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This allows you to discuss the meaning of the individual terms in equation (1.4.1), without considering the term with divv, but remember that when divv ^ O results for w, valid for S / p, provided that during the adiabatic, and the liquid is well mixed .
We have already started to discuss the meaning of the term (u-grad) v after the formula, when it was shown that if the fluid is inviscid and isentropic or (well-mixed and adiabatic) or has a constant density, the number of flux lines penetrating the circuit, all the time consisting of the same particle is constant. Consequently, the vortex lines move with the fluid.
Imagine that there is a lot of liquid tracer lines and that they are a vector field, which is determined by these lines as follows: at the point of the vector coincides with the direction of the tangent to the line, and its absolute value is the number of lines passing through a unit area. On the other hand, the vortex lines can be marked in such a way that the distance
between two consecutive marks equal value of a. Then where lines are spaced far apart, the intervals between the marks will be small, which indicates that, cates a small absolute value of the vector. For vortex tubes in such a mark the volume enclosed in it between the two adjacent grades, constant over the entire length of the tube. Naturally, the vortex tube can be marked up in this way only if the diva = 0.
If any course has zero divergence, the volume occupied by a given set of particles remains standing up, so that the relationship between the set of flow lines and defined by this set of vector field preserves nyaetsya when the current lines carried along with the flow. If the vector and is now considered as a segment of one of the lines of current, the time At its start and end points will be shifted to the velocity field v At the distances and (v +6 v) A /, where 6v - the difference between the velocities of the particles in the beginning at and at the end of a.

The first term on the show that if you already have a positive component of vorticity in the x-direction, the vorticity will increase if the value of dv / dy + dw / dz is negative. This simply reflects the fact that when the liquid expands and contracts in planes perpendicular to the x-axis, the moment of inertia about this axis, respectively increases or decreases, and by the law of conservation of momentum the speed of rotation about the x-axis also increases or decreases respectively.