Boussinesqközelítés

The Boussinesq approximation is a simplification used in fluid dynamics and heat transfer problems. It is valid when density variations within a fluid are small but significant enough to drive flow. This typically occurs in situations involving temperature or concentration gradients, where these gradients lead to buoyancy forces.

The core idea of the Boussinesq approximation is to assume that density differences are negligible for all terms in the equations of motion except for those contributing to gravity or buoyancy forces. This means that the fluid is treated as incompressible in terms of its inertia and other properties, but its weight is allowed to vary.

Mathematically, the approximation simplifies the momentum equation by neglecting density variations in the inertial and viscous terms, but retaining them in the gravitational term. This allows for the development of simpler governing equations, which are often easier to solve numerically or analytically.

Common applications of the Boussinesq approximation include the study of natural convection in the atmosphere, oceans, and in various engineering systems like heat exchangers. It is also widely used in geophysics for modeling mantle convection and in astrophysics for studying stellar atmospheres. The approximation significantly reduces the computational cost of simulations while still capturing the essential physics of buoyancy-driven flows.