COMBINED CURRENT/WAVE SHEAR STRESS

Technical Note DOER-N1

April 1998

COMBINED CURRENT/WAVE SHEAR STRESS

The method incorporated into LTFATE to estimate bottom stresses due to combined current and

wave action (τbm in Equation 1) is described in this section. Large water bodies such as lakes, oceans,

and estuaries are subject to both current velocities and wave-generated orbital velocities. As a result,

the bottom shear stress will depend on the relative magnitude of both velocities and the angle

between them. In general, the bottom shear stress is assumed to follow a quadratic law:

ρ f c u2

τcb =

(2)

where τcb is the near-bottom shear stress due to currents (lbf/ft2), ρ is the density of water, fc is the

current-related friction factor, and u is the current velocity outside the boundary layer. For pure

currents, fc ranges from 0.002-0.005, depending upon the bed roughness. If waves are present, a

similar equation for the wave-related shear stress τwb is assumed:

ρ fw U 2

τwb

(3)

where U is the near-bottom orbital velocity for the wave and fw is the wave-related friction factor.

The coefficient fw ranges from 0.002-0.05, depending on U and the wave period Ts.

Often, for simplicity, these two effects are simply added together. As will be described later, this

will produce a shear stress that is too low, often by a factor of two or more.

The physical problem is described by Grant and Madsen (1979). Summarizing the main points of

the wave-current interaction, the near-bottom flow is influenced by the relatively low-frequency

currents and high-frequency surface waves. The bottom boundary layer is assumed to consist of an

oscillatory wave boundary layer nested within a relatively steady current boundary layer. When the

maximum bottom orbital velocities of the waves are of the same order as the steady current

velocities, the small scale of the wave boundary layer causes the boundary shear stress that would

be associated with the wave to be much greater than that associated with the current alone. The

wave and current interact to generate a shear stress that is different from that generated by the sum

of the two components. This interaction is a nonlinear process and numerous assumptions are

necessary to derive it.

The process discussed here relies upon the same basic physical description as that provided by

Grant and Madsen (1979) but is somewhat simpler in its description of bottom shear stress. Bottom

shear stresses are predicted using a method developed by Christoffersen and Jonsson (1985),

referred to hereafter as CJ. Shear stresses predicted by the CJ model compare well with experimental

data.