The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

Species distribution models (SDMs) use spatial environmental data to make inferences on species' range limits and habitat suitability. Conceptually, these models aim to determine and map components of a species' ecological niche through space and time, and they have become important tools in pure and applied ecology and evolutionary biology. Most approaches are correlative in that they statistically link spatial data to species distribution records. An alternative strategy is to explicitly incorporate the mechanistic links between the functional traits of organisms and their environments into SDMs. Here, we review how the principles of biophysical ecology can be used to link spatial data to the physiological responses and constraints of organisms. This provides a mechanistic view of the fundamental niche which can then be mapped to the landscape to infer range constraints. We show how physiologically based SDMs can be developed for different organisms in different environmental contexts. Mechanistic SDMs have different strengths and weaknesses to correlative approaches, and there are many exciting and unexplored prospects for integrating the two approaches. As physiological knowledge becomes better integrated into SDMs, we will make more robust predictions of range shifts in novel or non-equilibrium contexts such as invasions, translocations, climate change and evolutionary shifts.

http://max2.ese.u-psud.fr/epc/conservation/PDFs/HIPE/Kearney2009.pdf

Mechanistic niche modelling: combining physiological and spatial data to predict species' ranges.

An efficient ghost-cell immersed boundary method (GCIBM) for simulating turbulent flows in complex geometries is presented. A boundary condition is enforced through a ghost cell method. The reconstruction procedure allows systematic development of numerical schemes for treating the immersed boundary while preserving the overall second-order accuracy of the base solver. Both Dirichlet and Neumann boundary conditions can be treated. The current ghost cell treatment is both suitable for staggered and non-staggered Cartesian grids. The accuracy of the current method is validated using flow past a circular cylinder and large eddy simulation of turbulent flow over a wavy surface. Numerical results are compared with experimental data and boundary-fitted grid results. The method is further extended to an existing ocean model (MITGCM) to simulate geophysical flow over a three-dimensional bump. The method is easily implemented as evidenced by our use of several existing codes.

A Ghost-Cell Immersed Boundary Method for Flow in Complex Geometry

In this work we describe an autonomous soft-bodied robot that is both self-contained and capable of rapid, continuum-body motion. We detail the design, modeling, fabrication, and control of the soft fish, focusing on enabling the robot to perform rapid escape responses. The robot employs a compliant body with embedded actuators emulating the slender anatomical form of a fish. In addition, the robot has a novel fluidic actuation system that drives body motion and has all the subsystems of a traditional robot onboard: power, actuation, processing, and control. At the core of the fish's soft body is an array of fluidic elastomer actuators. We design the fish to emulate escape responses in addition to forward swimming because such maneuvers require rapid body accelerations and continuum-body motion. These maneuvers showcase the performance capabilities of this self-contained robot. The kinematics and controllability of the robot during simulated escape response maneuvers are analyzed and compared wit...

/pdf/autonomous-soft-robotic-fish-capable-of-escape-maneuvers-4w5jc261h9.pdf

Autonomous Soft Robotic Fish Capable of Escape Maneuvers Using Fluidic Elastomer Actuators.

Effects of large computational time steps on the computed turbulence were investigated using a fully implicit method. In turbulent channel flow computations the largest computational time step in wall units which led to accurate prediction of turbulence statistics was determined. Turbulence fluctuations could not be sustained if the computational time step was near or larger than the Kolmogorov time scale.

