Boussinesq

Boussinesq is the surname of Joseph Valentin Boussinesq, a French mathematician and physicist of the late 19th and early 20th centuries, noted for foundational work in hydrodynamics and elasticity. His contributions have given rise to several widely used concepts in fluid mechanics and solid mechanics, and his name appears in multiple closely related models.

In fluid dynamics, the Boussinesq approximation is a simplifying assumption for flows with small density variations. It treats density as constant in the momentum and continuity equations, except where it multiplies gravity to produce buoyancy. This allows the study of natural convection and atmospheric or oceanic flows without solving the full compressible equations, while retaining essential buoyancy effects.

Related to wave motion in shallow water, the Boussinesq equations form a family of nonlinear dispersive partial differential equations derived as extensions of the shallow-water equations. They model long surface gravity waves with both nonlinearity and dispersion and are used in coastal engineering, tsunami research, and other applications where shallow-water dynamics are important. Numerous variants and refinements, known as Boussinesq-type systems, have been developed to suit different depth ranges and physical settings.

In elasticity theory, the Boussinesq problem concerns the response of an elastic half-space to surface or point loads, yielding classical solutions that underpin geophysical and civil engineering analyses.

The term Boussinesq thus denotes several interconnected formulations and approximations arising from his investigations, spanning fluid dynamics and elasticity, and reflecting his broad impact on continuum physics.