## 1 Introduction  
The norm of the geometric configuration of the flow channels of the central circulation remains in the field of empirical studies and lacks a formal description, despite the significant amount of accumulated data. This is due to the fact that there is no generally accepted concept of the hydrodynamic structure of blood flow in these departments, which is intrinsically linked to the geometry of the flow channels. The circulatory system is a self-organizing system, as during the process of evolution and ontogenesis, the formation of a complex geometrical configuration of the vascular channel should occur in such a way that the resulting blood flow fully provides the function of blood circulation, i.e., it has sufficient pressure and flow characteristics and maintains the stability of biologically active components in the blood and vascular wall. This task is only possible if the blood flow has a certain structure, the nature of which is still insufficiently understood. Since the 1930s, increasing attention has been paid to the swirling structure of blood flow in cardiac cavities and large vessels [1, 2], but the lack of an adequate hydrodynamic model and the difficulty of setting correct initial and boundary conditions have prevented a formal description of the blood flow. Such a description is necessary both for solving practical problems in cardiology and cardiac surgery and for modeling flow in normal and pathological conditions. In fact, ordered flow, including swirling, is more energetically favorable than turbulent flow because of the absence of chaotic vortices, which increase resistance and energy consumption through additional friction losses and turbulent diffusion. Furthermore, any natural process obeys the principle of minimum action, i.e., where the flow can self-organize into an ordered structure, turbulent flow should not occur. In previous publications, we proposed a method for analyzing the structure of swirling flows based on exact solutions of the unsteady hydrodynamic equations of Kiknadze-Krasnov [3], reduced to quasi-stationary solutions for the Burgers vortex [4]. In particular, it was argued in these works that the longitudinal-radial profile of the flow channel should satisfy the condition \(xr^{2}=const\) (where \(z\) is the current longitudinal coordinate and \(r\) is the corresponding radius) at all stages of blood jet evolution. This statement was based on experimental data [5]. In this study, we propose a formal algorithm and present results of the geometric reconstruction of the flow channel along the length of the channel from the left atrium to the aortic bifurcation, confirming the validity of this condition. This result creates the prerequisites for the creation of a formal geometric model of the blood channel of the central parts of the circulatory system. Such a model is not only necessary for the formal setting of hydrodynamically correct initial and boundary conditions to describe the blood flow in a given segment, but also provides an understanding of what the geometric configuration of the channel should be in the norm. This is important for diagnosing the blood flow state when the channel geometry changes, for planning and performing adequate surgical correction of geometric changes resulting from cardiac and aortic remodeling, and for physical and mathematical modeling of the blood circulation. Hydrodynamic-based geometric modeling of cardiovascular segments is key to the design and technological development of new, more efficient implants, such as prosthetic heart and vascular valves, implantable assist pumps, and artificial hearts. The aim of this study was to formally describe the normal geometric configuration of the aorta, taking into account the swirling hydrodynamic structure of the flow according to quasi-stationary solutions of the basic equations of hydrodynamics.