A Bio-Energetic Model for North Atlantic Right Whales: Locomotion, Anatomy and Diving Behavior

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1 A Bio-Energetic Model for North Atlantic Right Whales: Locomotion, Anatomy and Diving Behavior Douglas P. Nowacek Department of Oceanography Florida State University 117 N. Woodward Ave. Tallahassee, FL phone: (850) fax: (850) Award Number: N LONG-TERM GOALS To investigate the energetics of locomotion in North Atlantic right whales, Eubalaena glacialis To explore the effect(s) of the right whale filter feeding mechanism on locomotion energetics To investigate the contribution of adaptations, behavioral or anatomical, specific to locomotion (e.g., fluke aspect ratio) To calculate lift and drag for various surfaces and overall for the whole whale OBJECTIVES The goal of our research is to investigate the physical forces that right whales (Eubalaena glacialis) experience in their marine environment and understand how the ecology of right whales is adapted to deal with them. Locomotion in a marine environment involves drag, lift and buoyant forces, and we plan to estimate these for North Atlantic right whales (NARW) using two primary methods. APPROACH Due to their large size and marine environment, indirect methods will be used to estimate the forces involved in locomotion. We have developed various three-dimensional geometries that represent various swimming positions used by right whales and will investigate the forces incurred with a numerical simulation of the flow of water around the animal. In addition to calculating forces from a numerical simulation, we will estimate some of these forces from the behavior and movement of free-ranging right whales. A digital recording tag was attached temporarily to right whales, and their three-dimensional orientation was recorded continuously for a variety of durations. From records, we have identified distinctive behaviors and identified temporal and demographic patterns in their usage. These data will also allow us to make predictions about the energetic costs and consequences of various behaviors, e.g., migratory deviations. 1

2 WORK COMPLETED 1. New static three-dimensional geometries have been created by making minor modifications to the original whale geometry: (1) a whale with its flukes in the point of maximum upward excursion of the fluke stroke, (2) a whale with its flukes in the maximum downward excursion of the fluke stroke, (3) a whale with its pectoral flippers flush against its body, (4) a whale with its flippers extended partially, and (5) a whale with no pectoral flippers. 2. Numerical simulations of early geometries were completed, producing pressure and velocity distributions around the whale. 3. Further analysis of the morphometrics of live whales was completed. Fluke aspect ratio was measured from photographs in the North Atlantic Right Whale Consortium database, and inter- and intra-individual variations in aspect ratio were quantified. 4. An open-mouthed whale geometry that includes internal mouth features such as baleen plates, lips and tongue is being developed to measure the changes in drag present when animals are feeding. 5. Effects of body condition on diving manuscript reaching completion 6. Dive classification manuscript reaching completion RESULTS 1. Model whales: A total of 7 static model whales have been completed and transformed for numerical flow simulation (see figures 1-5). Now that the gross morphology of the model has been completed it is possible to make relatively minor adjustments in-house. Although they are minor from a mesh modeling perspective, they may have important consequences for fluid dynamics. Examples of such changes are making the pectoral flippers flush to the body, and changing the fluke span and area. It should also be possible to make further refinements to existing models as knowledge of the morphology of E. glacialis is improved. 2. Numerical simulations: Computational fluid dynamics allows us to estimate the flow around an entire right whale and has the additional advantage that we can make modifications to a basic whale shape to understand the effect of changes in shape and orientation on flow. The chosen simulation uses a coupled level set/volume-of-fluid method to estimate incompressible flow (Sussman 2005), and we have created a number of whale geometries to use in the simulation. Two of these geometries, the neutral whale and the tail-up whale, have been used in the simulation code. Pressure contours have been plotted on the surface, and the velocity distribution around the animal can be visualized in Amira software (Figures 6 12). Qualitative observations about the flow around these geometries are already possible. For both geometries, areas of high pressure were found at the tip of the rostrum, where the whale encounters unaltered flow, and on the leading edge of the pectoral fins and flukes. The raised tail geometry had an area of raised pressure on the leading edge of the tail stock and on the trailing edge of the flukes, both which were not present for the neutral geometry (Figs. 6-8). The influence of these differences on drag and lift has yet to be determined. Counter to Werth s (2004) hypothesis that low pressure at the back of the animal s mouth helps to draw water and prey through the oral cavity, these models showed that lower pressure areas are found at the sides of the mouth (along the lip edges) instead of at the back of the mouth (Fig. 7). This flow pattern may change when the animal opens its 2

