Energy Of Short Waves Research Articles

The influence of the topographic structure of the sea surface on the error of determining the surface wind by satellite optical scanners

The error in determining the surface wind speed by use of optical scanners is analyzed as due to the variety of physical factors forming the topographical structure of the sea surface. It is shown that this error can be divided into two components. The first component is caused by the stochastic character of the relation between the wind speed and energy of short surface waves; it does not depend on the average wind speed and amounts to 0.2 m/s. The second component is caused by deviations of the slope distribution from the Gaus-sian distribution; it increases with an increase in wind and varies from 0.1 m/s at a wind speed of 1.5 to 0.4 m/s at a wind speed of 15 m/s.

Development of a bimodal structure in ocean wave spectra

Traditionally, the directional distribution of ocean waves has been regarded as unimodal, with energy concentrated mainly on the wind direction. However, numerical experiments and field measurements have already demonstrated that the energy of short waves tends to be accumulated along two off‐wind directions, generating a bimodal directional distribution. Here, numerical simulations of the potential Euler equations are used to investigate the temporal evolution of initially unimodal directional wave spectra. Because this approach does not include external forcing such as wind and breaking dissipation, spectral changes are only driven by nonlinear interactions. The simulations show that the wave energy spreads outward from the spectral peak, following two characteristic directions. As a result, the directional distribution develops a bimodal form as the wavefield evolves. Although bimodal properties are more pronounced in the high wave number part of the spectrum, in agreement with previous field measurements, the simulations also show that directional bimodality characterizes the spectral peak.

Nuclear spin relaxation in integral and fractional quantum Hall systems

We report on a numerical study of the relaxation rates of nuclear spins coupled through the hyperfine interaction to a two dimensional electron gas (2DEG) at magnetic fields corresponding to both fractional and integral Landau level (LL) fillings $\ensuremath{\nu}.$ The Hamiltonians of up to 20 interacting electrons are diagonalized exactly in the spherical geometry, neglecting finite layer width, disorder, and LL mixing. The spectral functions ${\ensuremath{\tau}}^{\ensuremath{-}1}(E)$ describing response of the 2DEG to the reversal of an embedded localized spin are calculated. In a (locally) incompressible $\ensuremath{\nu}=1$ or $\frac{1}{3}$ state, the finite Coulomb energy of short spin waves, together with the small nuclear Zeeman energy, prevent nuclear spin relaxation even in the limit of vanishing electron Zeeman energy ${(E}_{\mathrm{Z}}).$ However, we find that the nuclear spins can couple to the internal excitations of mobile finite-size skyrmions that appear in the 2DEG at sufficiently low ${E}_{\mathrm{Z}}$ and at $\ensuremath{\nu}$ slightly different from 1 or $\frac{1}{3}.$ The experimentally observed dependence of nuclear spin relaxation rate on ${E}_{\mathrm{Z}}$ and $\ensuremath{\nu}$ is qualitatively explained in terms of the occurrence of skyrmions and antiskyrmions of various topological charge.

Nonmodal Growth on a Sphere at Various Horizontal Scales

Nonmodal growth (NG) and unstable normal mode growth are considered in spherical geometry. Two groups of initial conditions (IC) are studied: "connected" IC (common in Cartesian studies) and "separated" IC (based on observed conditions prior to cyclogenesis). Time series of growth rates are emphasized in conjunction with eigenmode projections. Projections show that early on normal mode growth was much stronger for connected IC and that NG caused negative growth early on of some variables for separated IC. Projections explain why amplitude, kinetic energy (KE), and potential vorticity have more NG than available potential energy (APE). Though varying between ICs and with initial phase shift, NG increases with wavenumber. For middle wavelengths, NG is significant and positive using connected IC but negative or small using separated IC. Total energy and KE growth rates of short waves are very similar during the first 2 days for both ICs. Amplitude time series closely follow KE in all cases studied. APE has less overlap than does KE between the main modes present, so less NG occurs for APE than for KE. In separated IC cases, APE growth rates evolve consistent with emergence of an unstable normal mode and little NG.

Intra-seasonal variations of kinetic energy of lower tropospheric zonal waves during northern summer monsoon

Space spectral analysis of zonal (u) and meridional (v) components of wind and time spectral analysis of kinetic energy of zonal waves at 850 hPa during monsoon 1991 (1st June 1991 to 31st August 1991) for the global belt between equator and 40°N are investigated. Space spectral analysis shows that long waves (wavenumbers 1 and 2) dominate the energetics of Region 1 (equator to 20°N) while over Region 2 (20°N to 40°N) the kinetic energy of short waves (wavenumbers 3 to 10) is more than kinetic energy of long waves. It has been found that kinetic energy of long waves is dominated by zonal component while both (zonal and meridional) the components of wind have almost equal contribution in the kinetic energy of short waves. Temporal variations of kinetic energy of wavenumber 2 over Region 1 and Region 2 are almost identical. The correlation matrix of different time series shows that (i) wavenumber 2 over Regions 1 and 2 might have the same energy source and (ii) there is a possibility of an exchange of kinetic energy between wavenumber 1 over Region 1 and short waves over Region 2. Wave to wave interactions indicate that short waves over Region 2 are the common source of kinetic energy to wavenumber 2 over Regions 1 and 2 and wavenumber 1 over Region 1. Time spectral analysis of kinetic energy of zonal waves indicates that wavenumber 1 is dominated by 30-45 day and bi-weekly oscillations while short waves are dominated by weekly and bi-weekly oscillations. The correlation matrix, wave to wave interaction and time spectral analysis together suggest that short period oscillations of kinetic energy of wavenumber 1 might be one of the factors causing dominant weekly (5-9 day) and bi-weekly (10-18 day) oscillations in the kinetic energy of short waves.