Effects of the computational time step on numerical solutions for turbulent flow

We employ numerical simulation to investigate the hydrodynamics of carangiform locomotion as the relative magnitude of viscous and inertial forces, i.e. the Reynolds number (Re), and the tail-beat frequency, i.e. the Strouhal number (St), are systematically varied. The model fish is a three-dimensional (3D) mackerel-like flexible body undulating with prescribed experimental kinematics of carangiform type. Simulations are carried out for three Re spanning the transitional and inertial flow regimes, Re=300 and 4000 (viscous flow), and infinity (inviscid flow). For each Re there is a critical Strouhal number, St*, at which the net mean force becomes zero, making constant-speed self-propulsion possible. St* is a decreasing function of Re and approaches the range of St at which most carangiform swimmers swim in nature (St approximately 0.25) only as Re approaches infinity. The propulsive efficiency at St* is an increasing function of Re while the power required for swimming is decreasing with Re. For all Re, however, the swimming power is shown to be significantly greater than that required to tow the rigid body at the same speed. We also show that the variation of the total drag and its viscous and form components with St depend on the Re. For Re=300, body undulations increase the drag over the rigid body level, while significant drag reduction is observed for Re=4000. This difference is shown to be due to the fact that at sufficiently high Re the drag force variation with St is dominated by its form component variation, which is reduced by undulatory swimming for St>0.2. Finally, our simulations clarify the 3D structure of various wake patterns observed in experiments--single and double row vortices--and suggest that the wake structure depends primarily on the St. Our numerical findings help elucidate the results of previous experiments with live fish, underscore the importance of scale (Re) effects on the hydrodynamic performance of carangiform swimming, and help explain why in nature this mode of swimming is typically preferred by fast swimmers.

Numerical investigation of the hydrodynamics of carangiform swimming in the transitional and inertial flow regimes.

Curvilinear immersed boundary method for simulating fluid structure interaction with complex 3D rigid bodies

We carry out fluid-structure interaction simulations of self-propelled virtual swimmers to investigate the effects of body shape (form) and kinematics on the hydrodynamics of undulatory swimming. To separate the effects of form and kinematics, we employ four different virtual swimmers: a carangiform swimmer (i.e. a mackerel swimming like mackerel do in nature); an anguilliform swimmer (i.e. a lamprey swimming like lampreys do in nature); a hybrid swimmer with anguilliform kinematics but carangiform body shape (a mackerel swimming like a lamprey); and another hybrid swimmer with carangiform kinematics but anguilliform body shape (a lamprey swimming like a mackerel). By comparing the performance of swimmers with different kinematics but similar body shapes we study the effects of kinematics whereas by comparing swimmers with similar kinematics but different body shapes we study the effects of form. We show that the anguilliform kinematics not only reaches higher velocities but is also more efficient in the viscous (Re approximately 10(2)) and transitional (Re approximately 10(3)) regimes. However, in the inertial regime (Re=infinity) carangiform kinematics achieves higher velocities and is also more efficient than the anguilliform kinematics. The mackerel body achieves higher swimming speeds in all cases but is more efficient in the inertial regime only whereas the lamprey body is more efficient in the transitional regime. We also show that form and kinematics have little overall effect on the 3-D structure of the wake (i.e. single vs double row vortex streets), which mainly depends on the Strouhal number. Nevertheless, body shape is found to somewhat affect the small-scale features and complexity of the vortex rings shed by the various swimmers.

/pdf/on-the-role-of-form-and-kinematics-on-the-hydrodynamics-of-2c33l4ri8e.pdf

On the role of form and kinematics on the hydrodynamics of self-propelled body/caudal fin swimming

