scholarly journals Short and long waves over a muddy seabed

2010 ◽  
Vol 643 ◽  
pp. 33-58 ◽  
Author(s):  
CHIANG C. MEI ◽  
MIKHAEL KROTOV ◽  
ZHENHUA HUANG ◽  
AODE HUHE
Keyword(s):  
Water Waves ◽  
Short Distance ◽  
Water Layer ◽  
Fluid Mud ◽  
Leading Order ◽  
Infragravity Waves ◽  
Narrow Frequency Band ◽  
Shallow Seas ◽  
Time Periodic ◽  
Slow Modulation

The available experimental results have shown that in time-periodic motion the rheology of fluid mud displays complex viscoelastic behaviour. Based on the measured rheology of fluid mud from two field sites, we study the interaction of water waves and fluid mud by a two-layered model in which the water above is assumed to be inviscid and the mud below is viscoelastic. As the fluid-mud layer in shallow seas is usually much thinner than the water layer above, the sharp contrast of scales enables an approximate analytical theory for the interaction between fluid mud and small-amplitude waves with a narrow frequency band. It is shown that at the leading order and within a short distance of a few wavelengths, wave pressure from above forces mud motion below. Over a much longer distance, waves are modified by the accumulative dissipation in mud. At the next order, infragravity waves owing to convective inertia (or radiation stresses) are affected indirectly by mud motion through the slow modulation of the short waves. Quantitative predictions are made for mud samples of several concentrations and from two different field sites.

Characteristics of Low-Frequency Horizontal Noise of Ocean-Bottom Seismic Data

2021 ◽  
Author(s):  
Chao An ◽  
Chen Cai ◽  
Lei Zhou ◽  
Ting Yang
Keyword(s):  
Water Waves ◽  
Noise Source ◽  
Random Noise ◽  
Low Frequency ◽  
Ocean Bottom ◽  
Coherent Noise ◽  
Infragravity Waves ◽  
Low Frequencies ◽  
Bottom Currents ◽  
Ocean Bottom Seismographs

Abstract Horizontal records of ocean-bottom seismographs are usually noisy at low frequencies (< 0.1 Hz). The noise source is believed to be associated with ocean-bottom currents that may tilt the instrument. Currently horizontal records are mainly used to remove the coherent noise in vertical records, and there has been little literature that quantitatively discusses the mechanism and characteristics of low-frequency horizontal noise. In this article, we analyze in situ ocean-bottom measurements by rotating the data horizontally and evaluating the coherency between different channels. Results suggest that the horizontal noise consists of two components, random noise and principle noise whose direction barely changes in time. The amplitude and the direction of the latter are possibly related to the intensity and direction of ocean-bottom currents. Rotating the horizontal records to the direction of the principle noise can largely suppress the principle noise in the orthogonal horizontal channel. In addition, the horizontal noise is incoherent with pressure, indicating that the noise source is not ocean surface water waves (infragravity waves). At some stations in shallow waters (<300 m), horizontal noise around 0.07 Hz is found to be linearly proportional to the temporal derivative of pressure, which is explained by forces of added mass due to infragravity waves.

scholarly journals Nonlinear long waves over a muddy beach

2013 ◽  
Vol 718 ◽  
pp. 371-397 ◽  
Author(s):  
Erell-Isis Garnier ◽  
Zhenhua Huang ◽  
Chiang C. Mei
Keyword(s):  
Boundary Layer ◽  
Thin Layer ◽  
Surface Waves ◽  
Nonlinear Waves ◽  
Water Waves ◽  
Long Waves ◽  
Fluid Mud ◽  
Weakly Nonlinear ◽  
Sea Bottom ◽  
Oscillatory Boundary Layer

AbstractWe analyse theoretically the interaction between water waves and a thin layer of fluid mud on a sloping seabed. Under the assumption of long waves in shallow water, weakly nonlinear and dispersive effects in water are considered. The fluid mud is modelled as a thin layer of viscoelastic continuum. Using the constitutive coefficients of mud samples from two field sites, we examine the interaction of nonlinear waves and the mud motion. The effects of attenuation on harmonic evolution of surface waves are compared for two types of mud with distinct rheological properties. In general mud dissipation is found to damp out surface waves before they reach the shore, as is known in past observations. Similar to the Eulerian current in an oscillatory boundary layer in a Newtonian fluid, a mean displacement in mud is predicted which may lead to local rise of the sea bottom.

