Turbulent transport of angular momentum in magnetized fluids and torsional oscillations of the sun

Abstract

Fluxes of angular momentum produced by turbulence in rotating fluids are derived with the effects of a magnetic field included. It is assumed that the rotation is slow but that the magnetic field is of arbitrary strength. A mean magnetic field is shown to produce qualitative changes of the sources of the differential rotation rather than the quenching of differential rotation usually expected. A new equatorward flux of angular momentum arises through the influence of the toroidal magnetic field. The possibility of interpreting the torsional oscillations of the Sun as a consequence of the magnetic perturbations of the turbulent angular momentum fluxes is discussed.     

On the role of the Asian monsoon in the angular momentum and kinetic energy balances of the tropics

The balance conditions of relative angular momentum and time-mean kinetic energy and their annual variations are studied for the Northern Hemisphere tropical belt. The belt is divided into two roughly equal size parts, the monsoon and the extramonsoon regions. The data used consist of all available daily rawinsonde reports from the world areological network for the two 5-year periods 1958–63 and 1968–73.In winter, the trade winds in the monsoon and extramonsoon regions are both sources of westerly relative angular momentum for the middle latitude circulation. However, it is found that the angular momentum gained in the extramonsoon region of the Tropics is mostly destroyed by a net southward flow of mass in that region, and becomes regenerated in the monsoon region by a net northward flow of mass there. This excess of angular momentum together with the angular momentum picked up locally in the monsoon region is almost all exported across its northern boundary. It is further found that in winter the Tropics are also an important source of mean kinetic energy for middle latitudes. Again almost all export of kinetic energy was found to take place across the northern boundary of the monsoon sector. Most of this energy must be generated through the pressure gradient term inside the monsoon region itself, the transformation from transient eddy kinetic energy being very small. The proper evaluation of the pressure gradient appears to be the main stumbling block in the present study, preventing us from estimating the generation and thereby, as a residual, the frictional dissipation in the two regions.In summer, the extramonsoon region remains a source of angular momentum, but the monsoon region with its surface westerlies acts as a sink, leading to a sharp reduction (and even a midsummer reversal) of the export into middle latitudes. Also the export of mean kinetic energy almost vanishes in summer, except for a small southward transfer across the equator. The calculations for two 5-year periods give very similar estimates and thereby show the reliability of the results.Parts of this paper were presented at the International Symposium on Monsoons, March 7–12, 1977 in New Delhi, India.     

A semi-analytical method for predicting the outflow hydrograph due to dam-break in natural valleys

The paper presents a semi-analytical method for predicting the flow rate hydrograph due to a hypothetical sudden and total dam failure in a natural valley. The method generalizes the approach proposed by Hunt for the dam-break problem in a rectangular frictionless sloping channel to a valley with a cross-section area expressed by a power-law function of water depth, in order to take into account the most common shapes of natural valleys. The parameters of the deriving model can be set by exploiting data usually available concerning the dam section geometry and the reservoir storage-depth curve. The application of the technique to three different reservoirs is discussed. The results show that the flow rate hydrographs obtained at the dam site agree with the ones calculated by means of a finite volume numerical code based on two-dimensional shallow water equations. The method requires moderate computational and data collecting effort, so it can be regarded as a useful alternative to other procedures commonly adopted in the practice.     

On the meridional circulation and balance of momentum in the Southern Ocean of POP

 The circulation of the Southern Ocean is studied in the eddy-resolving model POP (Parallel Ocean Program) by an analysis of zonally integrated balances. The TEM formalism (Transformed Eulerian Mean) is extended to include topography and continental boundaries, thus deviations from a zonally integrated state involve transient and standing eddies. The meridional circulation is presented in terms of the Eulerian, eddy-induced, and residual streamfunctions. It is shown that the splitting of the meridional circulation into Ekman and geostrophic transports and the component induced by subgrid and Reynolds stresses is identical to a particular form of the zonally integrated balance of zonal momentum. In this balance, the eddy-induced streamfunctions represent the interfacial form stresses by transient and standing eddies and the residual streamfunction represents the acceleration of the zonal current by density fluxes in a zonally integrated frame. The latter acceleration term is directly related to the surface flux of density and interior fluxes due to the resolved and unresolved eddies. The eddy-induced circulation is extremely vigorous in POP. In the upper ocean a shallow circulation, reversed in comparison to the Deacon cell and mainly due to standing eddies, appears to the north of Drake Passage latitudes, and in the Drake Passage belt of latitudes a deep-reaching cell is induced by transient eddies. In the resulting residual circulation the Deacon cell is largely cancelled and the residual advection of the zonal mean potential density is balanced by diapycnal eddy and subgrid fluxes which are strong in the upper few hundred meters but small in the ocean interior. The balance of zonal momentum is consistent with other eddy-resolving models; a new aspect is the clear identification of density effects in the zonally integrated balance. We show that the wind stress and the stress induced by the residual circulation drive the eastward current, whereas both eddy species result in a braking. Finally, we extend the Johnson–Bryden model of zonal transport to incorporate all relevant terms from the zonal momentum balance. It is shown that wind stress and induction by the residual circulation carry an eastward transport while bottom form stress and the stress induced by standing eddies yield westward components of transport. Received: 26 June 2001 / Accepted: 2 November 2001     

Coupled Process Models of Fluid Flow and Heat Transfer in Hydrothermal Systems in Three Dimensions

Geothermal fields and hydrothermal mineral deposits are manifestations of the interaction between heat transfer and fluid flow in the Earth’s crust. Understanding the factors that drive fluid flow is essential for managing geothermal energy production and for understanding the genesis of hydrothermal mineral systems. We provide an overview of fluid flow drivers with a focus on flow driven by heat and hydraulic head. We show how numerical simulations can be used to compare the effect of different flow drivers on hydrothermal mineralisation. We explore the concepts of laminar flow in porous media (Darcy’s law) and the non-dimensional Rayleigh number (Ra) for free thermal convection in the context of fluid flow in hydrothermal systems in three dimensions. We compare models of free thermal convection to hydraulic head driven flow in relation to hydrothermal copper mineralisation at Mount Isa, Australia. Free thermal convection occurs if the permeability of the fault system results in Ra above the critical threshold, whereas a vertical head gradient results in an upward flow field.     