3 mouth to feed, but since the curvature of the animal s head should remain approximately the same, these pressure distributions may still exist. An open-mouthed geometry for CFD simulation is necessary to test Werth s (2004) hypothesis. Velocity profiles taken in different planes and locations along the animal also demonstrate differences in flow around the animal for these two positions. For both geometries, vortices can be observed detaching from the end of the pectoral fins (Fig. 9). With its flukes raised, the whale generates a counter-clockwise vortex below the peduncle that is not evident in the neutral position (Fig. 10). Vertical profiles of the flowfield show that this vortex is formed from two vortices counter-rotating around the midline axis of the animal, while the neutral position creates a single vortex traveling along the midline axis of the animal (Figs ). These vortices continue along the animal, traveling vertically away from the body in the neutral position and horizontally from the body in the tail-up position. Quantitative measurements of the amount and type of drag will be possible with further analysis and more insights on how these forces change with different behaviors is possible once more of our geometries are tested in the simulation. 3. Open mouthed model: Right whales feed by swimming through patches of prey with open mouths. Large baleen plates cover the sides of their mouths and filter prey from the water flowing through these structures. This feeding method is predicted to increase the amount of drag experienced by whales when feeding in comparison to whales swimming with a closed mouth. Consequently, the amount of thrust that must be generated by the animal must increase if it is to maintain forward speed. Foraging basking sharks have been shown to swim more slowly than non-foraging sharks (Sims 2000), a possible consequence of increased drag while feeding. The difference in horizontal distance covered by feeding and non-feeding right whales seems to follow a similar pattern (McGregor et al., in prep.). However, the mouth morphology of bowhead whales (Balaena mysticetus) may reduce such changes in drag by creating a Venturi effect (Werth 2004). CFD simulations of the flow through a right whale open mouth will allow us to estimate if filter-feeding does increase drag. Observations of the size and shape of internal mouth parts relative to each other were made from photographs taken during the necropsy of a dead whale in 2005, and we have constructed an initial open-mouth model (Figure 13) though it is truly a work in progress as we have yet to attach the baleen plates. Additionally, published measurements of these structures in dead bowhead whales were used to visualize the position of various mouth features (Lambertsen et al. 2005; Werth 2004). 4. Additional morphometric analysis: The aspect ratio of tail flukes was measured using aerial photographs from the NARW consortium database. Images that were as perpendicular to the plane of the flukes as possible were selected, often with multiple images per individual. As these photographs were taken using hand held cameras during surveys for indentification purposes it was not possible to measure absolute biometrics, as was previously done with aerial photogrammetric images. However, these digital images could be measured on a computer screen using Universal Desktop Ruler software, which counts the number of pixels in a given distance or area. Thus, the fluke span (fluke tip to fluke tip) and fluke planar area were measured in pixels. The aspect ratio was then calculated as: AR = span 2 / planar area (Woodward et al. 2006) The sample obtained had a high variance within each individual sampled. The overall mean aspect ratio of 5.07 (± 0.07) was lower than the previously published value of 6.31 (Woodward et al. 2006), which was close to the maximum value measured from photographs (6.38). The reasons for this discrepancy are still being investigated. However, it may be valuable to produce two static and/or 3

4 animated models with fluke aspect ratios at the extremes of these values to determine whether this has a significant effect on important flow characteristics. Woodward et al (2006) commented that the high value that their study found for E. glacialis was in contradiction to the slow swimming speed typical of this species. However, they hypothesized that this may be because the ram feeding technique that is used by balaenids may require a more efficient propulsor to overcome increased drag. Thus our finding that right whales may have a lower aspect ratio than measured by Woodward et al (2006) may mean that drag during open mouth feeding may be lower than expected, as hypothesized by Werth (2004). 5. Body condition effects: Blubber is an efficient source of energy storage for right whales, but these whales also use the positive buoyancy of these stores to passively ascend from their dives (Nowacek et al. 2001). Significant changes based on reproductive state and sex were observed in the thickness of the blubber layer of individual right whales (Angell 2006; Moore et al. 2001), but the influence of these changes in body condition on positive buoyancy have not been investigated. We are preparing a manuscript with our collaborators that compares blubber thickness with dive behavior and then also uses the duration of ascent glides to infer differences in buoyancy and the thickness of the blubber layer in animals not directly measured, to assess body condition. Animals with thinner blubber layers had shorter ascent glides, indicating that there is a relationship between body condition and positive buoyancy. Right whales must trade-off the energetic savings from passive locomotion for the ability to mobilize their blubber stores when food is unavailable. 6. Dive classification: This manuscript relates distinctive dive types that appear in the time-depth profiles with the behaviors that produced them and quantified the characteristic features that distinguish different dive types. The influence of key aspects of the animal s ecology on diving behavior is discussed. IMPACT/APPLICATIONS The impacts of this work will primarily be in furthering our understanding of: i) cetacean locomotion; ii) the use of CFD models to investigate fluid dynamics of animals that are too large to study in a controlled environment; iii) the energy required by a whale to swim and to feed while swimming this result will be important for understanding some anthropogenic impacts on cetaceans (e.g., avoidance of an area due to noise). RELATED PROJECTS We are conducting several related projects that will continue to inform the present ONR project: 1. Obtain accurate measurements of density of non-blubber tissues and of internal mouth features from a dead whale. The influence that variations in blubber amounts have on a right whale can not be determined by measuring the buoyancy of blubber alone. Other tissues such as bone, muscle and tongue will affect the extent to which the buoyant force of blubber affects the entire animal. 2. Develop quantitative predictions of drag and lift to compare results of numerical simulations between whale geometries. Drag and lift measurements derived from numerical flow solutions can be reduced in accuracy by several aspects of the specific simulation, and methods such as wake integration may reduce these inaccuracies (Giles and Cummings 1999; Hunt et al. 1999). Further investigation of these methods and their compatibility with our numerical model will be completed to obtain drag and lift measurements for our whale geometries. Additionally, predicting drag with these 4

