Coastal Engineering 51 (2004) 1067 1084
Wave momentum flux parameter: a descriptor for
Steven A. Hughes*
US Army Engineer Research and Development Center, Coastal and Hydraulics Laboratory, 3909 Halls Ferry Road,
Vicksburg, MS 39180-6199, USA
Received 23 April 2003; received in revised form 29 June 2004; accepted 16 July 2004
Available online 7 October 2004
A new parameter representing the maximum depth-integrated wave momentum flux occurring over a wave length is
proposed for characterizing the wave contribution to nearshore coastal processes on beaches and at coastal structures. This
parameter has units of force per unit crest width, and it characterizes flow kinematics in nonbreaking waves at a given depth
better than other wave parameters that do not distinguish increased wave nonlinearity. The wave momentum flux parameter can
be defined and estimated for periodic and nonperiodic (transient) waves. Thus, it has potential application for correlating to
processes responding to different types of waves. This paper derives the wave momentum flux parameter for linear, extended
linear, and solitary waves; and it presents an empirical formula estimating the parameter for nonlinear steady waves of
permanent form. Guidance is suggested for application to irregular waves. It is anticipated that the wave momentum flux
parameter may prove useful for developing improved semiempirical formulas to describe nearshore processes and wave/
structure interactions such as wave runup, overtopping, reflection, transmission, and armor stability. Surf zone processes where
waves break as plunging or spilling breakers may not benefit from use of the wave momentum flux parameter because the
breaking processes effectively negates the advantage of characterizing the wave nonlinearity.
D 2004 Elsevier B.V. All rights reserved.
Keywords: Coastal structures; Iribarren number; Nonlinear waves; Solitary waves; Wave forces; Wave momentum flux; Wave parameters
criteria associated with the specified design wave.
For example, a rubble-mound breakwater design
Coastal shore protection and navigation struc-
must assure armor stability; and there may be
tures are designed to withstand waves up to an
specified values for maximum wave runup, allow-
expected level (sometimes referred to as the bdesign
able average rate of wave overtopping, and max-
waveQ), and there are often multiple structure design
imum height of transmitted waves. These design
criteria are dependent on project functional require-
ments, so specified criteria may vary between
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0378-3839/$ - see front matter D 2004 Elsevier B.V. All rights reserved.