Tidal
Currents |
Description
of Model |

## Velocity Profile

*One of the aims of the project is to better understand how
the bathymetry of a site affects the tidal flow. The approach
decided on was to identify some of the key flow characteristics
in sections of interest. The rational behind the method is that
if shear profile is known for a channel section, velocity, pressure,
flow rates and fluxes may be determined. Therefore a model to
analyse the current velocity in arbitrary channel sections has
been developed.*

Due to a lack of freely available data on site flow characteristics,
a model has been developed in order to assess the effects of the
local bathymetry and roughness on energy production.

The current options for developers include, in reverse order of
cost:

- Sonar readings from the site which would yield accurate velocity and other data for the vast majority of the site
- Direct velocity measurements on site which would yield velocity profiles for all the depths that the measurement was taken
- Full CFD which could feasibly calculate velocities, pressures and other useful information
- Parametric models incorporating integration of governing equations of fluid motion. (3)(4)(5)

Massive expense excluded the first two options for initial site evaluation. The argument against CFD (covering the whole spectrum of finite different approaches) is that the grid required for accurate modelling must include depth-wise integration if it is to give some indication of regions of suitable velocities for device deployment. The addition of this extra dimension makes a large problem massive, if one considers the varying scales of eddies that must be resolved on a grid if accurate (let alone precise) measurements should be taken. The fact that eddies exist from a few centimetres up to hundreds of metres is indicative that the number of grid points would have to be exceptionally high, increasing computing time considerably, and as such grid sizes are often massive, with one minute arc (ie 1 nautica mile) being a common resolution.(6) Approximations, such as the St Venant (or Shallow Water) system (15) allow non-depth integrated surface velocities to be calculated, but often require that geometry be hugely simplified to allow the calculation to proceed in a timely manner. The 1-D St Venant equations relate wall shear stresses in unsteady, non-uniform flow to flow velocities via Newton's Second Law (N2). As such, it is the belief of the project group that a quick and simple integral approach is the best option, allowing rapid calculation of velocity profiles.(8)(15)

Existing methods include the Chezy & Manning equations. Developed in the 1900s for use with canals, they are semi-empirical relationships for velocity and flowrate. Although derived from wall shear stress considerations, these do not directly take them into consideration and as both are concerned with bulk flow characteristics, e.g. mean velocity. Therefore they offer no real insight into the suitability of regions within a section of interest for, say, different technology types.

A velocity profile is constructed based on an integral turbulent boundary layer solution, using:

- Bathymetric data from admiralty charts (2)
- Combined with knowledge of seabed roughness

**This model, coupled with the flow velocity and device
models described elsewhere, allows a potential developer to rapidly
assess the available resource at a particular site, at a relatively
low computational cost and fast turnaround. **

Tidal
Currents |
Description
of Model |

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