Drift-dissipation (DD) instability of non-uniform plasma in known experiments is identified with its linear threshold theory. Abnormal wave convection of the plasma, which considerably surpasses its classical outflow, is also measured. However, stimulated by experiments various theoretical models overlooked the phenomena of abnormal plasma flow, which was called to explain that instability. This and previous works (see refs. in the text) devoted to construction of nonlinear theory of the DD instability, which is coordinated with recovery of anomalous wave plasma and thermal electron convection. Generalization of asymptotic decomposition represents some kind of regularization of the perturbation theory. The normal functions, connecting, for example, amplitudes of wave fluctuations of electric potential with amplitudes of density fluctuations, include dissipative parts (i.e. influence of electron-ion friction responsible for instability of drift waves), which result in a phase difference between them and, as result, in abnormal wave convection of plasma. Convection of electron heat is similarly investigated. Correlation between failure of phases and abnormal convection is proved to be true by experiment. Nonlinear DD structure, studied in a series of done works, includes drift waves unstable in the linear theory, their fading maximum harmonics and zero-frequency modes, which are the beatings of unstable waves. As a result of research of stability of nonlinear stationary modes it is received, that owing to strong nonlinear connection of unstable waves by means of zero-frequency modes, these modes together with some drift waves fade. The dominant drift wave, which is stabilized by of energy in the maximum harmonics, survives. A wave vector of the dominant wave grows together with the after-threshold parameter, which could be represented as the external magnetic field (effect of reorganization of waves). This has essential influence on the coefficient of the plasma convection which changes in oscillating fashion depending on confining magnetic field at given gradient after-threshold. The serious deviation of the threshold frequency of DD instability from the linear law of a dispersion (with respect to the azimuthal component of the wave number), accounting for perturbations of electron temperature and also for non-potential nature of the equations, which does not have an initial form for possessing vortices solutions, allows one to refuse research of excitation of whirlwinds. Research of the influence non-potential property on excitation of DD structures at final β≤ν_ei / ω_He gives an opportunity to carry over results on non-linear DD structures and anomalous flow to studies of the role of boundary oscillations and drift waves inside the core of thermonuclear plasma under magnetic confinement.