Boris Galperin

A Quasi-equilibrium Turbulent Energy Model for Geophysical Flows

Abstract The Mellor-Yamada hierarchy of turbulent closure models is reexamined to show that the elimination of a slight inconsistency in their analysis leads to a quasi-equilibrium model that is somewhat simpler than their level 2½ model. Also the need to impose realizability conditions restricting the dependence of exchange coefficients on shearing rates is eliminated. The model is therefore more robust while the principal advantage of the level 2½ model, namely the solution of a prognostic equation for turbulent kinetic energy is retained. Its performance is shown to be not much different from that of level 2½.

The ubiquitous zonal jets in the atmospheres of giant planets and Earth's oceans

[1]xa0Recent eddy-permitting simulations of the North Pacific Ocean have revealed robust patterns of multiple zonal jets that visually resemble the zonal jets on giant planets. We argue that this resemblance is more than just visual because the energy spectrum of the oceanic jets obeys a power law that fits spectra of zonal flows on the outer planets. Remarkably, even the non-dimensional proportionality coefficient, CZ, determined by data under that spectral law, appears to be constant for all cases and approximately equal to 0.5. These results indicate that the multiple jet sets in the ocean and in the atmospheres of giant planets are governed by the same dynamics characterized by an anisotropic inverse energy cascade, i.e., the flow of energy from isotropic small-scale eddies to anisotropic large-scales structures, as well as the unique anisotropic spectrum. Implications of these results for climate research and future designs of observational missions are discussed.

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 ...

A time-dependent, three-dimensional model of the Delaware Bay and River system. Part 1: Description of the model and tidal analysis

Abstract A three-dimensional, time-dependent numerical model is used to simulate the dynamics and thermodynamics of Delaware Bay, River and adjacent continental shelf. This study describes the first attempt to model an estuary and the contiguous shelf as a coupled hydrodynamic and thermodynamic system. Here, in Part 1, a description of the model, boundary conditions and forcing information is provided. Numerical results are compared with surface elevation data at several locations throughout the Bay and the River, as well as with the observations collected by the National Ocean Service during their 1984–1985 circulatory study. It is shown that a vertically-integrated, two-dimensional version of the model predicts realistic amplitudes but with some phase error. The full three-dimensional model reduces the phase error but underpredicts the tidal range; this is due to the higher values of horizontal viscosity required by the three-dimensional model. The model accounts for non-linear, shallow-water effects and reproduces the observed amplification of the high-frequency tidal components from the mouth of the Bay to the head of the River at Trenton.

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.

The Martian atmospheric boundary layer

The planetary boundary layer (PBL) represents the part of the atmosphere that is strongly influenced by the presence of the underlying surface and mediates the key interactions between the atmosphere and the surface. On Mars, this represents the lowest 10 km of the atmosphere during the daytime. This portion of the atmosphere is extremely important, both scientifically and operationally, because it is the region within which surface lander spacecraft must operate and also determines exchanges of heat, momentum, dust, water, and other tracers between surface and subsurface reservoirs and the free atmosphere. To date, this region of the atmosphere has been studied directly, by instrumented lander spacecraft, and from orbital remote sensing, though not to the extent that is necessary to fully constrain its character and behavior. Current data strongly suggest that as for the Earths PBL, classical Monin-Obukhov similarity theory applies reasonably well to the Martian PBL under most conditions, though with some intriguing differences relating to the lower atmospheric density at the Martian surface and the likely greater role of direct radiative heating of the atmosphere within the PBL itself. Most of the modeling techniques used for the PBL on Earth are also being applied to the Martian PBL, including novel uses of very high resolution large eddy simulation methods. We conclude with those aspects of the PBL that require new measurements in order to constrain models and discuss the extent to which anticipated missions to Mars in the near future will fulfill these requirements.

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...

A time-dependent, three-dimensional model of the Delaware Bay and river system. Part 2: Three-dimensional flow fields and residual circulation

Abstract The three-dimensional model of Delaware Bay, River and adjacent continental shelf was described in Part 1. Here, Part 2 of this two-part paper demonstrates that the model is capable of realistic simulation of current and salinity distributions, tidal cycle variability, events of strong mixing caused by high winds and rapid salinity changes due to high river runoff. The 25-h average subtidal circulation strongly depends on the wind forcing. Monthly residual currents and salinity distributions demonstrate a classical two-layer estuarine circulation wherein relatively low salinity water flows out at the surface and compensating high salinity water from the shelf flows at the bottom. The salinity intrusion is most vigorous along deep channels in the Bay. Winds can generate salinity fronts inside and outside the Bay and enhance or weaken the two-layer circulation pattern. Since the portion of the continental shelf included in the model is limited, the model shelf circulation is locally wind-driven and excludes such effects as coastally trapped waves and interaction with Gulf Stream rings; nevertheless, a significant portion of the coastal elevation variability is hindcast by the model. Also, inclusion of the shelf improves simulation of salinity inside the Bay compared with simulations where the salinity boundary condition is specified at the mouth of the Bay.

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.