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Turbulent planetary boundary layers (PBLs) control the exchange processesbetween the atmosphere and the ocean/land. The key problems of PBL physicsare to determine the PBL height, the momentum, energy and matter fluxes atthe surface and the mean wind and scalar profiles throughout the layer in arange of regimes from stable and neutral to convective. Until present, thePBLs typical of stormy weather were always considered as neutrallystratified. Recent works have disclosed that such PBLs are in fact verystrongly affected by the static stability of the free atmosphere and must betreated as factually stable (we call this type of the PBL "conventionallyneutral" in contract to the "truly neutral" PBLs developed against theneutrally stratified free flow).It is common knowledge that basic features of PBLs exhibit a noticeabledependence on the free-flow static stability and baroclinicity. However, theconcern of the traditional theory of neural and stable PBLs was almostwithout exception the barotropic nocturnal PBL, which develops at midlatitudes during a few hours in the night, on the background of a neutral orslightly stable residual layer. The latter separates this type of the PBLfrom the free atmosphere. It is not surprising that the nature of turbulencein such regimes is basically local and does not depend on the properties ofthe free atmosphere.Alternatively, long-lived neutral (in fact only conditionally neutral) orstable PBLs, which have much more time to grow up, are placed immediatelybelow the stably stratified free flow. Under these conditions, the turbulenttransports of momentum and scalars even in the surface layer - far awayfrom the PBL outer boundary - depend on the free-flowBrunt-V\ue4is\ue4l\ue4 frequency, N.Furthermore, integral measures of the long-lived PBLs (their depths and theresistance law functions) depend on N and also on the baroclinic shear, S. Inthe traditional PBL models both non-local parameters N and S were overlooked.One of possible mechanisms responsible for non-local features of thelong-lived PBLs could be the radiation of internal gravity waves (IGW) fromthe PBL upper boundary to the free atmosphere and the IGW-induced transportof the squared fluctuations of velocity and potential temperature.The free-flow stability plays an especially important role in is theconventionally neutral PBLs (those with the zero potential-temperature fluxat the surface: Fθ=0 at z=0, developed against non-zero staticstability in the free atmosphere: N>0).The above reasoning obviously calls for a comprehensive revision of thetraditional theory. In a series of papers (quoted below in References) anadvanced theory has been proposed. It includes the following developments

Atmospheric boundary layers in storms: advanced theory and modelling applications