Inverse estimation of horizontal pressure gradients and vertical eddy viscosity profiles in shallow waters

• Main Author: Bang, Bohyun
• Format: Others
• Language: English
• Published: W&M ScholarWorks 1994
• Subjects: Oceanography
• Online Access: https://scholarworks.wm.edu/etd/1539616559; https://scholarworks.wm.edu/cgi/viewcontent.cgi?article=2127&context=etd

A least-squares inverse method was devised to estimate horizontal pressure gradients and vertical eddy-viscosity profiles simultaneously, from current profiles. The method was designed mostly for observations of deterministic or near-deterministic wave currents. Tidal-current observations were chosen for the present study. The inverse system was constructed from a linearized momentum equation. The viscosity was modeled with a time-constant and harmonic function in time, but without its vertical structure predefined. The least-squares problem was solved with the singular value decomposition, by taking current harmonic profiles as input. at first, the method was tested with current profiles simulated by a numerical model employing the mixing-length theory for vertical eddy viscosity. Analyses were done on fourteen sets of real measurements at 6 stations in Chesapeake Bay and one of its tributaries. Thirteen were from current-meter moorings, and one was from a bottom-mounted acoustic Doppler current profiler. It turned out that the proposed method performed well enough to diagnose a linearized dynamic balance which involved a friction term with time-constant, but depth-dependent eddy viscosity. Eddy-viscosity profiles appeared to have linear-exponential structure. The apparent maximum varied significantly in season, implying some stratification effect. Using the primary results, values of drag coefficient (&C\sb{lcub}d{rcub}&) and depth-average TKE production were deduced. Results of &C\sb{lcub}d{rcub}& indicated some seasonal variation of bottom roughness. Depth-average TKE production in the lower bay appeared to be &{lcub}\sim{rcub}&8 times higher than in the mid- or upper bay. The production in the upper part of the York River appeared to be 3&{lcub}\sim{rcub}&4 times higher than the lower part. Among them, the upper part of the York River appeared to have the highest production. The approach will be a good tool for the analysis of ADCP measurements in field, due to the simplicity, yet the diagnostic power. The application, however, is limited mostly to deterministic current measurements. The approach is not appropriate to strongly advective flows. Even for weakly advective flows, it is incapable of determining the oscillatory part of the viscosity successfully, due to truncated nonlinear-advective terms.