Instability of a geostrophic front and its energetics

Abstract

The instability of a current with a geostrophic surface density front is investigated by means of a reduced gravity model having a velocity profile with nearly uniform potential vorticity. It is shown that currents are unstable when the mean potential vorticity decreases toward the surface front at the critical point of the frontal trapped waves investigated by Paldor (1983). This instability is identical with that demonstrated by Killworth (1983) in the longwave limit.

The cross-stream component of mass flux and the rates of energy conversions among the five energy forms defined by Orlanski (1968) are also calculated. The main results are as follows, (a) The mass flux toward the surface front is positive near the front and negative around the critical point. The positive mass flux near the front does not vanish at the position of the undisturbed surface front, so that the mean position of the front moves outward and the region of the strong current spreads. (b) The potential energy of the mean flow integrated over the fluid is released through the work done by the force of the pressure gradient of the mean flow on the fluid, and is converted into the kinetic energy of the mean flow. (c) In the critical layer, the mean flow is rapidly accelerated with the growth of the unstable wave. This acceleration is caused by the rapid phase shift of the unstable wave in the critical layer.     

Characteristics of the ionospheric correction in ULF wave diagnostics of the magnetosphere

Summary Amplitude and energy correction character istics of the vertical propagation of ULF wave from the magnetosphere through the ionosphere to the Earth's surface, necessary for micropulsation wave diagnostics of the magnetosphere by means of ground-based observations, are introduced on the basis of matrices ofR–T coefficients [1–3]. The coefficients of vertical reflexibility, penetrability, transmissibility (or limpidity) and the absorption of the electromagnetic energy flux are defined, as well as analogous coefficients in the dimensions of the magnetic amplitude of the ULF wave, propagating through the given layer of the ionosphere. An examplary model of the ionosphere is used to demonstrate the frequency variations of these characteristics in the ULF wave range.     

Non-hydrostatic and non-linear contributions to the internal wave energy flux in sill regions

A three-dimensional non-linear, non-hydrostatic model in cross-sectional form is used to determine the factors influencing the relative importance of the linear, non-hydrostatic and non-linear contributions to the internal wave energy flux in sill regions due to tidal forcing. The importance of the free surface elevation term is also considered. Idealised topography representing the sill at the entrance to Loch Etive, the site of a recent measurement programme, is used. Calculations show that the non-linear terms in the energy flux become increasingly important as the sill Froude Number (F _s) increases and the sill aspect ratio is increased. The vertical profile of the stratification, in particular its value close to the sill crest where internal waves are generated, has a significant influence on unsteady lee wave and mixed tidal–lee wave generation and the non-linear contribution to the energy flux. Calculations show that as F _s increases, the energy flux due to the non-linear and non-hydrostatic terms increases more rapidly than the linear term. The importance of the non-linear terms in the energy flux also increases as the sill aspect ratio is increased. Increasing the buoyancy frequency reduces the contribution of the non-hydrostatic and non-linear terms to the total energy flux. Also, as the buoyancy frequency is increased, this reduces unsteady lee wave and mixed tidal–lee wave generation. In essence, these calculations show that the energy flux due to the non-hydrostatic and non-linear terms is appreciable in sill regions.     

Dynamics and spectra of cumulant update closures for two-dimensional turbulence

Abstract

Non-Markovian closure theories are compared with ensemble averaged direct numerical simulations (DNS) for decaying two-dimensional turbulence at large scale Reynolds numbers ranging from ≈ 50 to ≈ 4000. The closures, as well as DNS, are formulated for discrete wave numbers relevant to flows on the doubly periodic domain and are compared with the results of continuous wave number closures. The direct interaction approximation (DIA), self-consistent field theory (SCFT) and local energy-transfer theory (LET) closures are also compared with cumulant update versions of these closures (CUDIA, CUSCFT, CULET). The cumulant update closures are shown to have comparable performance to the standard closures but are much more efficient allowing long time integrations.

The discrete wave number closures perform considerably better than continuous wave number closures as far as evolved energy and transfer spectra and skewness are concerned. The discrete wave number closures are in reasonable agreement with DNS in the energy containing range of the large scales for Reynolds numbers ranging from ≈ 50 to ≈ 4000. The closures tend to underestimate the enstrophy flux to high wave numbers, increasingly so with increasing Reynolds number, resulting in underestimation of small-scale kinetic energy.     

