(a)An Application of a Two-Layer Model to Wind Driven Sub-Tidal Currents in Puget Sound (Journal of Oceanography, 1995）

(b)Wind Effects on Sub-Tidal Currents in Puget Sound(Journal of Oceanography, 1997)

Wind effects on sub-tidal currents in Puget Sound are studied by using both data analysis and analytical models. When stratification near the surface is strong, direct wind effects are limited in depth from the surface to about 30m, and counter currents develop below. The transport in this lower layer almost balances the transport in the upper layer, and in over all, the current responses to wind are strongly baroclinic. When stratification is weak, direct wind effects on current can be tracked to about 100m. There is no clear and consistent depth at which one can separate upper and lower layer in these cases; therefore, the continuously stratified normal mode model is applied when stratification is weak while the two layer model is applied when stratification is strong. The result of EOF analysis shows that EOF mode 1 is highly correlated to the local wind speed and 69% of total variance contributes to this mode. The vertical distribution of eigenvector shows maximum at the surface and local maximum but opposite sign at the mid-depth which indicates existence of return flow. The EOF mode 1 time series are almost identical to the upper layer transport when stratification is strong.

The solution for the baroclinic transport of a two layer normal mode model with linear friction as an initial/boundary value problem, originally solved for the surface layer thickness by Farmer(1976, JPO), is obtained. The model reproduced the reduction of the acceleration and eventual reversal of the sign of the acceleration during wind events. The result of this model indicates that this phenomena is mainly caused by the phase lag between the forcing and the resistance. This phase lag decreases almost linearly as forcing frequency decreases at low frequency range using the friction coefficient chosen for Puget Sound. As forcing frequency increases, the phase lag between the forcing and the resistance increases and the mismatch between them has a large effect on the acceleration while the amplitude of the baroclinic pressure gradient decreases and thus its effect on acceleration decreases. The effect of baroclinic pressure gradient is significant when forcing frequency is low because its amplitude increases as forcing frequency decreases; however, it required time to propagate from the boundaries.

A continuously stratified normal mode model with linear friction is constructed for the weakly stratified conditions. The result of the continuously stratified model shows that dynamical modal (normal mode) currents of mode 2 and mode 3 are as important as mode 1. EOF mode 1 between the model and the observations agree. The EOF analysis of the model output suggests that the EOF mode 1 is the combination of the many dynamical modes although the resultant vertical structure of current shows two layer type pattern with only one zero crossing; i.e. surface current and reversed current at deeper depths. These dynamical modal currents are so highly correlated with each other that it is not possible to separate them by statistical methods but they are not identical. The model indicates that the difference between dynamical modal velocities of lowest modes increases as eddy viscosity increases. These differences are due to the baroclinic pressure gradient, phase differences and low pass filtering effects. The last two are affected by effective friction coefficients and originated from the differences between the stress function of different modes. Mode 1 dynamical modal current is most effectively excited by the wind of the forcing frequency at about 0.2 cpd. This is the frequency where wind has relatively large energy. Dynamical modal velocities of higher modes are almost identical except for the amplitudes and are less affected by the forcing frequency compared with lower modes. The amplitudes of dynamical modal velocities generally decrease as the mode number increase or the eddy viscosity increases. The baroclinic pressure gradient is only significant for the lowest dynamical mode, and therefore, the vertical distribution of total amplitude of baroclinic pressure gradient follows the vertical distribution of dQ/dz of dynamical mode 1 while other terms do not. This results that the baroclinic pressure gradient has comparable amplitude with other terms near the bottom but has considerably smaller amplitude compared with other terms near the surface

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