On Instability of Hydrodynamical Flows

A new analytical approach to studying a wide spectrum of linear problems in theory of hydrodynamical stability is described. The essence of this approach is constructing the regular Lyapunov functionals which grow in time on solutions to corresponding initial‐boundary value problems for small perturbations. This approach allows either to prove absolute instability, or to derive sufficient conditions of instability with respect to small perturbations for the hydrodynamical flows under study. It is important that the concrete form of solutions to boundary value and/or initial‐boundary value problems which describe the flows and perturbations is not needed. In the work, this approach is applied to a linear problem on stability with respect to small spatial perturbations for steady 3‐D flows in a homogeneous ideal incompressible fluid. It is stated that the equilibrium states of inviscid incompressible fluid are absolutely stable with respect to small 3‐D perturbations, whereas steady spatial flows are absolutely unstable. Lower a priori estimates are constructed; exponential growth in time is proven for small perturbations under study.