We investigate numerically vortex-induced vibrations (VIV) of two identical two-dimensional elastically mounted cylinders in tandem in the proximity–wake interference regime at Reynolds number Re = 200 for systems having both one (transverse vibrations) and two (transverse and in-line) degrees of freedom (1-DOF and 2-DOF, respectively). For the 1-DOF system the computed results are in good qualitative agreement with available experiments at higher Reynolds numbers. Similar to these experiments our simulations reveal: (1) larger amplitudes of motion and a wider lock-in region for the tandem arrangement when compared with an isolated cylinder; (2) that at low reduced velocities the vibration amplitude of the front cylinder exceeds that of the rear cylinder; and (3) that above a threshold reduced velocity, large-amplitude VIV are excited for the rear cylinder with amplitudes significantly larger than those of the front cylinder. By analysing the simulated flow patterns we identify the VIV excitation mechanisms that lead to such complex responses and elucidate the near-wake vorticity dynamics and vortex-shedding modes excited in each case. We show that at low reduced velocities vortex shedding provides the initial excitation mechanism, which gives rise to a vertical separation between the two cylinders. When this vertical separation exceeds one cylinder diameter, however, a significant portion of the incoming flow is able to pass through the gap between the two cylinders and the gap-flow mechanism starts to dominate the VIV dynamics. The gap flow is able to periodically force either the top or the bottom shear layer of the front cylinder into the gap region, setting off a series of very complex vortex-to-vortex and vortex-to-cylinder interactions, which induces pressure gradients that result in a large oscillatory force in phase with the vortex shedding and lead to the experimentally observed larger vibration amplitudes. When the vortex shedding is the dominant mechanism the front cylinder vibration amplitude is larger than that of the rear cylinder. The reversing of this trend above a threshold reduced velocity is associated with the onset of the gap flow. The important role of the gap flow is further illustrated via a series of simulations for the 2-DOF system. We show that when the gap-flow mechanism is triggered, the 2-DOF system can develop and sustain large VIV amplitudes comparable to those observed in the corresponding (same reduced velocity) 1-DOF system. For sufficiently high reduced velocities, however, the two cylinders in the 2-DOF system approach each other, thus significantly reducing the size of the gap region. In such cases the gap flow is entirely eliminated, and the two cylinders vibrate together as a single body with vibration amplitudes up to 50% lower than the amplitudes of the corresponding 1-DOF in which the gap flow is active. Three-dimensional simulations are also carried out to examine the adequacy of two-dimensional simulations for describing the dynamic response of the tandem system at Re = 200. It is shown that even though the wake transitions to a weakly three-dimensional state when the gap flow is active, the three-dimensional modes are too weak to affect the dynamic response of the system, which is found to be identical to that obtained from the two-dimensional computations.

Vortex-induced vibrations of two cylinders in tandem arrangement in the proximity-wake interference region.

INTRODUCTION The majority of fishes use body/caudal fin (BCF) undulations for propulsion. Only about 12% of 450 extant fish families discussed by Nelson (Nelson, 1984) use undulations of median or pectoral fins (MPF) as their routine propulsive mode (Videler, 1993). However, many more species use median or pectoral fins for stability and maneuverability, especially at low speeds, while many MPF swimmers use BCF mode to reach high speeds during escape reactions (Videler, 1993). Within the general MPF and BCF propulsion modes there are several other sub-modes of steady straight-line swimming, as initially classified (Breder, 1926) and later expanded (Lindsey, 1978) (for recent reviews, see Sfakiotakis et al., 1999; Lauder and Tytell, 2006). Carangiform swimming is a mode of BCF propulsion in which the large amplitude of the undulations is mostly restricted to the one-half or even one-third posterior part of the body and increases sharply in the caudal area (Lindsey, 1978). This mode of swimming is used by many fishes such as mackerel Scomber scombrus (Teleostei: Scombridae). Fishes in the Scombridae family are characterized by their streamlined body with a homocercal caudal fin and can achieve high swimming speeds (Jordan et al., 1930). The two non-dimensional parameters that characterize the steady inline performance of a carangiform swimmer are the Reynolds number (Re) of the flow and the Strouhal number (St) of the undulatory body motion, which can be defined as follows (Triantafyllou et al., 2000; Lauder and Tytell, 2006):

/pdf/numerical-investigation-of-the-hydrodynamics-of-anguilliform-2emtcwzkpi.pdf

Iman Borazjani

Papers

Numerical investigation of the hydrodynamics of carangiform swimming in the transitional and inertial flow regimes.

Curvilinear immersed boundary method for simulating fluid structure interaction with complex 3D rigid bodies

On the role of form and kinematics on the hydrodynamics of self-propelled body/caudal fin swimming

Vortex-induced vibrations of two cylinders in tandem arrangement in the proximity-wake interference region.

Numerical investigation of the hydrodynamics of anguilliform swimming in the transitional and inertial flow regimes