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Download Aeroguide 26 - British Aerospace Harrier GR Mk. 5/ Mk. 7 by Roger Chesneau PDF

By Roger Chesneau

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Extra info for Aeroguide 26 - British Aerospace Harrier GR Mk. 5/ Mk. 7

Example text

81) The four terms here have distinct physical meanings. The first term we can label KEζ : it represents the part of the kinetic energy which comes from the relative vorticity. The second term is proportional to the fluid’s excess angular momentum, past what it has from the rotation of the planet, and therefore we can dub it AM . The third term is the part of the kinetic energy which comes from the fluid, and therefore fits the label KEδ . The final term, labelled IM , is related to the moment of inertia of the fluid within the rotating system.

This further allows us to set the relative vorticity ζ and δ, which we write as ζ = ∇ × u = ∇ × uψ = ∆ψ and δ = ∇ · u = ∇ · uΦ = ∆Φ, where ψ is the stream function and where Φ is the velocity potential. 61) The Shallow-Water Equation energy function is cubic: the integrand is quadratic in the velocities (or equivalently in the gradients of the stream function and the velocity potential), and is linear in the height h. Since we are going to represent this model with a spatial lattice formation where the generalized spins are relative vorticity, horizontal, and surface height, we will integrate by parts the kinetic energy expression in order to get cubic terms that are linear in the stream function or in the velocity potential, linear in the Laplacian of these potentials — the relative vorticity ζ and the horizontal δ — and linear in h.

The second term is proportional to the fluid’s excess angular momentum, past what it has from the rotation of the planet, and therefore we can dub it AM . The third term is the part of the kinetic energy which comes from the fluid, and therefore fits the label KEδ . The final term, labelled IM , is related to the moment of inertia of the fluid within the rotating system. These separate labels will be convenient. 83) S 2 (R) where the flat bottom of the atmosphere is taken to be the zero-reference level for the potential energy.

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