Boussinesq transformations

By modifying Boussinesq s transformation to allow for unsteady state, the time-dependent temperature distribution in potential flow past a spherical bubble was recently obtained (B6) numerically. For low Peclet numbers (2 < (Npf)c < 100), where the conduction contribution cannot be neglected, graphical integration of the steady-state temperature profiles yields approximately... 

Odemark s transformation method has been widely used for pavement response analyses (Ullidtz 1987). Comparisons of measured and calculated stresses, strains and deflections have shown that the simple combination of Odemark s transformation with Boussinesq s equations (modified for nonlinearity) results in an agreement between measured and calculated values that is as good as that obtained with the finite element method. Linear elastic methods normally result in rather poor agreement (Ullidtz 1999). 

Development of numerical models for time-domain wave transformation has been tried by many researchers, but random wave-breaking process has not been well reproduced in these models. One of the exceptions is the Boussinesq-type model developed by Hirayama et and Hirayama and Hiraishi, who employed the breaking criterion of the vertical pressure gradient by Nadaoka et alJ They raised the threshold gradient from 0 to 0.5 to compensate the insufficiency in numerical accuracy due to the features of weak nonlinearity inherent to the Boussinesq equation. They have succeeded in reproducing the pc /variation across the surf zone. 

As the tsunamis propagate over a continental shelf and approach a coastal area, the dispersion effect of waves becomes weak, and the nonlinearity and bottom fi-iction of waves dominantly influence the transformation of the tsimamis. However, the linear Boussinesq-type wave equation does not include the nonlinear and bottom friction terms. Thus, the nonlinear shallow-water equations (NSWE) are employed for the near-field transformation of tsunamis. 

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