5 methods allows the relative contributions of different types of drag (induced drag, profile drag) to be assessed. 3. Animate whale geometry and run through numerical simulation to investigate how drag and lift change throughout swimming motion. Because the cetacean swimming motion incorporates the entire body into thrust generation, the relationship between movements of each body part must be modeled to create an accurate swimming motion. High-speed video of a bottlenose dolphin swimming in captivity will be used to model the sinusoidal motion of a cetacean body and the cambering of the flukes (Fish et al. 2000; Fish et al. 2006). Measuring the phase difference between key points on the dolphin s body and then scaling the difference to the size of a right whale will allow a rough approximation of cetacean movements. 4. Analyze blubber samples obtained from dead whales to determine the buoyancy of blubber. Lipids are used by these whales to provide energy during migration, and whales have been shown to undergo significant seasonal changes in the thickness of their blubber layers related to their physiological energy usage (Angell 2006). Because right whales also appear to rely on their blubber stores for buoyancy (Nowacek et al. 2001), physiological changes in the amount of blubber an animal has may alter its buoyancy. Two frozen samples of blubber from the mid-dorsal region of stranded dead right whales were obtained from Michael Moore s lab at the Woods Hole Oceanographic Institution. The overall buoyant force of these samples will be measured by multiplying the gravitational acceleration constant by the difference in mass of their weights in air and water (Fish et al. 2002). Analysis of the fatty-acid content of these samples would reveal the specific gravity and therefore the buoyancy of lipid as well as non-lipid components of the blubber samples, we are working with other collaborators to conduct these chemical analyses. The buoyant force of these tissues will then be subtracted from the total buoyant forces to determine the contribution of the lipids to buoyancy. REFERENCES Angell, C.M Body fat condition of free-ranging right whales, Eubalaena glacialis and Eubalaena australis. PhD thesis, Department, Boston University, Boston. Cheer, A.Y., Ogami, Y. and Sanderson, S.L Computational fluid dynamics in the oral cavity of ran suspension-feeding fishes. J. Theor. Biol. 10: Fish, F.E., Peacock, J.E. and Rohr, J.J Phase relationships between body components of odontocete cetaceans in relation to stability and propulsive mechanisms. In First International Symposium on Aqua Bio-mechanisms, University of the Pacific Center. Honolulu, HI, pp Fish, F.E., Smelstoys, J., Baudinette, R.V. and Reynolds, P.S Fur does not fly, it floats: buoyancy of pelage in semi-aquatic mammals. Aquat. Mamm. 28(2): Fish, F.E., Nusbaum, M.K., Beneski, J.T. and Ketten, D Passive cambering and flexible propulsors: cetacean flukes. Bioinspiration & Biomimetics 1: S42-S48. Giles, M.B. and Cummings, R.M Wake integrations for three-dimensional flowfield computations: theoretical development. Journal of Aircraft 36(2): Hunt, D.L., Cummings, R.M. and Giles, M.B Wake integration for three-dimensional flowfield computations: Applications. Journal of Aircraft 36(2): Lambertsen, R.H., Rasmussen, K.J., Lancaster, W.C. and Hintz, R.J Functional morphology of the mouth of the bowhead whale and its implications for conservation. J. Mammal. 86(2): Moore, M.J., Miller, C.A., Morss, M.S., Arthur, R., Lange, W., Prada, K.G., Marx, M.K. and Frey, E.A Ultrasonic measurements of blubber thickness in right whales. J. Cetacean Res. Manage. Spec. Issue 2:

