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| The conceptual model proposed for the case of waves only (Equation 90) can be extended to the interaction between waves and current. Assuming that ''U''<sub>''s''</sub> is proportional to the shear velocity at the bottom, a dependence on <math>{ {\left| {{\theta }_{cw,onshore}}+{{\theta}_{cw,offshore}}\right| }^{1/2} }</math> may be assumed for ''U''<sub>''s''</sub>, where the interaction between waves and current is taken into account. The representative shear stresses θ<sub>''cw'',''onshore''</sub> and θ<sub>''cw'',''offshore''</sub> are defined based on the instantaneous Shields parameter in the direction of the wave for positive and negative values of θ<sub>''cw''</sub>(''t''), respectively (Figure 29). For an arbitrary angle ( between the waves and the current, this yields the same equations as Equation 88, where θ<sub>''w''</sub> is replaced by θ<sub>''cw''</sub>, and ''T''<sub>''wc''</sub> and ''T''<sub>''wc''</sub> are the half-periods where the instantaneous velocity <math>u\left( t \right)={{U}_{c}}\cos \varphi \ +{{u}_{w}}\left( t \right)</math> (or instantaneous Shields parameter) is onshore (''u''(''t'') > 0) or offshore (''u''(''t'') < 0), respectively (Figure 29). The representative shear stresses θ<sub>''cw,onshore''</sub> and θ<sub>''cw'',''offshore''</sub> are defined as quadratic values of the instantaneous Shields parameter in the direction of the wave for positive and negative values of θ<sub>''cw''</sub>(''t''), respectively (Figure 29). For an arbitrary angle ( between the waves and the current, this yields:
| | <math>\approx</math> 0.80 |
| | |
| | \approx 0.20 |
Revision as of 15:22, 15 September 2011
0.80
\approx 0.20