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Unformatted text preview: we define a new parameter h0 :
h0 = H12 − ZSEA 2 (ε + 1)
ε ⋅ (ε + 1) (35) This parameter, h0 , is a length scale on the same order as the thickness of the freshwater lens
imposed at the inland boundary (upstream). The solution of the homogenous problem σ = 0 can now
be expressed as:
Z SEA − δZ − Z SALT ( x) ≈ h0 ε ⋅ x
LX (36) This simple analytical expression (36) shows that there exists, for the homogeneous case, a
quadratic transform which makes the saltwater profile exactly linear in x. For the heterogeneous
case, with random field permeability, this suggests applying the same quadratic transform to the
nonlinear random function ZSALT(x,y). The transformed field is a new random “potential” field
Φ SALT = ( Z SEA − δZ − Z SALT ) 2 (37) We may expect that the random ΦSALT(x,y) has a roughly linear trend. Furthermore, it is possible to
derive analytically the mean and variance of ZSALT from the moments of the random field
ΦSALT(x,y). Let us first normalize ZSALT and ΦSALT by ZSEA as follows: Z=(ZSALT-δZ)/ZSEA;
φ = ΦSALT/ZSEA. The Φ-...
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This document was uploaded on 01/19/2014.
- Winter '14
- The Land, In French