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First published online August 31, 2004
Journal of Experimental Biology 207, 3569-3580 (2004)
Published by The Company of Biologists 2004
doi: 10.1242/jeb.01202
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Models of hydrodynamic flow in the bowhead whale filter feeding apparatus

Alexander J. Werth

Department of Biology, Hampden-Sydney College, Hampden-Sydney, VA 23943, USA



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Fig. 1. Morphology of balaenid head. Schematic lateral views showing the narrow, arched rostrum and huge, scoop-shaped, lower jaw with mouth closed (A) and open, in feeding position, with abducted lips (B). (A) When the mouth closes the baleen folds back, the lip overlaps the upper jaw, and the central furrow of tongue (light broken lines) contacts the palate. Heavy broken lines indicate the orolabial sulcus between tongue and lip; the dotted line denotes oropharynx and esophageal orifice. (B) In the less streamlined open-gape feeding profile, note the large lower lip above the mandible (broken line) and the overlapping extent of the freely suspended baleen rack (dotted line), with the shortest plates at rear. The arrow indicates where filtered water exits posterior to the lip after passing along the gutter-like orolabial sulcus.

 


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Fig. 2. Anterior (A) and lateral (B) views of 1/15 scale model of bowhead mouth photographed in the flow chamber before videotaping. Compare to other figures for descriptions of morphology.

 


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Fig. 3. Schematic diagrams showing landmarks for measurements of the bowhead mouth's anterior and posterior openings (AO and PO, respectively) used in constructing mathematical and physical models. (A) Transverse section at front of oral cavity shows the relationships of tongue, lips and baleen, and the locations of anterior vertical (dorsoventral; AV) and horizontal (frontal plane; AH) dimensions. Specific demarcations of all measures defined in text and in Table 1. (B) Lateral view at rear of mouth, showing locations of posterior vertical and horizontal (PV, PH, respectively) dimensions where filtered water exits this unidirectional flow system; compare to Fig. 1 for a wider view.

 


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Fig. 4. Diagrammatic frontal section through the balaenid oral cavity for the model of continuous ram filtration powered by forward locomotion, showing the relationships of tongue, lips and baleen, and the flow of water-borne prey through the mouth: inward through the anterior subrostral gap between baleen racks, rearward to the center of mouth, and outward through the fringed medial side of baleen (filtration step) into the gutter-like channel inside lip (orolabial sulcus). Areas of mouth's anterior and posterior (paired) openings (AO and PO, respectively; see Fig. 2) are used in modeling. Incurrent/excurrent flow through AO and PO are shown by open arrows.

 


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Fig. 5. Elementary fluid dynamics serves as the basis for mathematical and physical modeling. If volume flow rate holds constant as the diameter (and hence cross-sectional area) of the flow pipe decreases, flow velocity increases and pressure decreases. (A) Venturi manometer showing pressure drop as flow speed increases through the constriction in the pipe. (B) Flow tank data from 1/15 scale physical model showing changes in flow rate (recorded via videotape) as water moves from the upstream current through the anterior opening (AO) and out via the posterior opening (PO), plus pressures (recorded via transducers) at front and back of the oral cavity, showing a drop of 501 Pa (3.76 mmHg). Values are means ± S.E.M.

 


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Fig. 6. Data (from Table 2) showing results of fluid mathematical modeling for whales of varying body length foraging at speeds of 4 km h–1 (solid symbols) or 6 km h–1 (open symbols). Pressure differential values were derived from four equations: Bernoulli (circle), two formulations of Hagen–Poiseuille (triangle, square) and Navier–Stokes (diamond). Calculations for Lb=5 m are not included here, as these were based on extrapolated morphometric data. For comparison, there was a mean 500 Pa pressure drop, measured via transducer, in the flow tank testing of the 1/15 scale physical model (33 cm head length; equivalent of Lb ~1 m).

 





© The Company of Biologists Ltd 2004