Turbulent mixing in stratified fluids : layer formation and energetics
MetadataShow full item record
A turbulent mixing experiment was conducted to observe the dynamics and the energetics of layer formation along with the region of layer formation in the Reynolds number (Re) and the overall Richardson number (Rio) space. A salt stratified fluid was mixed uniformly throughout its depth with a vertical rod that moved horizontally at a constant speed. The evolution of density was measured with a conductivity probe. As the instability theory of Phillips (1972) and Posmentier (1977) shows, an initially uniform density profile turns into a series of steps when Rio is larger than a critical value Ric, which forms a stability boundary. For fixed Re, as Rio decreases to Ric, the steps get weaker; the density difference across the interface and the difference of density gradient between layers and interfaces become small. Ric increases as Re increases with a functional relation log Ric ≈ Re/900. The steps evolve over time, with small steps forming first, and larger steps appearing later through merging and decay of the interfaces. After some time the interior seems to reach an equilibrium state and the evolution of the interior steps stops. The length scale of the equilibrium step, ls, is a linear function of U /Ni, where U is the speed of the rod and Ni is the buoyancy frequency of the initial profile. The functional relationship is ls = 2.6U / Ni + l.Ocm. For Rio < Ric, the mixing efficiency, Rf, monotonically decreases to the end of a run. However, for Rio > Ric, the evolution of Rf is closely related to the evolution of the density field. Rf changes rapidly during the initiation of the steps. For Rio » Ric, R1 increases initially, while for Rio ≥ Ric, Rf ecreases initially. When the interior reaches an equilibrium state, Rf becomes uniform. Posmentier (1977) theorized that when steps reach an equilibrium state, a density flux is independent of the density gradient. The present experiments show a uniform density flux in the layered interior irrespective of the density structure, and this strongly supports the theory of Posmentier. The density flux generated in the bottom boundary mixed layer goes through the interior all the way to the top boundary mixed layer without changing the interior density structure. Thus, turbulence can transport scalar properties further than the characteristic length scale of active eddies without changing a density structure. When the fluid becomes two mixed layers, the relation between Rf and Ril was found for Ril > 1. Here, Ril is the local Richardson number based on the thickness of the interface. R, does decrease as Ril increases, which is the most crucial assumption of the instability theory.
Submitted in partial fulfillment of the requirements for the degree of Master of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 1993
Showing items related by title, author, creator and subject.
Tochko, John Steven (Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, 1978-02)The design and operation of a unique flow measuring instrument for bottom boundary layer studies in the marine environment is documented. The effectiveness of the instrument in acquiring data with which models of near ...
Notes on the 1977 summer study program in geophysical fluid dynamics at the Woods Hole Oceanographic Institution Veronis, George; Thayer, Mary C. (Woods Hole Oceanographic Institution, 1977-12)The lectures by Marten Landahl, recorded in the first part of this report, served as the introduction to the study of turbulence which was the principal theme of the nineteenth summer program in Geophysical Fluid Dynamics ...
Shaw, William J. (Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, 1999-09)The bottom boundary layer is an important dynamical region of shallow water flows. In this thesis, the problem of turbulent mixing in the coastal bottom boundary layer is investigated with a unique set of field measurements ...