= Solution
At fixed <friction velocity>, unstable heating gives $B_0>0$ and $\zeta<0$. The usual similarity closure has $\phi_m<1$, so it reduces the mean velocity gradient relative to the neutral <law of the wall>. Rising warm and descending cool parcels mix momentum efficiently; less mean shear is needed to transport the same stress. Relative to a fixed near-wall reference, the speed difference aloft is reduced.
Stable cooling gives $B_0<0,\zeta>0$ and $\phi_m>1$. The restoring buoyancy suppresses vertical parcel excursions and reduces the effective momentum diffusivity, requiring a steeper shear for the same stress. The speed difference from the wall reference is correspondingly larger. These are comparisons at prescribed stress; fixing an outer wind instead would allow $u_*$ and the stress to change, so it would not be the same comparison.
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