Fluid Dynamics of the Atmosphere and Ocean - Problem Set 4 | Widener University - Edubirdie

University:
Widener University
Course:
ESSC 103 | Intriduction To Earth Science
Academic year:

2023
Views:

107

Pages:

1
Author:

Jaslyn Nolan

Problem set 4 1) In the last problem set you derived the momentum equation up to the form ρ Du = ρg + ∇ ⋅ τ . Dt Now show that ∇ ⋅ τ = −∇p + µ∇ 2u + µ ∇(∇ ⋅ u) 3 by following the derivation done in class and carefully describing the steps taken and assumptions made. 2) In class we derived the heat equation by conserving total energy and then removing the mechanical energy component. Starting from ρ ρC p De = − p(∇ ⋅ u ) + φ − ∇ ⋅ q , produce the relationship Dt DT = φ −∇⋅q Dt without resorting to the relationship de = Cv dT . Hints: Use de = − pdα + Tdη where α = 1 ρ , and η is the entropy per unit mass (the intensive version of entropy). You’ll need to know how C p is related to entropy per mass, and you’ll have to make assumptions about certain terms being small.

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