Water resour res 184 1053 1067 spiller m 2004 physical

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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 φSALT(x,y) with: 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.

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