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We have explored here the case of three-dimensional non-stationary flows ofhelical type for the incompressible couple stress fluid with givenBernoulli-function in the whole space (the Cauchy problem). In ourpresentation, the case of non-stationary helical flows with constantcoefficient of proportionality alpha between velocity and the curl field offlow is investigated. Conditions for the existence of the exact solution forthe aforementioned type of flows are obtained, for which non-stationary helicalflow with invariant Bernoulli-function is considered satisfying to Laplaceequation. The spatial and time-dependent parts of the pressure field of thefluid flow should be determined via Bernoulli-function, if components of thevelocity of the flow are already obtained. Analytical and numerical findingshave been outlined including outstandung graphical presentations of varioustypes of constructed solution in illuminating dynamical snap-shots whichdemonstrate developing in time the structural behaviour of topology of theaforepresented solutions.

On a new type of non-stationary helical flows for incompressible couple stress fluid