On the wave field generated by a variable wind

Abstract

By using an empirical expression relating the rate of increase in wave energy to the local wind speed, an equation for the phase speed at the peak of the wave spectrum is derived. The solution of the equation is determined for some simple wind fields. In particular, the wave field caused by a localised storm moving steadily over an unbounded ocean is considered. It is also shown that only a small fraction of the momentum transferred from the wind into the water propagates away from a local storm area in the form of wave momentum.     

Effects of wave-wave and wave-mean flow interactions on the evolution of a baroclinic wave

Abstract

The weakly nonlinear evolution of a free baroclinic wave in the presence of slightly supercritical, vertically sheared zonal flow and a forced stationary wave field that consists of a single zonal scale and an arbitrary number of meridional harmonics is examined within the context of the conventional two-layer model. The presence of the (planetary-scale) stationary wave introduces zonal variations in the supercriticality and is shown to alter the growth rate and asymptotic equilibrium of the (synoptic-scale) baroclinic wave via two distinct mechanisms: The first is due to the direct interaction of the stationary wave with the shorter synoptic wave (wave-wave mechanism), and the second is due to the interaction of the synoptic wave with that portion of the mean field that is corrected by the zonally rectified stationary wave fluxes (wave-mean mechanism). These mechanisms can oppose or augment each other depending on the amplitude and spatial structure of the stationary wave field. If the stationary wave field is confined primarily to the upper (lower) layer and consists of only the gravest cross-stream mode, conditions are favorable (unfavorable) for nonzero equilibrium of the free wave.

In addition to the time dependent heat flux generated by baroclinic growth of the free wave, its interaction with a stationary wave field consisting of two or more meridional harmonics generates time dependent heat fluxes that vary with period of the free wave. However, if the stationary wave field contains several meridional harmonics of sufficiently large amplitude, the free baroclinic wave is destroyed.     

Richardson number profiles in laboratory experiments applied to shallow seas

Abstract

A unified analysis is given of the critical conditions for the onset of stratification due to either a vertical or a horizontal buoyancy flux, with tidal or wind stirring.

The critical conditions for the onset of stratification with a horizontal buoyancy flux are found to be of the form of ratios of the tidal slope, or wind setup, to the equivalent surface slope due to the lateral density gradient. These ratios, which are easily determined from sea data, indicate that the profiles of critical flux Richardson Number, averaged over the stirring cycle, are similar to those inferred from the laboratory experiments of Hopfinger and Linden (1982) in which there is zero mean shear turbulence with a stabilising buoyancy flux, and also that the efficiency for the conversion of kinetic energy to potential energy for tidal stirring is similar to that for wind stirring.

The observed much greater efficiency for wind stirring, compared with tidal stirring with a vertical buoyancy flux, is also consistent with the existence of flux Richardson Number profiles in the sea similar to those occurring in the corresponding laboratory experiments. Using the solution of the turbulent kinetic energy equation for the water column, the relative importance of the production of turbulent kinetic energy, and its diffusion by turbulence are assessed, and the critical conditions for the onset of stratification with a vertical buoyancy flux are shown to reduce the classical Simpson—Hunter form.     

Wave-mean flow interaction and its relationship with the atmospheric energy cycle with diabatic heating

In a linear system, the wave characteristics depend strongly on the distributions with height of wind ve-locity and static stability. The simplest case is for con-stant wind and static stability (e.g., isothermal atmos-phere with pressure and density exponentially de-creasing with height). In such circumstances there is no convergence or divergence in wave energy flux, therefore, no energy exchange between the wave and mean flow. In the atmosphere wind speed varies with increasing height, inte…     

Why ripples become sweiis,and swells in shallow water decay rapidly

Abstract

In an ocean with a horizontal bottom where no wind is blowing it is shown that the spin (angular momentum) of the ocean is conserved. Thus, when energy is dissipated, at least one of three things will happen: i) Wave spectra may move towards lower frequencies. ii) The directional distribution may be changed towards long-crested waves. iii) Shear currents may be generated. By neglecting ii) and iii), the frequency shift of a spectrum is calculated due to molecular dissipation. When all energy transforming phenomena as e.g. wave breaking and turbulence generation are taken into account, the conservation of spin seems to be able to explain the frequency shift of wave spectra. In shallow water it is shown that there is energy transfer from the waves to shear currents.     

