- Hydrodynamic instability (or dynamic instability) of parcel displacements or, more usually, of waves in a moving fluid system governed by the fundamental equations of hydrodynamics, to which the quasi-hydrostatic approximation may or may not apply. (See Helmholtz instability, inertial instability, shearing instability, baroclinic instability, barotropic instability, rotational instability.)
The space scale of unstable waves is important in meteorology: Thus Helmholtz, baroclinic, and barotropic instability give, in general, unstable waves of increasing wavelength. The timescale is also important: A perturbation that grows for two days before dying out is effectively unstable for many meteorological purposes, but this is an initial-value problem and one cannot assume the existence of permanent waves. These meteorological types of hydrodynamic instability must not be confused with the phenomenon often referred to by mathematicians and physicists by the same term. A great deal of study has been devoted to the problem of the onset of turbulence in simple flows under laboratory conditions, and here viscosity is a source of instability.
See computational instability.
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