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June 2017
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10 Reads
Correlation between different Reynolds numbers. The swimming–speed Reynolds number Re vs. Relat (⚫; blue), Relat,L (♦; purple), and Rewave (◼; red) for the swimmers considered in [4], along with the lines of best fit. The best fit lines are given by log Re = 1.803 + 1.340log Relat, log Re = −0.4058 + 1.2306log Relat,L, and log Re = −1.450 + 1.083log Rewave. (EPS)
June 2017
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14 Reads
Supporting appendix. Section 1 shows the correlation between swimming–speed, wave–speed, and lateral Reynolds numbers. Section 2 discusses the nondimensionalization of the axial force simulation data included in Figs 5–9. Section 3 describes how to quantify the mechanisms underlying the OSW result. (PDF)
June 2017
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8 Reads
Qualitative analysis of the velocity mechanism. Mid–sheet (z = −0.05 cm) contours of axial fluid velocity for a stationary sheet simulation for various snapshots in time. Black dots represent the Lagrangian points of the undulating body. The plate has L = 1.0 cm, h = 0.1 cm, f = 3 Hz, a = 0.05 cm with (a) & (b) SW = 13.33, (c) & (d) SW = 10, (e) & (f) SW = 5. (EPS)
June 2017
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7 Reads
Dimensionless axial force data from Fig 6. Dimensionless axial propulsive force F^ generated by a stationary undulating sheet plotted against specific wavelength. In both cases (a) & (b), plate length was varied. These data represent cases where Relat = 3.37 × 102. Data are available in S2 Data. (EPS)
June 2017
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12 Reads
Dimensionless axial force data from Fig 7. Dimensionless axial propulsive force F^ vs. specific wavelength for additional small–sheet simulations in which (a) frequency and (b) amplitude were varied. These data represent cases where (a) 2.53 ≤ Relat ≤ 10.11 and (b) 0.28 ≤ Relat ≤ 10.16. Data are available in S2 Data. (EPS)
June 2017
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7 Reads
Observational and robotic data plotted in Figs 1–3. (XLS)
June 2017
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8 Reads
Momentum transfer by an undulatory swimmer. At the front of the swimmer, the body sucks stationary fluid with negligible momentum min and accelerates it downstream. This ejected fluid is often manifested as a wake with momentum mwake∼ℳwave(λf). Finally, this wake eventually dissipates further downstream as it loses momentum. (TIFF)
June 2017
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8 Reads
Dimensionless axial force data from Fig 9. Dimensionless axial propulsive force F^ generated by a stationary undulating sheet with prescribed anguilliform (▲) and carangiform (⚫) amplitude profiles plotted against specific wavelength. These data represent cases where Relat = 4.49. Data are available in S2 Data. (EPS)
June 2017
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7 Reads
Dimensionless axial force data from Fig 5. Dimensionless axial propulsive force F^ generated by a stationary undulating sheet plotted against specific wavelength. In both cases (a) & (b), plate span was varied. These data represent cases where (a) Relat = 8.43 × 10−1 and (b) Relat = 4.49. (EPS)
June 2017
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384 Reads
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32 Citations
What wavelengths do undulatory swimmers use during propulsion? In this work we find that a wide range of body/caudal fin (BCF) swimmers, from larval zebrafish and herring to fully–grown eels, use specific wavelength (ratio of wavelength to tail amplitude of undulation) values that fall within a relatively narrow range. The possible emergence of this constraint is interrogated using numerical simulations of fluid–structure interaction. Based on these, it was found that there is an optimal specific wavelength (OSW) that maximizes the swimming speed and thrust generated by an undulatory swimmer. The observed values of specific wavelength for BCF animals are relatively close to this OSW. The mechanisms underlying the maximum propulsive thrust for BCF swimmers are quantified and are found to be consistent with the mechanisms hypothesized in prior work. The adherence to an optimal value of specific wavelength in most natural hydrodynamic propulsors gives rise to empirical design criteria for man–made propulsors.
... Since its introduction, the IB method has emerged as a powerful tool for modeling biological FSI problems, with applications spanning from animal locomotion [4][5][6][7][8][9][10][11] to cardiac mechanics. [12][13][14][15][16][17][18] Because the IB method discretizes the structural and Eulerian degrees of freedom separately, it avoids the difficulties of grid generation associated with body-fitted approaches. ...
June 2017
![Variability in SW and OSW as a function of Relat and AR
Intraspecies mean specific wavelength vs. (a) lateral Reynolds number, (b) aspect ratio for observed non-anguilliform(⚫) and anguilliform(▲) swimmers. Of these, orange (green) points represent swimmers with (without) well–defined caudal fins. Red crosses (×) represent the optimal specific wavelength for simulations done in the present study. Blue asterisks (*) represent the optimal specific wavelengths for robotic undulating sheets reported in [11, 12]. Error bars indicate ± one s.d. from the species mean. For some species, the error bars are not visible at this scale, while for others, only one observation is recorded and no error bars are available; see Table 1 for more details. Data are available in S1 Data and Table 1.](https://www.researchgate.net/publication/318381552/figure/fig3/AS:11431281257856780@1719900408728/Variability-in-SW-and-OSW-as-a-function-of-Relat-and-AR-Intraspecies-mean-specific_Q320.jpg)
