Drag force acting on a neuromast in the fish lateral line trunk canal. I. Numerical modelling of external–internal flow coupling by Charlotte Barbier, and Joseph A.C. Humphrey Interface Volume 6(36): July 6, 2009 ©2009 by The Royal Society

Schematics of a typical LLTC on the side of a fish and of the motion-sensing neuromast between a pair of pores inside the canal. Charlotte Barbier, and Joseph A.C. Humphrey J. R. Soc. Interface 2009;6: ©2009 by The Royal Society

Plan view profiles (shown to scale) for the elongated (a) prism and (b) the pikeperch used in the external flow calculations. Charlotte Barbier, and Joseph A.C. Humphrey J. R. Soc. Interface 2009;6: ©2009 by The Royal Society

Calculation domain and boundary conditions for the two-dimensional external flow field generated by an elongated prism and a fish fixed in a flow of water moving at speed U=3 cm s−1. Charlotte Barbier, and Joseph A.C. Humphrey J. R. Soc. Interface 2009;6: ©2009 by The Royal Society

Field values of (a) instantaneous vorticity, Ωz (s−1), and (b) pressure, Pinst−Pmean (Pa), for the two-dimensional external flow past a prism–fish pair. Charlotte Barbier, and Joseph A.C. Humphrey J. R. Soc. Interface 2009;6: ©2009 by The Royal Society

Comparison between two-dimensional numerical (solid curves) and wave model (triangles) calculations of the relative pressure P−P∞ (Pa) for three consecutive pores (n−1, n and n+1) located approximately one-quarter of the way along the length of the side sur... Charlotte Barbier, and Joseph A.C. Humphrey J. R. Soc. Interface 2009;6: ©2009 by The Royal Society

Geometrical layout for the numerical calculations inside a two-dimensional segment of the fish LLTC. Calculations were performed for (a) three pores and (b) five pores labelled Li. The neuromasts, labelled Ni, are approximated as rectangles. Charlotte Barbier, and Joseph A.C. Humphrey J. R. Soc. Interface 2009;6: ©2009 by The Royal Society

(a) Contours of instantaneous velocity magnitude, Vmag (m s−1), for a segment of the fish LLTC with three and five pores. Charlotte Barbier, and Joseph A.C. Humphrey J. R. Soc. Interface 2009;6: ©2009 by The Royal Society

(a) Contours of instantaneous pressure (Pa) and (b) pressure profiles plotted as a function of y at two locations ‘a’ (red line) and ‘b’ (blue line) near pore L3. Charlotte Barbier, and Joseph A.C. Humphrey J. R. Soc. Interface 2009;6: ©2009 by The Royal Society

Drag force per unit length (μN m−1) acting on neuromasts (a) N2 and (b) N3 in a two-dimensional segment of the fish LLTC with three (solid curve) and five pores (dashed curve), respectively. Charlotte Barbier, and Joseph A.C. Humphrey J. R. Soc. Interface 2009;6: ©2009 by The Royal Society

Drag force per unit length (μN m−1) acting on neuromasts N2 (red), N3 (orange), N4 (green) and N5 (blue) in a two-dimensional segment of the fish LLTC with five pores. Charlotte Barbier, and Joseph A.C. Humphrey J. R. Soc. Interface 2009;6: ©2009 by The Royal Society

Cyclic variation of the total absolute drag force acting on a neuromast for different flow oscillation frequencies for the three-dimensional model of the flow in the fish LLTC segment. Charlotte Barbier, and Joseph A.C. Humphrey J. R. Soc. Interface 2009;6: ©2009 by The Royal Society

Cyclic variation of the average velocity (left ordinate) in the middle of the three-dimensional model of the fish LLTC segment with a neuromast present, and the pressure gradient (right ordinate) applied at the ends of the canal segment for different flow o... Charlotte Barbier, and Joseph A.C. Humphrey J. R. Soc. Interface 2009;6: ©2009 by The Royal Society

Definition of the phase shift, Φ, between the pressure gradient (dashed curve) applied at the ends of the LLTC segment and the drag force (solid curve) experienced by the neuromast. Charlotte Barbier, and Joseph A.C. Humphrey J. R. Soc. Interface 2009;6: ©2009 by The Royal Society

(a) Drag force amplitude and (b) the corresponding phase lag for the oscillating flow past a neuromast in the canal segment at different frequencies. Charlotte Barbier, and Joseph A.C. Humphrey J. R. Soc. Interface 2009;6: ©2009 by The Royal Society

Instantaneous velocity profiles for the flow around the neuromast in the vertical mid-plane of the fish LLTC at t/Tper=5 with f=5 Hz. Charlotte Barbier, and Joseph A.C. Humphrey J. R. Soc. Interface 2009;6: ©2009 by The Royal Society

(a) Instantaneous pressure contours with selected streamlines superimposed for the flow around the neuromast in the vertical mid-plane of the fish LLTC. (b) Pressure profile at y=200 μm (dashed line in (a)) and t/Tper=5 with f=5 Hz. Charlotte Barbier, and Joseph A.C. Humphrey J. R. Soc. Interface 2009;6: ©2009 by The Royal Society

(a) Time variation of the pressure gradient applied along the fish LLTC segment with WN superimposed. Charlotte Barbier, and Joseph A.C. Humphrey J. R. Soc. Interface 2009;6: ©2009 by The Royal Society

Power spectrum of the drag force acting on the neuromast in the presence of WN superimposed on a 5 Hz flow oscillation frequency. Charlotte Barbier, and Joseph A.C. Humphrey J. R. Soc. Interface 2009;6: ©2009 by The Royal Society

The x-coordinate locations at which the mean and r.m.s. velocity profiles in figures 20 and 21 are plotted. Charlotte Barbier, and Joseph A.C. Humphrey J. R. Soc. Interface 2009;6: ©2009 by The Royal Society

Transverse (y-directed) profiles of the mean streamwise (x-directed) component of velocity plotted for two grid refinements (a) 228×202 and (b) 332×202 at x-coordinate locations A (solid line), B (dashed line) and C (dotted line) shown in figure 19. Charlotte Barbier, and Joseph A.C. Humphrey J. R. Soc. Interface 2009;6: ©2009 by The Royal Society

Transverse (y-directed) profiles of the r.m.s. streamwise (x-directed) component of velocity plotted for two grid refinements (a) 228×202 and (b) 332×202 at x-locations A (solid line), B (dashed line) and C (dotted line) shown in figure 19. Charlotte Barbier, and Joseph A.C. Humphrey J. R. Soc. Interface 2009;6: ©2009 by The Royal Society

Comparison at t=1 s between calculated (squares) and analytical (solid line) profiles of the longitudinal (streamwise) velocity component for a fluid oscillating in a tube at 0.7 Hz. Charlotte Barbier, and Joseph A.C. Humphrey J. R. Soc. Interface 2009;6: ©2009 by The Royal Society

Grid comparison of calculated viscous, pressure and total drag forces acting on a neuromast of dimensions 150 μm×150 μm×150 μm for the flow in the LLTC oscillating at 150 Hz. Charlotte Barbier, and Joseph A.C. Humphrey J. R. Soc. Interface 2009;6: ©2009 by The Royal Society