ABSTRACT
An L-infinity type of matrix norm IIAII is computed by finding the sum of each row (sum over j, at each i) in the A matrix, and selecting the maximum sum as the norm. The offdiagonal elements of the A matrix are then divided by this norm, which gives the off-diagonal transilient elements
(18.7)
(18.8)
while the conservation of tracer is given by
For surface drag in integrated form, the split into two parts becomes:
• BC1: M(t') = M(t)
[1 + M(t)· Cd' (t:..t/t:..Z)best] (18.15)
• BC2: M(t')
M(t + t:..t) = {1 + M(t'), Cd' [(t:..t/t:..z) - (t:..t/t:..Z)best)]} (18.16)
(18.17)
(18.18)
ZN (18.19)
TRANSILIENT MATRICES 375
57 91105335141 0 a 57 91319121141. a 0 a =c
Figure 18.2: Transilient turbulence matrices for the neutral boundary layer at t = 6 h. All matrices are shown in atmospheric orientation (with destination grid index increasing upward from bottom to top), resulting in a main diagonal that runs from lower left to upper right (Le., flipped upside-down from the usual mathematical orientation). Also, all matrices are multiplied by the scaling factors indicated below to produce these displays, and the resulting matrix elements are truncated to integer values to save space in this figure. (a) Initial symmetric mixing-potential matrix, Y, multiplied by 105 . (b) Final asymmetric mixing-potential matrix, A, adjusted to incorporate variable grid spacing (multiplied by 105 ). (c) Transilient turbulence matrix, c, multiplied by 103, and rounded to the nearest integer. Note that each column and row of the actual c matrix indeed sums to exactly 1.0, even though the scaled and rounded numbers displayed here do not sum to 1000.
