## Drag Coefficients Reconfiguration and the Vogel Number

The decrease in the standard deviations of the drag coefficients as the velocity increased, as found in this study, was probably due to the multifactorial optimization of the seaweed blade with respect to physiological and mechanical boundary conditions [30]. The variability of blade shapes is high at low velocities, which are mechanically harmless. Under these conditions, the shape of a blade can be optimized with respect to other, nonmechanical requirements, e.g., light interception or nutrient uptake [31,32]. At higher velocities, the different shapes all reconfigure into streamlined bundles with similar overall shapes. This seems to be the case for seaweeds with highly variable morphotypes such as Durvillaea and also for a whole range of flexible seaweeds in general [33].

The Vogel numbers found for Durvillaea are similar to those reported from other studies on flexible seaweeds [11]. Because the mean was close to B = -1, an almost linear increase of drag with velocity can thus be explained. The least negative value

- Linear

Quadratic

FIGURE 3.15 Hypothetical drag forces, assuming a linear increase and a quadratic increase with velocity, respectively. For the individual represented in the graph, the reduction in drag due to streamlining and subsequent linear (rather than a quadratic) increase is about 52% at a velocity of 5 m s-1 and 75% at 10 m s-1. The experimental range is shaded in gray. F is the drag force, and u is the velocity of the fluid.

FIGURE 3.15 Hypothetical drag forces, assuming a linear increase and a quadratic increase with velocity, respectively. For the individual represented in the graph, the reduction in drag due to streamlining and subsequent linear (rather than a quadratic) increase is about 52% at a velocity of 5 m s-1 and 75% at 10 m s-1. The experimental range is shaded in gray. F is the drag force, and u is the velocity of the fluid.

was found for the same individual that was an outlier below the 95% CI in the correlation of drag and length (Figure 3.7). Reduced in bulkiness, the shape of the blade could hardly be further optimized, making it comparable to a rope. The most effective reconfiguration process and subsequent reduction in actual drag compared with the drag predicted by Equation 3.1 will be achieved for a limited range of aspect ratios. The most negative Vogel number was found for an individual with wave-exposed morphology and a very massive blade with no apparent damage, the second outlier above the 95% CI (Figure 3.7). This type of morphology seems to be the optimized morphology for reconfiguration under very unsteady, rapidly changing flow conditions.

Assuming a Vogel number of B = -1, the theoretical reduction in drag due to reconfiguration can be calculated. The result of this simple extrapolation can be seen in Figure 3.15. At a velocity of 5 m s-1, the reduction in drag due to reconfiguration is already about 50%. At a velocity of 10 m s-1 — common in stormy conditions at exposed sites — the reduction is even more than 75%. It is noteworthy that similar findings have been reported for terrestrial plants, e.g., the giant reed Arundo donax [22,34]. Reconfiguration is therefore an effective general process of plants for adapting on a small temporal scale to variable flow conditions, which does not require any further mechanical changes at the "material" level of the organism.

How can Durvillaea grow to a size an order of magnitude larger than other intertidal seaweeds at that position on the shore given that its biomechanical properties are rather typical for a large spectrum of seaweeds [35]. The answer may lie in the way Durvillaea grows. Unlike other members of the Fucales, Durvillaea lacks an apical meristem but has diffuse growth. This allows two mechanisms to interact. First, broken tips can regrow, regardless of previous damage. Second, a strip of a blade fractured longitudinally at its distal end can change its growth form. The tip of the crack will become blunt to avoid crack propagation [36]. The strip of blade will then have two termini, which will both be able to grow in length. The tip of the crack, however, remains a permanent point of separation of the two newly generated termini, forming two only loosely connected mechanical subunits that are differentially agitated by wave action. It is thus possible for Durvillaea to change its morphology as it grows, adapting to the ambient wave exposure. The potentially endangered large unit blade is divided into many smaller subunits, possibly reducing the physiological efficiency of the photosynthetically active area, but more importantly, reducing the risk of total blade loss. The indeterminate morphology of Durvillaea, therefore, seems to be a key factor for the successful establishment of this seaweed in the wave-swept intertidal environment.

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