Understanding the mechanics of a turbulent boundary layer is important, since in most practical problems it is the turbulent boundary layer that is primarily responsible for the surface shear force or surface resistance. The velocity distribution in a turbulent boundary layer on a flat plate is considered parallel to the flow. It is important to know the correlations between the boundary layer thickness and shear stress. Therefore, the problem of controlling the flow in a boundary layer on a flat plate is one of the important problems of boundary layer mechanics. Methods for controlling the flow characteristics of the boundary layer are different, and their effectiveness is evaluated by the kinematic and dynamic indicators of the flow on the near-wall surface. The study aims to present a simple numerical method that can be used for various nonlinear problems of the mechanics of flow around surfaces in near-wall boundary layers of a planar shape in interaction with the energy of polarized oscillations of a given frequency. The paper considers the air flow on the surface of a plate in the near-wall boundary layer in interaction with the energy of polarized oscillations of a given frequency. A differential equation in dimensionless quantities is obtained and solved numerically by the Runge-Kutta method, which describes the velocity distribution in the boundary layer on a flat plate of flow. When the energy of a polarized wave is applied to the air flow, the tangential stresses change. With an increase in the frequency of oscillation of the polarized wave from 100 Hz to 1000 Hz at an air entry velocity on a streamlined flat surface of 330 m/s, the tangential stresses decrease by a factor of 3. At an air entry velocity on a streamlined flat surface of 1000 m/s, with an increase in the frequency of oscillation of the polarized wave from 100 Hz to 1000 Hz, the tangential stresses decrease by a factor of 2. At air entry velocities up to 100 m/s, the tangential stresses decrease slightly by 24%. The nature of the change in tangential stresses is linear in the initial coordinate, which corresponds to the beginning of the air flow entering the plate surface, with two transition points at Mach numbers 1 and 3. The presented method of modeling the velocity distribution and tangential stresses in the boundary layer on a flat surface of the air flow in interaction with the vibration energy makes it possible to calculate the force loads on the surface in the entire range of flow speeds.
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