6 Nowacek, D.P., Johnson, M.P., Tyack, P.L., Shorter, K.A., McLellan, W.A. and Pabst, D.A Buoyant balaenids: the ups and downs of buoyancy in right whales. Proc. R. Soc. Lond. B 268: Sims, D.W Filter-feeding and cruising swimming speeds of basking sharks compared with optimal models: they filter-feed slower than predicted for their size. J. Exp. Mar. Biol. Ecol. 249(1): Sussman, M A parallelized, adaptive algorithm for multiphase flows in general geometries. Computers and Structures 83: Werth, A.J Models of hydrodynamic flow in the bowhead whale filter feeding apparatus. J. Exp. Biol. 207: Woodward, B.L., Winn, J.P. and Fish, F.E Morphological specializations of baleen whales associated with hydrodynamic performance and ecological niche. J. Morphol. 267: PUBLICATIONS Hogg, C. Barton, K., Shorter, K.A., Miller, P.J.O., Nowacek, D.P., and Rogers, T. Determination of steroid hormones in whale blow: is it feasible? Marine Mammal Science [in press, refereed] Tyson, R.B., Nowacek, D.P., Miller, P.J.O. Nonlinear phenomena in the vocalizations of North Atlantic right whales (Eubalaena glacialis) and killer whales (Orcinus orca). Journal of the Acoustical Society of America 122(3): [published, refereed] Parks, S.E., Nowacek, D.P., Johnson, M.P., and Tyack, P.L. Right whales Social sounds. Journal of the Acoustical Society of America 119(5), pt. 2: [published, refereed] 6

7 FIGURES Figure 1. Static 3-D right whale model with the tail flukes in the maximum upwards displacement. Figure 2. Static 3-D whale model with the tail flukes in the maximum downwards displacement. 7

8 Figure 3. Static 3-D whale model with the pectoral flippers half way between flush (see model below) and the position in the original model Figure 4. Static 3-D whale model with the pectoral flippers flush against the body. 8

Dorsal view of pressure distributions from the results of a CFD simulation on

9 Figure 5. Static 3-D whale model with the pectoral flippers completely removed. Figure 6. Dorsal view of pressure distributions from the results of a CFD simulation on two whale geometries heading into the flow. Areas of higher pressure are shown in red-yellow and areas of lower pressure are shown in green-blue. 9

10 Figure 7. Lateral view of pressure distributions for two whale geometries. Areas of higher pressure are shown in red-yellow and areas of lower pressure are shown in green-blue. 10

11 Figure 8. Ventral view of pressure distributions for two whale geometries. Areas of higher pressure are shown in red-yellow and areas of lower pressure are shown in green-blue. 11

12 Figure 9. Vertical velocity profile taken from the results of a CFD simulation and viewed from the anterior end of the body for a single right whale geometry. This profile was taken from just behind the pectoral fins. Red and yellow show regions of highest velocity, while green and then blue show areas of reduced velocity. 12

13 Figure 10. Lateral velocity profile taken from the results of a CFD simulation of flow around two right whale geometries. Profiles were taken along the vertical midline of the animal. Red and yellow show regions of highest velocity, while green and then blue show areas of reduced velocity. 13

Figure 11. Vertical velocity profiles taken from the results of a CFD simulation and viewed from the posterior end of the animal for two right whale geometries.

14 Figure 11. Vertical velocity profiles taken from the results of a CFD simulation and viewed from the posterior end of the animal for two right whale geometries. Profiles were taken from approximately 70% of body length, where the tail stock begins to narrow. Red and yellow show regions of highest velocity, while green and then blue show areas of reduced velocity. 14

Figure 12. Vertical velocity profiles taken from the results of a CFD simulation and viewed from the posterior end of the animal for two right whale geometries.

15 Figure 12. Vertical velocity profiles taken from the results of a CFD simulation and viewed from the posterior end of the animal for two right whale geometries. Profiles were taken from approximately 85% of body length, just before where the fluke attach to the tailstock. Red and yellow show regions of highest velocity, while green and then blue show areas of reduced velocity. 15

16 Figure 13. Static 3-D model of a feeding right whale (incomplete). The lower jaw has been opened, and the tongue and internal mouth structures added. The baleen racks have yet to be added. 16

A Bio-Energetic Model for North Atlantic Right Whales: Locomotion, Anatomy and Diving Behavior

A Bio-Energetic Model for North Atlantic Right Whales: Locomotion, Anatomy and Diving Behavior Prof. Douglas Nowacek Duke University Marine Laboratory 135 Duke Marine Lab Road Beaufort, NC phone: (252)