Metamaterials have allowed unprecedented control of physical fields by harnessing material tensors derived from coordinate-transformation of governing equations. Among them, hydrodynamic metamaterials have recently received immense interests, showing the possibility of viscous flow control. However, the extant metamaterials cannot work for laminar flow which accompanies inertia force as well as viscous force. Herein, we propose a novel methodology for manipulating laminar flow to use the material tensors derived from the coordinate-transformed Navier–Stokes equations. The laminar flow manipulators for cloaking, concentrating, and rotating hydrodynamic flows are implemented numerically by applying both tensoric viscosity and density. The tensors give a direction for designing and fabricating metamaterials to control laminar flow.

超材料通过利用从控制方程的坐标变换得出的材料张量，实现了对物理场的空前控制。其中，流体动力超材料最近受到了广泛的关注，显示出粘性流控制的可能性。然而，现存的超材料不能用于层流，而层流却伴随着惯性力和粘性力。在这里，我们提出了一种新颖的方法来处理层流，以使用从坐标变换的Navier–Stokes方程导出的材料张量。通过施加张量粘度和密度，以数字方式实现用于隐蔽，集中和旋转流体动力流的层流操纵器。张量为设计和制造超材料以控制层流提供了方向。