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Earth and Space Sciences · 术语表

什么是 Boussinesq approximation？

Definition 19.2 University Earth and Space Sciences — Year 3 · 第 19 章 — Geophysical Fluid Dynamics

The Boussinesq approximation writes the density as ρ=ρ0+ρ′\rho = \rho_0 + \rho', with ρ0\rho_0 a constant and ∣ρ′∣≪ρ0|\rho'| \ll \rho_0, and keeps ρ′\rho' only where it is multiplied by gg. The continuity equation becomes ∇⋅u⃗=0\nabla\cdot\vec u = 0, and the momentum equation

Du⃗Dt+f k⃗×u⃗=−1ρ0∇p′+b k⃗+ν∇2u⃗,b=−g ρ′ρ0,\frac{\mathrm D\vec u}{\mathrm Dt} + f\,\vec k\times\vec u = -\frac{1}{\rho_0}\nabla p' + b\,\vec k + \nu\nabla^2\vec u , \qquad b = -g\,\frac{\rho'}{\rho_0} ,

where p′p' is the departure of the pressure from the hydrostatic pressure of the density ρ0\rho_0, k⃗\vec k the upward unit vector and bb the buoyancy.

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