Biofluiddynamic scaling of flapping, spinning and translating fins and wings
Biofluiddynamic scaling of flapping, spinning and translating fins and wings
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DOI：
10.1242/jeb.022251
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发表时间：
2009-08-15
影响因子：
2.8
通讯作者：
Dickinson, Michael H.
中科院分区：
文献类型：
--
作者：
Lentink, David;Dickinson, Michael H.
用鳍或翅膀游泳或飞行的生物体与周围的水和空气相互作用。相互作用由运动系统的形态学和运动学决定，运动系统形成Navier-Stokes（NS）方程的边界条件。这些方程代表了生物体周围流体的牛顿运动定律。几个无量纲的数字，如雷诺数和斯特劳哈尔数，测量形态和运动学对游泳和飞行的流体动力学的影响。然而，目前还没有一个连贯的理论框架来说明生物体的无量纲数量是如何与NS方程联系起来的。在这里，我们提出了一个综合的方法来缩放生物流体动力学的翅膀，皮瓣，旋转或平移。运动系统的形态学和运动学都耦合到NS方程，通过该方程，我们发现无量纲数表示由于机翼运动学和形态学而产生的流中的旋转加速度。三个相应的无量纲数是（1）角加速度数，（2）向心加速度数，和（3）罗斯比数，它测量科里奥利加速度。这些无量纲数由长度比例组成，便于几何解释。这种方法提供了基本的洞察力的物理机制，解释之间的性能差异扑翼，旋转和平移翅膀。虽然我们推导出这个新的框架模型苍蝇翅膀的特殊情况下，该方法是足够普遍的，使其适用于其他生物飞行或游泳使用翅膀或鳍。
Organisms that swim or fly with fins or wings physically interact with the surrounding water and air. The interactions are governed by the morphology and kinematics of the locomotory system that form boundary conditions to the Navier-Stokes (NS) equations. These equations represent Newton's law of motion for the fluid surrounding the organism. Several dimensionless numbers, such as the Reynolds number and Strouhal number, measure the influence of morphology and kinematics on the fluid dynamics of swimming and flight. There exists, however, no coherent theoretical framework that shows how such dimensionless numbers of organisms are linked to the NS equation. Here we present an integrated approach to scale the biological fluid dynamics of a wing that flaps, spins or translates. Both the morphology and kinematics of the locomotory system are coupled to the NS equation through which we find dimensionless numbers that represent rotational accelerations in the flow due to wing kinematics and morphology. The three corresponding dimensionless numbers are (1) the angular acceleration number, (2) the centripetal acceleration number, and (3) the Rossby number, which measures Coriolis acceleration. These dimensionless numbers consist of length scale ratios, which facilitate their geometric interpretation. This approach gives fundamental insight into the physical mechanisms that explain the differences in performance among flapping, spinning and translating wings. Although we derived this new framework for the special case of a model fly wing, the method is general enough to make it applicable to other organisms that fly or swim using wings or fins.