The first assumption is that the overturning displacements d are related to the
Ozmidov scales L O of largest overturns in stratified turbulence. As indicated by
Thorpe [36], after suitable (rms) averaging this is true to within a constant ratio of
c 1 = L O /d rms = 0.8. This value was empirically established by Dillon [37] as being
a mean in a distribution of about one order of magnitude wide. The distribution
reflects the various stages of turbulence development and the two principal turbulence processes of shear-induction and convection. Recently, the overturning
method was challenged from numerical simulations showing that convection leads
to an underestimate of the Ozmidov scale using the displacements. But, the high
Reynolds number (10
4
–10
6 ) turbulence in the stratified ocean is a mix of
shear-induction and convection rendering the average ratio very close to 1 [38] and
confirming Dillon’s observations. The second assumption is to use a constant value
m 1 = 0.2 for the mixing efficiency [39, 40]. As with the Ozmidov/Overturning
scale ratio, this constant is a mean from a distribution of about one order of
magnitude wide and thus requires some suitable vertical, horizontal and/or time
averaging. The third assumption was not necessary to make for Thorpe [36] as he
designed the method for use in lakes: It involves salinity and ship’s motions. The
disadvantages of using the overturning method in the ocean are the ship’s motion
by surface waves that are only partially compensated by a heave compensator and
the contribution of salinity to density variations. Both require corrections to the raw
data that approach the order of magnitude of turbulent overturns (e.g., [41–44]).
Quantifying Internal Wave Turbulent Mixing:
Moored Instruments
Instead of lowering instruments from a ship one can use Eulerian moored instrumentation fixed in space under water and have the flow go past it. Under the
assumption that one can separate via ‘Reynolds decomposition’ the turbulent
fluctuations from the ‘mean flow’, one may directly estimate the turbulent
momentum and/or heat (mass) fluxes with suitable current and temperature (conductivity) measurement devices. Although stand-alone instrumentation is heavily
limited by sufficient power supply, this method is reasonably successful for estimating momentum fluxes in shallow seas by a moored acoustic point source
measurement device like the Nortek Vector in shallow seas almost resolving the
dissipation scales (e.g., [45]). Resolving larger scales, moored acoustic profiling
instrumentation, especially operating in pulse-coherent mode, estimates statistically
significant momentum fluxes above ‘flat’ shallow sea floors with dominant tidal
friction (e.g., [46, 47]) and sloping topography [30]. However, the method has
seldom produced significant results from the deep ocean [48], possibly due to the
lack of sufficient scatterers. Few attempts have been made to actually estimate heat
(mass) fluxes, above sloping topography [48, 30]. It appeared difficult to match the
acoustic current measurements in slanted beams with data from a chain of
High-Resolution Observations of Internal Wave Turbulence …
131
Ozmidov scales L O of largest overturns in stratified turbulence. As indicated by
Thorpe [36], after suitable (rms) averaging this is true to within a constant ratio of
c 1 = L O /d rms = 0.8. This value was empirically established by Dillon [37] as being
a mean in a distribution of about one order of magnitude wide. The distribution
reflects the various stages of turbulence development and the two principal turbulence processes of shear-induction and convection. Recently, the overturning
method was challenged from numerical simulations showing that convection leads
to an underestimate of the Ozmidov scale using the displacements. But, the high
Reynolds number (10
4
–10
6 ) turbulence in the stratified ocean is a mix of
shear-induction and convection rendering the average ratio very close to 1 [38] and
confirming Dillon’s observations. The second assumption is to use a constant value
m 1 = 0.2 for the mixing efficiency [39, 40]. As with the Ozmidov/Overturning
scale ratio, this constant is a mean from a distribution of about one order of
magnitude wide and thus requires some suitable vertical, horizontal and/or time
averaging. The third assumption was not necessary to make for Thorpe [36] as he
designed the method for use in lakes: It involves salinity and ship’s motions. The
disadvantages of using the overturning method in the ocean are the ship’s motion
by surface waves that are only partially compensated by a heave compensator and
the contribution of salinity to density variations. Both require corrections to the raw
data that approach the order of magnitude of turbulent overturns (e.g., [41–44]).
Quantifying Internal Wave Turbulent Mixing:
Moored Instruments
Instead of lowering instruments from a ship one can use Eulerian moored instrumentation fixed in space under water and have the flow go past it. Under the
assumption that one can separate via ‘Reynolds decomposition’ the turbulent
fluctuations from the ‘mean flow’, one may directly estimate the turbulent
momentum and/or heat (mass) fluxes with suitable current and temperature (conductivity) measurement devices. Although stand-alone instrumentation is heavily
limited by sufficient power supply, this method is reasonably successful for estimating momentum fluxes in shallow seas by a moored acoustic point source
measurement device like the Nortek Vector in shallow seas almost resolving the
dissipation scales (e.g., [45]). Resolving larger scales, moored acoustic profiling
instrumentation, especially operating in pulse-coherent mode, estimates statistically
significant momentum fluxes above ‘flat’ shallow sea floors with dominant tidal
friction (e.g., [46, 47]) and sloping topography [30]. However, the method has
seldom produced significant results from the deep ocean [48], possibly due to the
lack of sufficient scatterers. Few attempts have been made to actually estimate heat
(mass) fluxes, above sloping topography [48, 30]. It appeared difficult to match the
acoustic current measurements in slanted beams with data from a chain of
High-Resolution Observations of Internal Wave Turbulence …
131