On the Nature of Turbulence in a Stratified Fluid. Part II: Application to Lakes

Abstract

A strong debate has continued for a number of years over the magnitude of the ratio of the buoyancy flux b to the rate of production of turbulent kinetic energy from the mean velocity sheer. This ratio has traditionally been called the flux Richardson number Rf. In part I of Ivey and Imberger this definition was generalized by broadening the denominator to include all sources and sinks of mechanical turbulent kinetic energy, the net being defined as m. It was shown that for mechanically energized turbulence (m > 0, b > 0) the magnitude of Rf was completely determined by the magnitude of the overturn Froude FrT and the Reynolds ReT numbers By contrast, for the penetrative convection case (b < 0) Rf was shown to be dependent only on the distance from the source of buoyancy. In the present contribution, scaling arguments are presented for the magnitudes of FrT and ReT. It is shown that these may vary widely and depend, in the first instance, on the physics of the underlying processes energizing the turbulence. By implication, from Part I, this means that the ratio of the buoyancy flux b to the net rate of input of mechanical energy m varies between 0 and 0.2 for events where b > 0. For events which are energized by a negative buoyancy flux, scaling arguments are used to recast the depth dependence, derived in Part 1, to a dependence on the Reynolds number ReT. The magnitude of the pair (FrT, ReT) are then derived directly from temperature microstructure measurements taken in lakes and spanning eight different phenomena: neutral surface layers, penetrative convection, shear layers, diurnal thermoclines, thermals, intrusions, hypolimnetic mixing and boundary mixing. The field data also show large variations in the values of FrT and ReT. Only in the thermocline region of the lake where all mixing events are governed by an inertia-buoyancy balance is FrT constant with a value of between 1 and 3. Thus, both scaling arguments and independent field measurements imply that FrT and ReT may vary greatly throughout a lake. It remains for a more detailed future analysis to verify that the field results and the results from the scaling arguments are compatible for each individual process.