Advective flow in sediments under the influence of compaction

Abstract

Models on flow and transport in surface water sediments currently neglect compaction, although it is well understood that compaction is one of the major processes below the free fluid-sediment interface. Porosity changes in the sediment layers, as a result of compaction, are measured in almost all probes: porosity decreases with the distance from the surface water-sediment interface. This paper provides a rigorous derivation of basic flux terms for a frame of reference that is moving with the fluid-sediment interface. It is shown how burial rate, interface velocity, velocities of fluid and solid phase and porosity are connected—under steady-state conditions. It turns out that porosity and the velocities in a one-dimensional column can be directly computed from each other. These findings are important not only for the understanding of compaction-driven flow itself; they are crucial for all studies on storage and transport of chemical components in sediments. As mass fluxes across the sediment-water interface may be affected, there is an indirect link on surface water quality, making these findings relevant also for research on eutrophication of surface water bodies and/or on biogeochemical cycles.     

Steady flows at the top of the core from geomagnetic field models: The steady motions theorem

Abstract

It is demonstrated that the steady tangential velocity v_s at the closed surface δK of a perfect fluid conductor bounded by a rigid, impenetrable exterior can be uniquely determined from knowledge of the normal component of the time varying magnetic flux density B _n, on δK. In the context of a simple earth model consisting of an electrically insulating mantle surrounding a perfectly conducting core, the assumption of steady flow provides enough extra information to eliminate the toroidal ambiguity in B _nv and to allow derivation of a unique, global flow at the top of the core from a model of the geomagnetic field.     

Tangential discontinuities and the optical analogy for stationary fields IV. High speed fluid sheets

Abstract

It was shown in the previous paper that a sufficiently strong pressure maximum applied to an equilibrium flux surface, by the fields on either side of the surface, produces a gap in the flux surface. The fields on either side make contact through the gap to produce a surface of tangential discontinuity (current sheet). It is shown in the present paper that there is a high speed sheet of fluid and field sliding over the surface of discontinuity when the applied pressure moves slowly across the flux surface. Conditions in the active X-ray corona of the sun suggest that such sheets are generally present, with velocities of the order of 10² km/sec, but with thicknesses too small to be observed. More substantial high speed sheets of fluid may occur in solar flares.     

On the coalescence of twisted flux tubes

Abstract

We study the problem of the coalescence of twisted flux tubes by assuming that the azimuthal field lines reconnect at a current sheet during the coalescence process and everywhere else the magnetic field is frozen in the fluid. We derive relations connecting the topology of the coalesced flux tube with the topologies of the initial flux tubes, and then obtain a structure equation for calculating the field configuration of the coalesced flux tube from the given topology. Some solutions for the two extreme cases of low-β plasma and high-β plasma are discussed. The coalesced flux tube has less twist than the initial flux tube. Magnetic helicity is found to be exactly conserved during the coalescence, but the assumptions in the model put a constraint on the energy dissipation so that we do not get a relaxation to the minimum-energy Taylor state in the low-β case. It is pointed out that the structure equation connecting the topology and the equilibrium configuration is quite general and can be of use in many two-dimensional flux tube problems.     

三峡水库香溪河库湾水-气界面热交换过程及水体稳定性

水库或湖泊的热分层结构是其动力与环境过程的重要研究方面,虽然很多学者针对水体分层结构和演变机理开展了大量研究,但水体通过水-气界面与大气进行热交换的过程,各气象因子的贡献机理等研究成果还很缺乏。本文基于三峡水库香溪河库湾2019年3月-2020年2月期间的水温、水位及气象等监测数据,针对水-气界面热交换过程如何影响水温垂向结构及表层水体湍流混合作用开展研究。结果表明,(1)香溪河水体年内呈高温期分层、低温期混合的基本特征,高温期混合层深度小于8 m,低温期混合层深度超过30 m。(2)太阳短波辐射是香溪河水体的主要热源,潜热通量和长波辐射是香溪河水体的主要冷源,感热通量贡献极小。(3)香溪河平均风速较弱,约为1.6 m/s,主要通过增强潜热和感热通量的方式影响水体垂向稳定性结构特征,其机械扰动作用较弱。(4)表层水体湍能通量在高温期较低(10^-7m³/s³量级),此时水体处于分层状态,风应力大概率主导表层水体湍流发育;低温期表层水体湍能通量较高(10^-6 m³/s^3<...     