scholarly journals Spectral gaps for water waves above a corrugated bottom

2013 ◽  
Vol 469 (2149) ◽  
pp. 20120545 ◽  
Author(s):  
V. Chiadò Piat ◽  
S. A. Nazarov ◽  
K. Ruotsalainen
Keyword(s):  
Asymptotic Analysis ◽  
Essential Spectrum ◽  
Water Waves ◽  
Linear Problem ◽  
Model Problem ◽  
Water Layer ◽  
Geometric Condition ◽  
Periodicity Cell ◽  
Spectral Gaps ◽  
Positive Real

In this paper, the essential spectrum of the linear problem on water waves in a water layer and in a channel with a gently corrugated bottom is studied. We show that, under a certain geometric condition, the essential spectrum has spectral gaps. In other words, there exist intervals in the positive real semi-axis that are free of the spectrum but have their endpoints in it. The position and the length of the gaps are found out by applying an asymptotic analysis to the model problem in the periodicity cell.

Numerical study on the dissipation of water waves over a viscous fluid-mud layer

2017 ◽  
Vol 158 ◽  
pp. 107-119 ◽  
Author(s):  
Bing-Qing Deng ◽  
Yi Hu ◽  
Xin Guo ◽  
Robert A. Dalrymple ◽  
Lian Shen
Keyword(s):  
Viscous Fluid ◽  
Water Waves ◽  
Numerical Study ◽  
Fluid Mud

scholarly journals Next-to-leading-order QCD corrections to heavy quark fragmentation into $${}^1S^{(1,8)}_0$$ quarkonia

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Feng Feng ◽  
Yu Jia ◽  
Wen-Long Sang
Keyword(s):  
Heavy Quark ◽  
Fragmentation Function ◽  
Short Distance ◽  
Decomposition Method ◽  
Heavy Quarkonium ◽  
Leading Order ◽  
Quark Fragmentation ◽  
Definition Of ◽  
Perturbative Corrections ◽  
Operator Definition

AbstractWithin NRQCD factorization framework, in this work we compute, at the lowest order in velocity expansion, the next-to-leading-order (NLO) perturbative corrections to the short-distance coefficients associated with heavy quark fragmentation into the $${}^1S_0^{(1,8)}$$ 1 S 0 ( 1 , 8 ) components of a heavy quarkonium. Starting from the Collins and Soper’s operator definition of the quark fragmentation function, we apply the sector decomposition method to facilitate the numerical manipulation. It is found that the NLO QCD corrections have a significant impact.

scholarly journals Three-dimensional surface gravity waves of a broad bandwidth on deep water

2021 ◽  
Vol 926 ◽  
Author(s):  
Yan Li
Keyword(s):  
Deep Water ◽  
Water Waves ◽  
Order Approximation ◽  
Three Dimensional ◽  
Finite Depth ◽  
Second Order ◽  
Leading Order ◽  
Broad Bandwidth ◽  
Stokes Waves ◽  
Deep Water Waves

A new nonlinear Schrödinger equation (NLSE) is presented for ocean surface waves. Earlier derivations of NLSEs that describe the evolution of deep-water waves have been limited to a narrow bandwidth, for which the bound waves at second order in wave steepness are described in leading-order approximations. This work generalizes these earlier works to allow for deep-water waves of a broad bandwidth with large directional spreading. The new NLSE permits simple numerical implementations and can be extended in a straightforward manner in order to account for waves on water of finite depth. For the description of second-order waves, this paper proposes a semianalytical approach that can provide accurate and computationally efficient predictions. With a leading-order approximation to the new NLSE, the instability region and energy growth rate of Stokes waves are investigated. Compared with the exact results based on McLean (J. Fluid Mech., vol. 511, 1982, p. 135), predictions by the new NLSE show better agreement than by Trulsen et al. (Phys. Fluids, vol. 12, 2000, pp. 2432–2437). With numerical implementations of the new NLSE, the effects of wave directionality are investigated by examining the evolution of a directionally spread focused wave group. A downward shift of the spectral peak is observed, owing to the asymmetry in the change rate of energy in a more complex manner than that for uniform Stokes waves. Rapid oblique energy transfers near the group at linear focus are observed, likely arising from the instability of uniform Stokes waves appearing in a narrow spectrum subject to oblique sideband disturbances.

