Quasi-geostrophic turbulence in a one-layer ocean affected by horizontal divergence

Two topics of quasi-geotstrophic (QG) turbulence are presented as regards the effect of horizontal divergence denoted by F = lambda(2), where lambda(-1) is the radius of deformation. Part I shows that strong F suppresses the so-called Rhines effect on a beta-plane, which effect refers to a characteristic pattern of zonal currents and the suppression of red cascade by Rossby waves. That is, when F is large and the tendency toward a barotropic flow is prohibited, QG turbulence on a beta-plane behaves as if on an f-plane; energy cascades up isotropically though in a slow pace due to F. The conclusion is not only confirmed by numerical experiments, but also proved by a limiting form of governing equation obtained by a transform of variables. Part II deals with three subjects of self-similar spectral evolution of QG turbulence on an f-plane affected by horizontal divergence. First, a similarity form is proposed for freely-decaying turbulence, which is reduced to that of Batchelor (1969) when F = 0. Next, inertial subranges are argued. The power of the stream function or kinetic energy is preferred to that of total energy. The kinetic energy spectrum in the inertial subrange is the same irrespective of F: k(-5/3) for energy cascade and k(-3) for enstrophy cascade, where k denotes a wavenumber. Finally self-similar spectral evolution is discussed in terms of the ordinary differential equations (ODEs) for the peak wavenumber, total energy and total enstrophy. The dynamics based on the ODEs gives a comprehensive explanation to the self-similar evolution of QG turbulence on an f-plane with and without horizontal divergence in various situations.