Timeplan 2024 Høst - lærer Igor Ezau - Professor

• Overview of the course activities
• Definition of wind vectors
• Review of wind modeling approaches
• Summary of required knowledge, skills, and deliverables

• Creation of data accounts
• Description of required datasets and data sources
• Dataset downloading with python scripts

• Review of wind statistics
• Vector statistics
• Circular statistics for wind directions
• Wind speed distributions
• Exercises with wind datasets
• Wind roses, Taylor diagrams, and other practical statistical plots

Home work: Students shall apply Weibull fitting to their datasets (observations and reanalysis) and obtain fraction of time for productive wind turbine operation at their wind park sites.

• Velocity as a vector quantity, definition
• Vector calculus, basic rules
• Linear vector algebra, refreshment of MAT101/102 courses
• Advanced vector operations, divergence, gradient, dot and vector products
• Exercises

Distribution of Wind park sites for the students' WRF-projects

Introduction to Computational Essay

• Presentation of the learning activity
• Introduction of the 1D EBL model template in Google Colab
• Simple exercises run with students

Home work for students:

1. Make yourself familiar with the 1D EBL Colab code
2. If needed refresh your knowledge of python scripting

• Introduction of equations of motions of fluid dynamics - the Navier-Stokes equations
• 2nd law of Newton, forces and accelerations
• Non-dimensionalization and numbers
• Explanation of different terms of the equations
• NSE in vector form, Euler form, and in velocity component (scalar) form
• Exercises 

• Introduction into spectral analysis with examples from fluid dynamics
• Fourier series decomposition (spectral form) of NSE
• Spectral solution schemes for linearized equations, differential operators in the spectral space
• Spectral solution schems for non-linear NSE in 1D case, the Burgers equation solution
• Exercises with python scripts for Fourier decomposition and Burgers equations
• Explanation of spectral effects of non-linearity, spectral energy cascade, aliasing/dealiasing
• Pseudo-spectral methods
• Exercises with 2D pseudo-spectral fluid dynamics model

Home work: Students shall apply spectral analysis to their observational datasets and compare observed and reanalysis data.

Introduction to the basic principles of the numerical scheme construction in computational fluid dynamics.

Presentation and analysis the most important numerical schemes used in the state-of-the-art wind modeling.

• From NSE to a dicrete numerical wind model - approaches and challenges
• Refreshment of the Taylor series expansion (MAT101)
• Galerkin schemes (briefly), Finite-difference schemes (in details)
• FDE schemes on the Arakawa C-grid, understanding of accuracy and approximation
• FDE schemes apllied for linear and non-linear equation terms
• Exercises with the 1D EBL model in the Computational Essay
• Time stepping schemes, the Runge-Kutta family of schemes in details
• CFL criterion, stability of the numerical schemes
• Exercises

Derivation of the Coriolis force term in the NSE following the Geophysical Fluid Dynamics by J. Pedloski

Presentation and discussion of the Coriolis force effects on the fluid flow.

Presentation and discussion of the Coriolis force effects on the winds inthe earth's atmosphere.

• Presentation and discussion of the general atmospheric circulation
• Winds in the atmosphere: driving forces
• Check the students' understanding of the Coriolis force
• Winds in the atmosphere: major patterns
• Wind and pressure climatology 
• NSE in vorticity form: Introduction of vorticity and streamfunction in 2D fluid motions
• Planetary Rossby waves and vorticity conservation equations
• Exercises: Derivation of phase and group speed of the Rossby waves

Home work: Students shall derive and explain the necessary conditions for the atmospheric blocking and dispersion of the barotropic planetary waves.

Introduction to turbulent fluid mechanics

• Turbulence - definition
• Turbulence - development and main properties
• Mathematical analysis, turbulent energy cascade
• Connection with spectral analysis of the NSE, aliasing
• Kolmogorov-Prandtl turbulence theories

Requirement: Student must be already familiarized with the WRF model and its installation

• General structure of WRF
• Coordinate systems
• Numerical schemes
• Parameterizations
• Input and output from WRF in connection with the atmospheric physics
• Wind modeling with WRF: parameterizations of turbulence and other physical processes

Introduction to 1D (single-column) atmospheric modeling.

Overview of 1D atmospheric models.

Structure of 1D atmospheric models - basic principles and implementation in the Computational Essay.

• Geostrophic equations
• Thermal wind equations
• Ekman boundary layer equations
• Turbulence parameterizations in single-column models
• Mellor-Yamade hierarchy of parameterizations
• Surface boundary conditions (Prandtl, Monin-Obukhov) in the atmospehric 1D models

Home work: Students shall work with the Google COLAB template to study and explain:

• Effect of the Coriolis term
• Turbulent stress term
• Variable formulation of the eddy viscosity/ turbulent length scale

Step-by-step introduction and discussion of the Monin-Obukhov Similarity Theory (MOST).

• MOST as the basis approach in atmospheric bulk turbulence models.
• K-theory, log- and power-law.
• MOST universal correction functions, examples
• Exercises with functions
• Atmospheric stability conditions and their reflection in MOST
• MOST iterative methods

Introduction of the basic elements of the complex terrains.

• Gaussian hill - Askervein hill
• Wall mounted cube - obstackle drag
• Forward and backward facing steps - reattachment points and recirculations
• Escarpment
• Double ridge
• Lid-driven cavity
• Main morphological parameters

Introduction of main modeling approaches to work with winds over complex terrains

• Internal boundary layers and their intrinsic parameters
• Roughness characteristics of the complex terrain (surface)
• Daeves&Harris model and other popular analytical wind models, EU wind load standard approach
• Davenport model for the disturbed flow over complex terrain
• Exercises wiith Davenport model, the height of the disturbed layer 

The industrial wind model WAsP

• Basic principles
• Structure
• Applications, Wind Atlas, Complex terrain

Exercises with WAsP - part 1

• Introduction and definitions
• Atmospheric physical processes affected by mountains
• Local mountain wind circulations
• Mountain gravity waves
• Weather effects of mountains
• Effects of the Norwegian mountains
• Exercises

Course evaluation 14:15 - 14:45

Seminar (project WRF preparation)

Examination procedure

Training

Q&A session

Students deliver their 15 min presentations on the given theoretical topics in front of the auditorium and answer the questions.

Presentation of the procedure of the oral examination.

Review of typical examination questions and tasks with solutions.

Q&A session with students.