Modulation of short wind waves by a long surface wave: a mechanism for feedback with an air flow

The paper concentrates on the evolution of a spectrum of short wind waves (SW) along the profile of a long surface wave (LW). Short wave spectral variations are considered in the relaxation approximation. The SW spectrum is modulated by the orbital velocities of long waves and by the variations of wind stress along the LW profile. The latter effect occurs due to wind flux perturbations induced by both the long wave proper and variations of the sea surface roughness induced by the SW modulations. To describe this effect, a feedback mechanism is introduces—the growth of energy of short waves results in the larger roughness of the sea surface, thereby contributing to the local wind stress, which facilitates, in turn, the growth of short waves. With moderate and strong winds being involved, this effect (aerodynamic feedback) is shown to be dominant in the short wave spectrum modulation. The mechanism becomes more efficient with intensification of the wind and decreasing of the long waves' frequency. Results of model calculations are in agreement with the known experimental data.

Propagation of oblique incident modulated waves past rigid, vertical thin barriers

Rigid thin barriers can be used to reduce energy of incoming short waves in coastal areas. The eigenfunction expansions method is used to study the incidence of monochromatic waves. The scattering of the long waves generated due to oblique incident bichromatic waves are also of great importance and have to be considered in the design of sheltered areas. It is shown that maximum short wave reflection is associated with maximum long wave transmission. Possible resonant effects may be attenuated choosing a barrier orientation which may cause minimal long wave transmission for the dominant incident waves.

Some features of tidal motion near the Guinean shelf

We have determined the energetic and spatial characteristics of baroclinic and barotropic tidal semi-diurnal fluctuations using the current temperature and velocity data collected by 12 self-contained buoy stations (SCBS) near the shelf of the Republic of Guinea at depths ranging from 50 to 1000 m. Intensive baroclinic motion was observed to prevail near the bottom within the depth range 100–1000 m. The energy of long waves largely propagated from the bottom to the surface, whereas the energy of short waves was transferred in the opposite direction.

On the energy of short period acoustic waves in the solar atmosphere

The amount of energy carried in the solar atmosphere by short period acoustic waves is particularly uncertain in the range of frequencies (ν ≥ 10mHz) which is potentially relevant for acoustic heating.

Intrinsic frequency spectra of short gravity‐capillary waves obtained from temporal measurements of wave height on a lake

Intrinsic frequency spectra of water waves in the range of 6–17 Hz were obtained as a function of both wind speed and wind stress from point measurements of wave height. In a lake with a limited fetch there are two types of surface motions causing Doppler shift in the frequencies of short waves: orbital velocity of long waves and surface wind drift. The former was estimated from long‐wave amplitude by using a linear wave theory. The error in this estimate is of the order of the long‐wave slope, and for this work it is typically 10%. The latter was approximated by the friction velocity. The friction velocity could be either taken as 3% of the mean wind speed measured at a height of 10 m or obtained from our direct measurements of the wind stress. The surface drift velocities obtained by these two approaches were found to be in close agreement. However, the estimate based on the mean wind speed was preferred because of its simplicity. Doppler frequency shift can be corrected in either the frequency or the equivalent spatial domain. A comparison of these techniques from both a theoretical and a practical point of view was made. The two techniques were found to produce comparable results. Experimental results showed that the spectral energy of short waves rapidly increased in response to increasing winds and jumped up by an order of magnitude when wave breaking occurred.

短周期地震波の方位依存性

Heuristic approach is made to derive the seismic directivity for short-waves. Since seismic wavelengths for engineering concerns are very short, such waves are inevitable to be distorted due to heterogeneities near the source region. The excitation of the short-waves is also controlled by the small-scale fault irregularities such as fault patches, asperities and harriers.Unilateral rupture along fault length L is considered. Fault patches are uniformly distributed on the fault with a number density of m per unit area. Since the fracture of fault patches is assumed to be random, the energy of short-waves would be additive. The maximum amplitude of short-waves is, therefore, expected to be amax=[mL2r2/Td]1/2F(K) where r2is a narrow-band average energy from one fault patch and Td is rupture time over fault length L as Td=L/c[c/v-cosθ] K corresponds to the number of peaks and troughs of the wave train considered, mL2, and F(K)=[lnK2/2π-lnlnK2/2π]1/2 The theory predicts seismic directivity for short-wave amplitudes as (c/v-cosθ)-1/2 whereas (c/v-cosθ)-1 is known for long-waves. Our previous result suggests that r2 is related to L, so that amax would increase in proportion to L.