450
14 Tides and Waves on Vegetated Coasts
maximum projected area of the object, and the coefficient 'Y expresses the
dependence of drag force on the relative flow velocity U r :
dx
U = u - -
r
dt'
(14.48)
where U is the velocity of the water, and the dx/dt is the velocity of the organism. From Gaylord et al. (1994) measurement follows that Sd ~ 0.041
and 'Y = 1.55 for kelp Eisenia and 0.042 and 1.23, respectively, for kelp Pterygophora.
Dubi and T0rum (1994) measured drag forces on stipes of Laminaria hyperporea in the Norwegian coastal waters by sharp towing, and in laboratory
using a shear plate on which 95 model kelp plants were fixed. The resulted drag
force showed a linear dependence on the current velocity instead of quadratic
dependence, which was expected, i.e.:
drag force ~ 9.33uc,
(14.49)
where U c is the current velocity.
Under wave conditions with the periods 11 < T < 14, the relationship between drag and maximum wave horizontal velocity u becomes:
drag force ~ 3u.
(14.50)
The second term on the right-hand side of Eq. (14.47) represents the contribution of inertia factor to the external force. Denny et al (1998) solved Eq. (14.42)
with right-hand side given by Eq. (14.47). Resulted stipe deflection becomes
non-linearly related to the applied force. Moreover, the maximum stress on
the stipe appears for the external forcing frequency, w, very close to the natural frequency, W n , i.e.: when w/wn ~ 1. The fact that inertia forces reach
the maximum values at certain frequencies provides some foundation for the
possibility that the structure of organisms can be tuned to avoid potentially
damaging loads.
More experimental data and theoretical results on dynamics of flexible marine
organisms can be found in papers of Carrington (1990), Gaylord et al. (1994),
Dubi and T0rum (1994), Friedland and Denny (1995), Bell (1996), Denny
and Gaylord (1996) and Utter and Denny (1996). In particular, Dubi and
T(2lrum (1994), unlike other studies, derived the model of the dynamics of kelp
in wave dominated environment when boundary conditions at sea surface are
present. This means that real vertical profile of wave-induced velocity is used
in calculations of stresses on kelp.
14 Tides and Waves on Vegetated Coasts
maximum projected area of the object, and the coefficient 'Y expresses the
dependence of drag force on the relative flow velocity U r :
dx
U = u - -
r
dt'
(14.48)
where U is the velocity of the water, and the dx/dt is the velocity of the organism. From Gaylord et al. (1994) measurement follows that Sd ~ 0.041
and 'Y = 1.55 for kelp Eisenia and 0.042 and 1.23, respectively, for kelp Pterygophora.
Dubi and T0rum (1994) measured drag forces on stipes of Laminaria hyperporea in the Norwegian coastal waters by sharp towing, and in laboratory
using a shear plate on which 95 model kelp plants were fixed. The resulted drag
force showed a linear dependence on the current velocity instead of quadratic
dependence, which was expected, i.e.:
drag force ~ 9.33uc,
(14.49)
where U c is the current velocity.
Under wave conditions with the periods 11 < T < 14, the relationship between drag and maximum wave horizontal velocity u becomes:
drag force ~ 3u.
(14.50)
The second term on the right-hand side of Eq. (14.47) represents the contribution of inertia factor to the external force. Denny et al (1998) solved Eq. (14.42)
with right-hand side given by Eq. (14.47). Resulted stipe deflection becomes
non-linearly related to the applied force. Moreover, the maximum stress on
the stipe appears for the external forcing frequency, w, very close to the natural frequency, W n , i.e.: when w/wn ~ 1. The fact that inertia forces reach
the maximum values at certain frequencies provides some foundation for the
possibility that the structure of organisms can be tuned to avoid potentially
damaging loads.
More experimental data and theoretical results on dynamics of flexible marine
organisms can be found in papers of Carrington (1990), Gaylord et al. (1994),
Dubi and T0rum (1994), Friedland and Denny (1995), Bell (1996), Denny
and Gaylord (1996) and Utter and Denny (1996). In particular, Dubi and
T(2lrum (1994), unlike other studies, derived the model of the dynamics of kelp
in wave dominated environment when boundary conditions at sea surface are
present. This means that real vertical profile of wave-induced velocity is used
in calculations of stresses on kelp.