Parametric equations for Shields parameter and wave orbital velocity in combined current and irregular waves

A fundamental requirement for any scour assessment and scour protection design is the ability
to determine the Shields parameter for combined wave and current conditions.
The Shields parameter can be calculated for current combined with monochromatic waves using the approach
of Soulsby (1997) in combination with the wave friction factor concept. For current in combination with irregular
waves, the same approach is suggested using a wave orbital velocity, Um, for representation of the irregular
sea state. Um is defined as 1.41 times the standard deviation of the near bed wave orbital velocity.
The Soulsby (2006) expression for Um is compared with a hyperbolic expression and validated using numerical
methods and laboratory measurements.
A large number of expressions exist for the wave friction factor as a function of relative bed roughness. From
a literature study, the paper proposes a combination of existing expressions to cover relative bed roughnesses
from sand over gravel to coarse armour rock.