scholarly journals NEXT-TO-LEADING ORDER CALCULATION OF THE COLOR-OCTET 3S1 GLUON FRAGMENTATION FUNCTION FOR HEAVY QUARKONIUM

2001 ◽  
Vol 16 (supp01a) ◽  
pp. 229-231
Author(s):  
JUNGIL LEE
Keyword(s):  
Fragmentation Function ◽  
Short Distance ◽  
Feynman Diagrams ◽  
Heavy Quarkonium ◽  
Leading Order ◽  
Light Cone Gauge ◽  
Color Octet ◽  
Feynman Gauge ◽  
Fragmentation Functions ◽  
Gluon Fragmentation

Next-to-leading order corrections to fragmentation functions in a light-cone gauge are discussed. This gauge simplifies the calculation by eliminating many Feynman diagrams at the expense of introducing spurious poles in loop integrals. As an application, the short-distance coefficients for the color-octet 3S1 term in the fragmentation function for a gluon to split into polarized heavy quarkonium states are re-calculated to order [Formula: see text]. We show that the ill-defined spurious poles cancel and the appropriate prescriptions for the remaining spurious poles can be determined by calculating a subset of the diagrams in the Feynman gauge. Our answer agrees with the recent calculation of Braaten and Lee in the Feynman gauge, but disagrees with another previous calculation.

The evolution of time-periodic long waves of finite amplitude

1970 ◽  
Vol 44 (1) ◽  
pp. 195-208 ◽  
Author(s):  
O. S. Madsen ◽  
C. C. Mei ◽  
R. P. Savage
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Finite Amplitude ◽  
Long Waves ◽  
Shallow Water Waves ◽  
Wave Maker ◽  
Steep Waves ◽  
Time Periodic ◽  
Moderate Magnitude ◽  
Approximate Equations

The breakdown of shallow water waves into forms exhibiting several secondary crests is analyzed by numerical computations based on approximate equations accounting for the effects of non-linearity and dispersion. From detailed results of two cases it is shown that when long waves are such that the parameter σ = ν*L*2/h*3 is of moderate magnitude, either due to initially steep waves generated at a wave-maker or due to forced amplification by decreasing depth, waves periodic in time do not remain simply periodic in space. Numerical results are compared with experiments for waves propagating past a slope and onto a shelf.

scholarly journals Gluon fragmentation into 3$$ {P}_J^{\left[1,8\right]} $$ quark pair and test of NRQCD factorization at two-loop level

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Peng Zhang ◽  
Ce Meng ◽  
Yan-Qing Ma ◽  
Kuang-Ta Chao
Keyword(s):  
Short Distance ◽  
Distance Matrix ◽  
Matrix Elements ◽  
Leading Order ◽  
Long Distance ◽  
Loop Level ◽  
Matching Procedure ◽  
Fragmentation Functions ◽  
Infrared Divergences ◽  
Gluon Fragmentation

Abstract The next-to-leading order (NLO) ($$ \mathcal{O} $$ O ($$ {\alpha}_s^3 $$ α s 3 )) corrections for gluon fragmentation functions to a heavy quark-antiquark pair in 3$$ {P}_J^{\left[1,8\right]} $$ P J 1 8 states are calculated within the NRQCD factorization. We use the integration-by-parts reduction and differential equations to semi-analytically calculate the fragmentation functions in full-QCD, and find that infrared divergences can be absorbed by the NRQCD long distance matrix elements. Thus, the NRQCD factorization conjecture is verified at two-loop level via a physical process, which is free of artificial ultraviolet divergences. Through the matching procedure, infrared-safe short distance coefficients and $$ \mathcal{O} $$ O ($$ {\alpha}_s^2 $$ α s 2 ) perturbative NRQCD matrix elements ⟨$$ {\mathcal{O}}^3{P}_J^{\left[1,8\right]} $$ O 3 P J 1 8 (3$$ {S}_1^{\left[8\right]} $$ S 1 8 )⟩ are obtained simultaneously. The NLO short distance coefficients are found to have significant corrections comparing with the LO ones.

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