Littoral Processes FM All Modules Scientific Documentation MIKE 2017 DHI headquarters Agern Allé 5 DK-2970 Hørsholm Denmark +45 4516 9200 Telephone +45 4516 9333 Support +45 4516 9292 Telefax [email protected] www.mikepoweredbydhi.com littoralprocessesfm_scientificdoc.docx/AJS/2016-10-03 - © DHI PLEASE NOTE COPYRIGHT This document refers to proprietary computer software, which is protected by copyright. All rights are reserved. Copying or other reproduction of this manual or the related programmes is prohibited without prior written consent of DHI. For details please refer to your ‘DHI Software Licence Agreement’. LIMITED LIABILITY The liability of DHI is limited as specified in Section III of your ‘DHI Software Licence Agreement’: ‘IN NO EVENT SHALL DHI OR ITS REPRESENTATIVES (AGENTS AND SUPPLIERS) BE LIABLE FOR ANY DAMAGES WHATSOEVER INCLUDING, WITHOUT LIMITATION, SPECIAL, INDIRECT, INCIDENTAL OR CONSEQUENTIAL DAMAGES OR DAMAGES FOR LOSS OF BUSINESS PROFITS OR SAVINGS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION OR OTHER PECUNIARY LOSS ARISING OUT OF THE USE OF OR THE INABILITY TO USE THIS DHI SOFTWARE PRODUCT, EVEN IF DHI HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. THIS LIMITATION SHALL APPLY TO CLAIMS OF PERSONAL INJURY TO THE EXTENT PERMITTED BY LAW. SOME COUNTRIES OR STATES DO NOT ALLOW THE EXCLUSION OR LIMITATION OF LIABILITY FOR CONSEQUENTIAL, SPECIAL, INDIRECT, INCIDENTAL DAMAGES AND, ACCORDINGLY, SOME PORTIONS OF THESE LIMITATIONS MAY NOT APPLY TO YOU. BY YOUR OPENING OF THIS SEALED PACKAGE OR INSTALLING OR USING THE SOFTWARE, YOU HAVE ACCEPTED THAT THE ABOVE LIMITATIONS OR THE MAXIMUM LEGALLY APPLICABLE SUBSET OF THESE LIMITATIONS APPLY TO YOUR PURCHASE OF THIS SOFTWARE.’ MIKE 2017 CONTENTS Littoral Processes FM All Modules Scientific Documentation 1 Introduction ...................................................................................................................... 1 2 Basic Sediment Transport ............................................................................................... 2 2.1 Introduction ........................................................................................................................................... 2 2.1.1 Vertical distribution ............................................................................................................................... 2 2.2 Hydrodynamics ..................................................................................................................................... 3 2.2.1 Mean Flow ............................................................................................................................................ 3 2.2.2 Wave Motion ........................................................................................................................................ 5 2.2.3 Bottom Boundary Layer ....................................................................................................................... 7 2.2.4 Turbulence ......................................................................................................................................... 10 2.2.5 Shear Stress ....................................................................................................................................... 13 2.2.6 Ripples ............................................................................................................................................... 15 2.3 Sediment Transport ............................................................................................................................ 17 2.3.1 Bed Load Transport in case of Sand sized bed material ................................................................... 18 2.3.2 Bed Load Transport in case of Shingle sized bed material ................................................................ 19 2.3.3 Suspended Load Transport ................................................................................................................ 23 2.3.4 Graded Sediment Description ............................................................................................................ 28 3 Littoral Transport ........................................................................................................... 32 3.1 Introduction ......................................................................................................................................... 32 3.2 Basic Equations – Longshore Current ............................................................................................... 32 3.2.1 Waves ................................................................................................................................................ 32 3.2.2 Wave Set-up and Set-down ............................................................................................................... 43 3.2.3 Flow Resistance ................................................................................................................................. 43 3.2.4 Littoral Current .................................................................................................................................... 47 3.3 Basic Algorithms – Longshore Transport ........................................................................................... 50 3.3.1 Discretization of the Hydrodynamic Parameters ................................................................................ 50 3.3.2 Point Selection ................................................................................................................................... 50 3.3.3 Sediment Transport Calculation ......................................................................................................... 52 3.3.4 Integration of Transport Rates ........................................................................................................... 54 3.3.5 Algorithms for Annual Littoral Drift ..................................................................................................... 54 4 Littoral Drift Table Generation ....................................................................................... 55 4.1 Introduction ......................................................................................................................................... 55 4.2 Table Layout ....................................................................................................................................... 55 4.2.1 Main outline ........................................................................................................................................ 56 4.2.2 Total transport rate ............................................................................................................................. 57 4.2.3 Distributed drift ................................................................................................................................... 57 4.3 Basic Algorithm .................................................................................................................................. 57 4.3.1 Determining table limits ...................................................................................................................... 57 4.3.2 Populating table .................................................................................................................................. 58 i 5 Coastline Evolution ........................................................................................................ 61 5.1 Introduction ......................................................................................................................................... 61 5.2 Continuity Equation for Sediment Volumes ....................................................................................... 62 5.3 Flow Diagram ..................................................................................................................................... 63 5.4 Modification of Transport Tables ........................................................................................................ 64 5.5 Local Wave Conditions....................................................................................................................... 64 5.5.1 Reference Wave Conditions .............................................................................................................. 64 5.5.2 Breaking Wave Conditions ................................................................................................................. 65 5.6 Determination of Q(x,θ) ...................................................................................................................... 66 5.6.1 Interpolation in Transport Tables ....................................................................................................... 66 5.6.2 Q(x,θ) along Coastline........................................................................................................................ 66 5.7 Structures ........................................................................................................................................... 67 5.7.1 General Parameters ........................................................................................................................... 67 5.7.2 Theoretical Adaptation Length ........................................................................................................... 68 5.7.3 Breakwaters ......................................................................................................................................