slopes. The temperature anomaly suggests a source 200 m higher-up, if coming from above against the background stratification, or a source sideways from the trench-walls. Both shear and Earth rotational processes leading to slanted convection still need a process that initiates the convection. Such initiating of convection bursts is not well established for a stratified environment. Recent observations suggested internal wave accelerations into weakly stratified waters from above to generate such convection (van Haren, 2015b). The present observations may lead to the same conclusion, albeit convection here occurs in shorter bursts that eventually follow slanted pathways. This is concluded from the spectra around z = -10.6 km pointing at dominant convective motions in the super-buoyancy range, with oscillatory isotherm motions that are coupled to free internal wave propagation higher up around z = -6.1 km. These observations demand future refinements of internal wave-turbulence modelling.
The turbulence values are expected to be sufficient for replenishment of nutrients and suspended materials, depending on available sources. Trenches collect elevated deposition of organic matter relative to the surrounding ocean floor, which results in twice larger biological oxygen consumption (Glud et al., 2013). Sources and their replenishment are thus expected to be abundant for turbulent redistribution, also near the trench floor.  vertically averaged temperature variance spectra. The spectra are scaled with the power law σ -5/3 , which reflects the turbulence inertial sub-range. In green, data around z = -6.1 km, in black around z = -10.6 km. Inertial frequency f, semidiurnal Earth rotation 2, and the mean N and maximum Nmax buoyancy frequencies are indicated. Extensions min < f and max > N are also indicated. They reflect the internal wave band under weakly stratified conditions accounting for the horizontal Coriolis parameter (see text). The purple dashed line has slope 0 (log-log plot) and represents dominant shear-induced turbulence. The red dashed line has slope +2/3 (log-log plot) and can indicate dominant convective turbulence.
The black-dashed line slopes at +5/3 and indicates instrumental white noise.