Improved Boussinesq-type equations for spatially and temporally varying bottom

ABSTRACT

Boussinesq-type equations with improved linear dispersion characteristics are derived for spatially and temporally varying bottom. Starting from the first principles, spatial variations and temporal movements of seabed due to underwater earthquakes, landslides and alike are incorporated into the Boussinesq-type equations. The momentum equation is then manipulated by the partial replacement technique so that a generalized Boussinesq set of equations with improved dispersion characteristics is obtained. For an impulsive bed motion-simulated wave profiles are compared with experimental measurements. Waves generated by an ellipsoidal slump moving down on an inclined plane are also numerically simulated to disclose the effect of a newly derived term. Overall, the new set of equations is expected to provide more accurate representation of wave motions due to bottom movements by correctly modeling accelerative bed effects and propagation of relatively shorter waves.

KEYWORDS:

• Boussinesq equations
• spatially and temporally varying bottom
• improved dispersion characteristics
• landslides and tsunamis

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ Some Boussinesq models are incorrectly termed as “fully” nonlinear while in essence no wave model based on truncated series expansions can be fully nonlinear.