Semion Sukoriansky

Anisotropic spectra in two-dimensional turbulence on the surface of a rotating sphere

The anisotropic characteristics of small-scale forced 2D turbulence on the surface of a rotating sphere are investigated. In the absence of rotation, the Kolmogorov k−5/3 spectrum is recovered with the Kolmogorov constant CK≈6, close to previous estimates in plane geometry. Under strong rotation, in long-term simulations without a large-scale drag, a −5 slope emerges in the vicinity of the zonal axis (kx→0), while a −5/3 slope prevails in other sectors far away from the zonal axis in the wave number plane. This picture is consistent with the new flow regime recently simulated by Chekhlov et al. [Physica D 98, 321–334 (1995)] and Smith and Waleffe [Phys. Fluids 11, 1608–1622 (1999)] on the beta plane. The concentration of energy in the zonal components and breaking of isotropy are caused by the strongly anisotropic spectral energy transfer and the stabilization of zonal mean flow by the meridional gradient of the planetary vorticity. The sharp tilt-up of the spectrum along the zonal axis was qualitatively ...

On the Arrest of Inverse Energy Cascade and the Rhines Scale

Abstract The notion of the cascade arrest in a β-plane turbulence in the context of continuously forced flows is revised in this paper using both theoretical analysis and numerical simulations. It is demonstrated that the upscale energy propagation cannot be stopped by a β effect and can only be absorbed by friction. A fundamental dimensional parameter in flows with a β effect, the Rhines scale, LR, has traditionally been associated with the cascade arrest or with the scale that separates turbulence and Rossby wave–dominated spectral ranges. It is shown that rather than being a measure of the inverse cascade arrest, LR is a characteristic of different processes in different flow regimes. In unsteady flows, LR can be identified with the moving energy front propagating toward the decreasing wavenumbers. When large-scale energy sink is present, β-plane turbulence may attain several steady-state regimes. Two of these regimes are highlighted: friction-dominated and zonostrophic. In the former, LR does not have...

The effect of small-scale forcing on large-scale structures in two-dimensional flows

Abstract The effect of small-scale forcing on large-scale structures in β-plane two-dimensional (2D) turbulence is studied using long-term direct numerical simulations (DNS). We find that nonlinear effects remain strong at all times and for all scales and establish an inverse energy cascade that extends to the largest scales available in the system. The large-scale flow develops strong spectral anisotropy: k − 5 3 Kolmogorov scaling holds for almost all φ, φ = arctan ( k y k x ) except in the small vicinity of kx = 0, where Rhiness k−5 scaling prevails. Due to the k−5 scaling, the spectral evolution of β-plane turbulence becomes extremely slow which, perhaps, explains why this scaling law has never before been observed in DNS. Simulations with different values of β indicate that the β-effect diminishes at small scales where the flow is nearly isotropic. Thus, for simulations of β-plane turbulence forced at small scales sufficiently removed from the scales where β-effect is strong, large eddy simulation (LES) can be used. A subgrid scale (SGS) parameterization for such LES must account for the small-scale forcing that is not explicitly resolved and correctly accommodate two inviscid conservation laws, viz. energy and enstrophy. This requirement gives rise to a new anisotropic stabilized negative viscosity (SNV) SGS representation which is discussed in the context of LES of isotropic 2D turbulence.

A quasinormal scale elimination model of turbulent flows with stable stratification

A new spectral model for turbulent flows with stable stratification is presented. The model is based on a quasi-Gaussian mapping of the velocity and temperature fields using the Langevin equations and employs a recursive procedure of small-scale mode elimination that results in a coupled system of differential equations for effective, horizontal and vertical, viscosities and diffusivities. With increasing stratification, the vertical viscosity and diffusivity are suppressed while their horizontal counterparts are enhanced thus explicitly accounting for the anisotropy introduced by stable stratification. The new model is used to derive various spectral characteristics of stably stratified turbulent flows. It accounts for energy accumulation in the horizontal components at the expense of the energy reduction in the vertical component. The scale elimination algorithm explicitly accounts for the combined effect of turbulence and internal waves. A modified dispersion relation for internal waves, a relationship...

Universal n−5 spectrum of zonal flows on giant planets

The energy spectra of the observed zonal flows on Jupiter and Saturn are shown to obey the scaling law EZ(n)=CZ(Ω/R)2n−5 in the range of total wave numbers n not affected by large scale friction (here, Ω and R are the rotation rate and the radius of the planet, and CZ is an order-one constant). These spectra broadly resemble their counterpart in recent simulations of turbulent flows on the surface of a rotating sphere [Huang et al., Phys. Fluids 13, 225 (2001)] that represents a strongly anisotropic flow regime evoked by the planetary vorticity gradient. It is conjectured that this regime governs the large scale circulations and the multiple zonal jets on giant planets. The observed strong equatorial jets that were not produced in the nearly inviscid simulations by Huang et al. are attributed to the combined effect of the energy condensation in the lowest zonal modes and the large scale friction.