Transport and deposition of fine sediment in open channels with different aspect ratios

This paper investigates by means of several large eddy simulations how the channel aspect ratio affects the transport and settling of suspended sediments. The numerical method is successfully validated using data of a physical experiment of fine sediment net deposition in an open channel flow. The channel aspect ratio, A, is known to be the determining factor for the development, strength and distribution of the turbulence‐driven secondary flow, and it is demonstrated that A influences the primary flow, turbulence quantities and the transport and fate of fine sediments. The secondary flow locally supports or hinders the falling of fine sediment particles in a turbulent flow, which results in a non‐uniform deposition of fine sediments over the cross‐section. While the channel aspect ratio has a large influence on the distribution of suspended sediments within the cross‐section, its effect on the cross‐sectional averaged deposition is negligibly small. Copyright © 2012 John Wiley & Sons, Ltd.     

A method for estimating spatially variable seepage and hydraulic conductivity in channels with very mild slopes

Infiltration along ephemeral channels plays an important role in groundwater recharge in arid regions. A model is presented for estimating spatial variability of seepage due to streambed heterogeneity along channels based on measurements of streamflow‐front velocities in initially dry channels. The diffusion‐wave approximation to the Saint‐Venant equations, coupled with Philip's equation for infiltration, is connected to the groundwater model MODFLOW and is calibrated by adjusting the saturated hydraulic conductivity of the channel bed. The model is applied to portions of two large water delivery canals, which serve as proxies for natural ephemeral streams. Estimated seepage rates compare well with previously published values. Possible sources of error stem from uncertainty in Manning's roughness coefficients, soil hydraulic properties and channel geometry. Model performance would be most improved through more frequent longitudinal estimates of channel geometry and thalweg elevation, and with measurements of stream stage over time to constrain wave timing and shape. This model is a potentially valuable tool for estimating spatial variability in longitudinal seepage along intermittent and ephemeral channels over a wide range of bed slopes and the influence of seepage rates on groundwater levels. Copyright © 2012 John Wiley & Sons, Ltd.     

Ungaged inflow and loss patterns in urban and agricultural sub-reaches of the Logan River Observatory

Streams in semi-arid urban and agricultural environments are often heavily diverted for anthropogenic purposes. However, they simultaneously receive substantial inflows from a variety of ungaged sources including stormwater returns, tile drainage, and irrigation runoff that help sustain flow during dry periods. Due to the inability to identify sources or directly gage many of these inflows, there is a clear need for methods to understand source origination while quantifying potential gains and losses over highly impacted reaches. In the context of the Logan River Observatory, historical gage data illustrate the importance of ungaged and unidentified inflows on maintaining or enhancing flows in both urban and agricultural reaches containing large diversions. To understand the inflows in this portion of the Logan River, we first analysed water samples for ions collected from a subset of representative inflow sources and applied clustering analyses to establish inflow source classifications and associated ion concentration ranges. These representative concentration ranges, combined with mainstem flow and river ion samples taken at sub-reach scales, allow for the application of flow and mass balances to quantify inflow rates from different sources as well as any losses. These calculations demonstrate significant gains and losses occurring in many sub-reaches during three sampling events. The dominant land use (urban or agriculture) and flow regime at the time of sampling were the primary drivers of gains and losses. These exchanges were found to be most important below large diversions during low flow conditions. This highlights the need to classify inflow sources (urban or agriculture, surface or groundwater) and estimate their contributions to anticipate instream consequences of land use and water management decisions. As irrigation and water conveyance practices become more efficient, a portion of these ungaged inflows could be diminished or eliminated, thus further depleting streamflow during dry periods.     

Dynamic,discontinuous stream networks: hydrologically driven variations in active drainage density,flowing channels and stream order

Despite decades of research on the ecological consequences of stream network expansion, contraction and fragmentation, surprisingly little is known about the hydrological mechanisms that shape these processes. Here, we present field surveys of the active drainage networks of four California headwater streams (4–27 km²) spanning diverse topographic, geologic and climatic settings. We show that these stream networks dynamically expand, contract, disconnect and reconnect across all the sites we studied. Stream networks at all four sites contract and disconnect during seasonal flow recessions, with their total active network length, and thus their active drainage densities, decreasing by factors of two to three across the range of flows captured in our field surveys. The total flowing lengths of the active stream networks are approximate power‐law functions of unit discharge, with scaling exponents averaging 0.27 ± 0.04 (range: 0.18–0.40). The number of points where surface flow originates obey similar power‐law relationships, as do the lengths and origination points of flowing networks that are continuously connected to the outlet, with scaling exponents averaging 0.36–0.48. Even stream order shifts seasonally by up to two Strahler orders in our study catchments. Broadly, similar stream length scaling has been observed in catchments spanning widely varying geologic, topographic and climatic settings and spanning more than two orders of magnitude in size, suggesting that network extension/contraction is a general phenomenon that may have a general explanation. Points of emergence or disappearance of surface flow represent the balance between subsurface transmissivity in the hyporheic zone and the delivery of water from upstream. Thus the dynamics of stream network expansion and contraction, and connection and disconnection, may offer important clues to the spatial structure of the hyporheic zone, and to patterns and processes of runoff generation. Copyright © 2014 John Wiley & Sons, Ltd.