Reynolds Number Dependence of Unbounded Stratified Shear Turbulence: A
New Framework for Comparing Ocean and Laboratory Scale Measurements
Abstract
Advances in understanding of stratified-shear turbulence have been made
over the last several decades through ocean measurements, which
typically quantify net turbulent quantities, and through laboratory and
direct numerical simulations (DNS), which have sufficient resolution to
investigate the internal dynamics of individual instabilities.
Stratified shear layer thicknesses in these environments can range from
cms for laboratory and DNS studies to 100s of m in ocean environments,
complicating extrapolation of results between environments. This study
provides a direct comparison of field measurements from oceanic
stratified shear environments with laboratory flows, demonstrating that
non-dimensional turbulent quantities at ocean scales can fall several
orders of magnitude below laboratory values for similar bulk Richardson
numbers, , suggesting that scale plays a critical role. Here, the
dependence of the non-dimensional turbulence intensity, expressed as ,
on a layer Reynolds number, , is evaluated via a ratio of the shear
layer thickness, , to the Kolmogorov turbulence length scale,η. Using a
mechanistically driven, empirical approach a parameterization for
turbulence is defined in parameter space, and by extension, - parameter
space. The mechanisms invoke a “building block” approach to initiation
of stratified shear turbulence, which explains the presence of
turbulence values exceeding the critical value of the gradient
Richardson number, , and increases in at low . The results describe a
new “turbulent geography” in the – plane that can build intuition
about stratified shear turbulence and facilitate interpretation of ocean
measurements in comparison to laboratory experiments and modeling.