Learning goal: A drifting reading combines local warming with movement into warmer water. A fixed thermometer helps separate the two contributions.
∂ₜT= ∇T·ẋ= g′= Full Jacobian: about propagations; JVP: about 2–3
With the tributary enabled, crossing x=400 m creates a jump. The spatial derivative is undefined there: the ordinary chain rule requires differentiability.