Single-Course English 5 ECTS

# Hydrodynamics 2

## Overall Course Objectives

To give students the basis for treatment of a number of hydrodynamic and hydraulic problems encountered in civil engineering, for example in relation to projects in rivers, on coasts or offshore.

Learning Objectives

• Describe the fundamental hydrodynamic equations and concepts (Navier-Stokes equations, Euler equations, vorticity vector), and derive solutions for various examples of laminar flow.
• Describe the fundamental equations and assumptions in linear wave theory for water waves (Laplace equation, Bernoulli equation, boundary conditions), and the basic concepts (dispersion relation, velocity kinematics, pressure field, particle traj
• Describe and apply the concepts of potential and kinetic wave energy, wave energy flux, group velocity and linear superposition.
• Describe and apply the concepts of linear shoaling and refraction (Snel’s law).
• Describe and calculate the phenomena involved in wave breaking in the surf zone (Radiation stress, wave height decay, set-up/set-down, wave induced currents).
• Describe laminar boundary layer processes, including the boundary layer equations.
• Describe turbulent flow processes, such as turbulent boundary layers (in open channels, in pipes, etc.) including laminar-to-turbulent transition in boundary layers.
• Describe the basic equations for turbulent flows (including Reynolds equations, and mixing length turbulence modelling).
• Undertake exercises/assignments on problems related to turbulent flows in “hands-on” problem sessions (in 2-3 person groups).
• Write up reports on the assignment upon the completion of each exercise.
• Be geared up with a full body of basic knowledge in Hydrodynamics which will enable him/her to take on further courses in Coastal and Hydraulic Engineering offered by MEK such as 41121, 41126, 41129, 41114, 41224, and 41225.

Course Content

Potential flow, the basis for description of ideal flows without energy loss.

Water waves over an arbitrary depth. Wave celerity, wave-induced velocities and pressure. Energy and momentum associated with water waves. Transformation of water waves: refraction and shoaling. Set-up and wave-driven currents.

Boundary layer flow. The flow equations for boundary layers. Laminar and turbulent boundary layers. Similarity and affine boundary layers.

Turbulent flow. Instabiliy of laminar flows. Reynolds averaging. Turbulent energy and transformation of energy in turbulent flows. The problem of closure, models for turbulence.

Recommended prerequisites

41101/41102/41312

Teaching Method

lectures, exercises

Faculty

See course in the course database.

## Registration

Language English 13 weeks DTU Lyngby Campus 41111 Candidate Week 35 Week 48 Tues 8-12
Price 7.500,00 DKK