Drag force acting on a neuromast in the fish lateral line trunk canal. I. Numerical modelling of external-internal flow coupling

Fishes use a complex, multi-branched. mechanoreceptive organ called the lateral line to detect the motion of water in their immediate surroundings. This study is concerned with a subset of that organ referred to as the lateral line trunk canal (LLTC). The LLTC consists of a long tube no more than a few millimetres in diameter embedded immediately under the skin of the fish on each side of its body. In most fishes, pore-like openings are regularly distributed along the LLTC, and a minute sensor enveloped in a gelatinous cupula, referred to as a neuromast, is located between each pair of pores. Drag forces resulting from fluid motions induced inside the LLTC by pressure fluctuations in the external flow stimulate the neuromasts. This study,Part I of a two-part sequence, investigates the motion-sensing characteristics of the LLTC and how it may be used by fishes to detect wakes. To this end, an idealized geometrical/dynamical situation is examined that retains the essential problem physics. A two-level numerical model is developed that couples the vortical How outside the LLTC to the How stimulating the neuromasts within it. First, using a Navier-Stokes solver, we calculate the unsteady flow past an elongated rectangular prism and a fish downstream of it, with both objects moving at the same speed. By construction. the prism generates a clean, periodic vortex street in its wake. Then, also rising the Navier-Stokes solver, the pressure field associated with this external flow is used to calculate the unsteady flow inside the LLTC of the fish, which creates the drag, forces acting on the neuromast cupula. Although idealized, this external-internal coupled flow model allows an investigation of the filtering properties and performance characteristics of the LLTC for a range of frequencies of biological interest. The results obtained here and in Part II show that the LLTC acts as a low-pass filter, preferentially damping high-frequency pressure gradient oscillations, and hence high-frequency accelerations, associated with the, external flow.