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Unformatted text preview: alysis of salt wedge via Φ-transform It is clear from both Fig. 4 (mean ZSALT) and Fig. 5 (random ZSALT) that the interface elevation
ZSALT(x,y) follows a nonlinear trend along x (for fixed y) and cannot be a stationary random function
of x. This observation has two consequences:
1. Given a single replicate of the coastal aquifer in (x,y), we can only sample in the shorewise
direction (y) to produce a statistical description of the salt wedge.
2. For theoretical purposes, we may seek a convenient transformation ZSALT → Φ to obtain an
approximate stationary field Φ from the non-stationary field ZSALT.
6.1 Transformation of ZSALT into a potential Φ Following this idea, consider first the analytical solution of the homogenous problem (σ = 0) using
the Badon-Ghyben-Herzberg assumption, modified to include a submarine outflow face of height
ΔZ at the seashore :
⎛ ε ΔZ ⎞
Z SALT ( x ) = Z SEA − ⎜
⎟ − ΔZ −
⎝ ε +1 ⎠ 2
x H 12 − Z SEA (ε + 1) ⎛ ε Δ Z ⎞
ε (ε + 1)
⎝ ε +1...
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- Winter '14
- The Land, In French