On the attenuation of sea waves by rain

Abstract

Some conflicting evidence on Reynolds' (1900) hypothesis that rain should attenuate any wave motion on the sea surface is discussed. It is concluded that rain drops ought to produce vortex rings in the sea which mix the water to a sufficient depth to affect most waves, as asserted by Reynolds. By introducing vertical and horizontal eddy viscosities to model the mixing process, an estimate is found for the rate of attenuation of wave energy by the rain. Consequently, the net effect on the wave field of attenuation by rain and generation by wind is calculated.     

A theory for the evolution of wind-generated gravity-wave spectra due to dissipation

Abstract

In Naeser (1979), later denoted N, it was shown that a frequency shift of a wave spectrum had to be expected as a result of dissipation of energy and conservation of spin of the waves. While time-dependency was treated in N, mainly space-dependency is treated here. In order to do this, the velocity of the spin of the waves is calculated. It is shown that this can be made equal to the group velocity by a second order coordinate transformation. In the limits of deep and shallow water the transformation becomes the identity, and leaves the Stokes drift at its usual value if the moment point is located at the mean water level.

By supposing that the dissipation is proportional to the molecular dissipation, and that the entire wind-wave interaction takes place at extremely high frequencies and at a constant rate, it is shown that the energy density at the high frequency slope of a fetch-dependent spectrum is inversely proportional to the fifth power of the frequency, while a spectrum which is only a function of the time for which the wind has blown is inversely proportional to the fourth power. The theory is compared with observations which it fits within the accuracy of the method. It is also compared with existing theories and reasons for the discrepancies are pointed out.     

Seismic energy release over a broad frequency band

There remains much uncertainty on the absolute elastic wave energy released by fault rupture. Few direct estimates of the partition of seismic wave energy in ground shaking have been made. In this work, ground particle velocities from integrated accelerograms are used to compute the kinetic energy crossing unit area per unit time. Simplified theory for the near-field strong-motion case would appear to give a valid lower energy bound; the wave attenuation does not present a major problem. The partition of energy in predominantly P, S, and surface wave portions, for given frequency windows, is tabulated using strong-motion accelerograms recorded at different azimuths to the fault-sources of six California earthquakes (5.5<M _L<7.2). Checks against earlier magnitudeM _L and momentM ₀ correlations indicate significantly higher overall wave energy outputs than expected, but further calibration is needed.The study demonstrates that stable estimates of frequency-dependent seismic wave energies in the nearfield can be obtained from strong-motion records. Hence, energy flux may have a wider application to risk mapping than previously thought. In particular, a shift from peak acceleration scaling to (kinetic) energy inputs for engineering design appears to involve only routine processing.     

An investigation on the relationship between high energy charged particle flux in the upper atmosphere and the earthquake activities

This paper presents the analytic result on the correlation between the high energy charged particle flux in the radiation belt around the earth and the earthquake activities. It points out that the increment of count-speed of high energy charged particle flux in the upper atmosphere has definite relationship with the intensity of seismic activities on the earth. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,14, 100–103, 1992.     

Scattering of rossby waves by partial barriers

Abstract

The scattering of Rossby waves by partial barriers is studied. It is found that only a small fraction of the wave energy will penetrate the gap between South America and Antarctica if the wave period is less than a month.     

Quantifying the effects of climate change and human activities on runoff in the water source area of Beijing,China

Abstract

Quantitative assessment of the effects of climate change and human activities on runoff is very important for regional sustainable water resources adaptive management. In this study, the non-parametric Mann-Kendall test is used to identify the trends in and change points of the annual runoff with the aim of analysing the changing characteristics of the hydrological cycle. The study presents the analytical derivation of a method which combines six Budyko hypothesis-based water–energy balance equations with the Penman-Monteith equation to separate the effects of climate change and human activities. The method takes several climate variables into consideration. Results based on data from the Yongding River basin, China, show that climate change is estimated to account for 10.5–12.6% of the reduction in annual runoff and human activities contribute to 87.4–89.5% of the runoff decline. The results indicate that human activities are the main driving factors for the reduction in runoff.

Editor Z.W. Kundzewicz; Associate editor C.Y. Xu