Large scale drag representation in simulations of two-dimensional turbulence

Numerical simulations of isotropic, homogeneous, forced and dissipative two-dimensional (2D) turbulence in the energy transfer subrange are complicated by the inverse cascade that continuously propagates energy to the large scale modes. To avoid energy condensation in the lowest modes, an energy sink, or a large scale drag is usually introduced. With a few exceptions, simulations with different formulations of the large scale drag reveal the development of strong coherent vortices and steepening of energy and enstrophy spectra that lead to erosion and eventual destruction of Kolmogorov–Batchelor–Kraichnan (KBK) statistical laws. Being attributed to the intrinsic anomalous fluctuations independent of the large scale drag formulation, these coherent vortices have prompted conjectures that KBK 2D turbulence in the energy subrange is irreproducible in long term simulations. Here, we advance a different point of view, according to which the emergence of coherent vortices is triggered by the inverse energy casc...

Large eddy simulation of two-dimensional isotropic turbulence

Large eddy simulation (LES) of forced, homogeneous, isotropic two-dimensional (2D) turbulence in the energy transfer subrange is the subject of this paper. A difficulty specific to this LES and its subgrid scale (SGS) representation is in that the energy source resides in high wave number modes excluded in simulations. Therefore, the SGS scheme in this case should assume the function of the energy source. In addition, the controversial requirements to ensure direct enstrophy transfer and inverse energy transfer make the conventional scheme of positive and dissipative eddy viscosity inapplicable to 2D turbulence. It is shown that these requirements can be reconciled by utilizing a two-parametric viscosity introduced by Kraichnan (1976) that accounts for the energy and enstrophy exchange between the resolved and subgrid scale modes in a way consistent with the dynamics of 2D turbulence; it is negative on large scales, positive on small scales and complies with the basic conservation laws for energy and enstrophy. Different implementations of the two-parametric viscosity for LES of 2D turbulence were considered. It was found that if kept constant, this viscosity results in unstable numerical scheme. Therefore, another scheme was advanced in which the two-parametric viscosity depends on the flow field. In addition, to extend simulations beyond the limits imposed by the finiteness of computational domain, a large scale drag was introduced. The resulting LES exhibited remarkable and fast convergence to the solution obtained in the preceding direct numerical simulations (DNS) by Chekhlovet al. (1994) while the flow parameters were in good agreement with their DNS counterparts. Also, good agreement with the Kolmogorov theory was found. This LES could be continued virtually indefinitely. Then, a simplified SGS representation was designed, referred to as the stabilized negative viscosity (SNV) representation, which was based on two algebraic terms only, negative Laplacian and positive biharmonic ones. It was found that the SNV scheme performed in a fashion very similar to the full equation and it was argued that this scheme and its derivatives should be applied for SGS representation in LES of quasi-2D flows.

Possibilities for Improvements in Liquid-Metal Reactors Using Liquid-Metal Magnetohydrodynamic Energy Conversion

AbstractPossibilities for increasing efficiency, simplifying the design of the energy conversion system, and reducing the probability of sodium/water interaction in liquid-metal reactors (LMRs) using liquid-metal magnetohydrodynamic (LMMHD) energy conversion technology are investigated. Of the six different LMMHD power conversion systems considered, the LMMHD Rankine steam cycle offers the highest efficiency—up to 15% greater than a conventional LMR. The LMMHD Ericsson gas cycles, on the other hand, offer a significantly simplified and compact LMR plant design. All the LMMHD power conversion systems eliminate the sodium/water interaction problem. In addition to commercial applications, LMMHD energy conversion technology opens interesting new possibilities for special terrestrial as well as space applications of LMRs.

Anisotropic turbulence and internal waves in stably stratified flows (QNSE theory)

The quasi-normal scale elimination (QNSE) theory is an analytical spectral theory of turbulence based upon successive elimination of small scales of motion and calculating ensuing corrections to the viscosity and diffusivity. The main results of the theory are analytical expressions for eddy viscosity, eddy diffusivity, and kinetic energy and temperature spectra. Partial scale elimination yields a subgrid-scale representation for large-eddy simulations, whereas the elimination of all fluctuating scales is analogous to the Reynolds averaging. The scale-dependent analysis enables one to put processes on different scales at the spotlight and elucidate their contributions to eddy viscosities and eddy diffusivities. In addition, the method traces the modification of the flow with increasing stratification and recovers growing anisotropy and the effect of the internal waves. The QNSE-based Reynolds-averaged models present a viable alternative to conventional Reynolds stress models. A QNSE model of this kind was tested in the numerical weather prediction system HIRLAM instead of the existing reference Reynolds stress model. The performance of the QNSE model was superior in all simulations where stable stratification was noticeable.

Direct numerical simulation tests of eddy viscosity in two dimensions

Two‐parametric eddy viscosity (TPEV) and other spectral characteristics of two‐dimensional (2‐D) turbulence in the energy transfer subrange are calculated from direct numerical simulation (DNS) with 5122 resolution. The DNS‐based TPEV is compared with those calculated from the test field model (TFM) and from the renormalization group (RG) theory. Very good agreement between all three results is observed.