Fluid dynamics of moving fish in a two-dimensional multiparticle collision dynamics model

Abstract

The fluid dynamics of animal locomotion, such as that of an undulating fish, are of great interest to both biologists and engineers. However, experimentally studying these fluid dynamics is difficult and time consuming. Model studies can be of great help because of their simpler and more detailed analysis. Their insights may guide empirical work. Particularly the recently introduced multiparticle collision dynamics method may be suitable for the study of moving organisms because it is computationally fast, simple to implement, and has a continuous representation of space. As regards the study of hydrodynamics of moving organisms, the method has only been applied at low Reynolds numbers (below 120) for soft, permeable bodies, and static fishlike shapes. In the present paper we use it to study the hydrodynamics of an undulating fish at Reynolds numbers 1100-1500, after confirming its performance for a moving insect wing at Reynolds number 75. We measure (1) drag, thrust, and lift forces, (2) swimming efficiency and spatial structure of the wake, and (3) distribution of forces along the fish body. We confirm the resemblance between the simulated undulating fish and empirical data. In contrast to theoretical predictions, our model shows that for steadily undulating fish, thrust is produced by the rear 2/3 of the body and that the slip ratio U/V (with U the forward swimming speed and V the rearward speed of the body wave) correlates negatively (instead of positively) with the actual Froude efficiency of swimming. Besides, we show that the common practice of modeling individuals while constraining their sideways acceleration causes them to resemble unconstrained fish with a higher tailbeat frequency.

Body dynamics and hydrodynamics of swimming fish larvae: a computational study

“…This position at the inflexion points of the body wave ensured that the force on the body due to the pressure differentials across the body had a substantial thrust component. Overall, the posterior body generated the highest force peaks and supplied most of the thrust, consistent with findings of other CFD models that evaluated pressure and shear stress in adult fish (Borazjani and Sotiropoulos, 2008;Reid et al, 2012).…”

“…Several studies varied tail beat frequency to compute wake topology over a range of Strouhal numbers from 0 to 1.3 for carangiform and anguilliform swimmers (Borazjani and Sotiropoulos, 2008;Borazjani and Sotiropoulos, 2009;Borazjani and Sotiropoulos, 2010;Reid et al, 2012). These studies predicted for both anguilliform and carangiform swimming that a double-row vortex street forms at high Strouhal numbers and a single-row vortex street forms at low Strouhal numbers; some of these studies tethered the fish (Borazjani and Sotiropoulos, 2008;Borazjani and Sotiropoulos, 2009) whereas others allowed one degree of freedom -swimming speed was not an input parameter to the model but was computed from the hydrodynamic forces generated by the fish (Borazjani and Sotiropoulos, 2010).…”

“…These studies predicted for both anguilliform and carangiform swimming that a double-row vortex street forms at high Strouhal numbers and a single-row vortex street forms at low Strouhal numbers; some of these studies tethered the fish (Borazjani and Sotiropoulos, 2008;Borazjani and Sotiropoulos, 2009) whereas others allowed one degree of freedom -swimming speed was not an input parameter to the model but was computed from the hydrodynamic forces generated by the fish (Borazjani and Sotiropoulos, 2010). So far, two free-swimming models have been developed that allow three degrees of freedom: a 2-D model (Reid et al, 2012) and a 3-D model (Kern and Koumoutsakos, 2006). These models both found similar relationships between wake shape and body wave kinematics.…”

The increased Efficiency of Fish Swimming in a School, a New Computational Model

“…METHODS AND RESULTS OF OUR EARLIER WORK ON SINGLE FISH [6] To represent the fluid we use a method that is new for fish schooling, namely a mesoscale particle-based simulation model, called Multi-Particle Collision Dynamics (MPCD). The model consists of a fluid of particles which move and collide, where the collisions conserve both mass and momentum.…”

“…In reality, however, fish swim in many configurations and hydrodynamic effects are complex. Since these hydrodynamic effects are difficult to study empirically, we here investigate them in a computer model by incorporating viscosity and interactions among wakes and with individuals [6,7].…”