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Curriculum::Courses::Introductory, Cross-Disciplinary Courses

XD I: Course Outline

Course Title:
"Multi-Scale Fluid Dynamics: Physical Concepts"
Course Number:
ME7953 (X-listed as PHYS7233, MATH7999-n, PETE7241)
Prerequisites:
MATH2090 or MATH4027 or MATH2065+MATH2085; PHYS2102 or PHYS1202
Text(s) & Readings:
  • Karniadakis, Beskok & Aluru ()
    " Microflows and Nonoflows "
  • Probstein or Levich ()
    " Physiochemical Hydrodynamics "
  • Vogel / Childress /Lighthill ()
    " Life in Moving Fluids / Mechanics of Swimming and Flying / Mathematical Biofluiddynamics "
  • Kundu or Panton ()
    " Fluid Mechanics "
  • Gill or Pedlosky or Pond ()
    " Dynamical Oceanography / Geophysical Fluid Dynamics "
  • Battaner or Choudhuri ()
    " Astrophysical Fluid Dynamics "
  • Brenner and/or Oran/Boris ()
    " Multiphase Flows / Reactive Flows "
Description
An introduction to fluid dynamics from a multi-disciplinary perspective. The first half of the course will emphasize how the principal concepts that underpin our understanding of fluid flows apply to a wide range of physical scales; the second half of the course will take the form of four separate, discipline-specific modules. Physical concepts initially will be presented without mathematics, using examples drawn from various disciplines. Then, the physical concepts will be expressed in mathematical terms to make them tangible for the solution of numerous problems. Example problems initially will be introduced on the simplest of levels and will be chosen so that they can be expanded upon and brought to a higher level (in terms of both formulation and solution method) during the second half of the course. The focus will be on problems with analytical or semi-analytical solutions, but close coordination with XD-II will allow extension to numerical solutions.
   
Schedule
  
Week
 Topic Instructor
1
"The Big Picture "
  • Nature
  • Conceptual Model
  • Mathematical Formulation - Solution
  • Prediction
  • Understanding - Intervention
Definitions of Fundamental Physical Variables;
Properties of Materials;
Shake the dust off Mathematics (covered as needed)
  • Scalars, Vectors, Tensors
  • Symbolic and Indicial Notation
  • Matrices & Determinants
  • Tensor Transformations
  • Eigenvalues and Eigenvectors
  • Tensor Fields & Tensor Calculus
  • Integral Theorems of Gauss and Stokes
Nikitopoulos
2
Equilibrium;
The Continuum Concept/Hypothesis;
Body/Surface Forces;
Traction and Stress 		Nikitopoulos
3
What Happens at Boundaries;
Kinematics of Deformation & Motion
  • Deformation
  • Motion and its Decomposition
Nikitopoulos
4
Kinematics of Deformation & Motion (cont.)
  • Material and Spatial Coordinates
  • Lagrangian & Eulerian (Field) Descriptions
  • Material Derivatives
  • Deformation Rate
  • Acceleration
  • Vorticity
Nikitopoulos
5
Conservation and Transport Processes (as seen from various disciplines)
  • Mass
  • Momentum - Moment of Momentum
  • Energy
  • Entropy - Dissipation
d p /dt = F eng + F ocean + F bio + F astro 		Nikitopoulos
6
Conservation Laws and Transport Processes (continued)
  • Formulations for Non-Inertial Frames
  • Constitutive Equations (Closures)
  • Auxiliary Relations
  • Boundary Conditions
The Issue of Scales
  • Dimensional Analysis
  • Similarity
Nikitopoulos
7
Biology Module (Part I: Internal Bio-Fluid-Mechanics)
  1. Laminar natural convection between vertical channels
  2. Flow through porous media: Derivation of Darcy's Law
  3. Flow through collapsible tubes

Lynn

Tyagi

8
Biology Module (Part II: External Bio-Fluid-Mechanics)
  1. Creeping Flow
  2. Undulating Fibre (Lighthill's propulsion theory)

Lynn

Tyagi

9
Engineering Module (Part I)
  1. Boundary Layer (Physical/Mathematical, Laminar/Turbulent)
  2. Burger's Problem (Non-linear, Smoothing of Discontinuities)
Nikitopoulos
10
Engineering Module (Part II)
  1. Isentropic Compressible Flow (with Shock Waves?)
  2. Electrokinetic Flow
Nikitopoulos
11
Oceanography Module (Part I)
  1. Thermohaline Circulation
  2. Shallow Water Theory

Rouse

Li

12
Oceanography Module (Part II)
  1. Western Boundary Current Solutions
  2. Wind-Driven Circulation - Eckman Layers

Rouse

Li

13
Astronomy Module (Part I)
  1. Hydrostatic Balance and the Structure of Stars
  2. The Gravitational Free-Fall Problem
Tohline
14
Astronomy Module (Part II)
  1. Slow contraction of a star due to Radiative Losses
  2. The Roche potential for Binary stars in Circular Orbits
Conclude with a return to " The Big Picture " (Bring it all back together) 		Tohline

 

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