An official website of the United States government
An analysis of coherent measurements of winds and waves from data collected during the ONR Southern California 2013 (SoCal2013) program from R/P FLIP off the coast of Southern California in November 2013 is presented. An array of ultrasonic anemometers mounted on a telescopic mast was deployed to resolve the vertical profile of the modulation of the marine atmospheric boundary layer by the waves. Spectral analysis of the data provides the wave-induced components of the wind velocity for various wind-wave conditions. Results show that the wave-induced fluctuations depend both on the spectral wave age [Formula: see text] and the normalized height [Formula: see text], where c is the linear phase speed of the waves with wavenumber k and [Formula: see text] is the mean wind speed measured at the height z. The dependence on the spectral wave age expresses the sensitivity of the wave-induced airflow to the critical layer where [Formula: see text]. Across the critical layer, there is a significant change of both the amplitude and phase of the wave-induced fluctuations. Below the critical layer, the phase remains constant while the amplitude decays exponentially depending on the normalized height. Accounting for this double dependency, the nondimensionalization of the amplitude of the wave-induced fluctuations by the surface orbital velocity [Formula: see text] collapses all the data measured by the array of sonic anemometers, where a is the amplitude of the waves.
more »
« less
This content will become publicly available on March 1, 2026
Internal solitary wave generation using a jet-array wavemaker
Abstract This paper evaluates the experimental generation of internal solitary waves (ISWs) in a miscible two-layer system with a free surface using a jet-array wavemaker (JAW). Unlike traditional gate-release experiments, the JAW system generates ISWs by forcing a prescribed vertical distribution of mass flux. Experiments examine three different layer-depth ratios, with ISW amplitudes up to the maximum allowed by the extended Korteweg-de Vries (eKdV) solution. Phase speeds and wave profiles are captured via planar laser-induced fluorescence and the velocity field is measured synchronously using particle imaging velocimetry. Measured properties are directly compared with the eKdV predictions. As expected, small- and intermediate-amplitude waves match well with the corresponding eKdV solutions, with errors in amplitude and phase speed below 10%. For large waves with amplitudes approaching the maximum allowed by the eKdV solution, the phase speed and the velocity profiles resemble the eKdV solution while the wave profiles are distorted following the trough. This can potentially be attributed to Kelvin-Helmholtz instabilities forming at the pycnocline. Larger errors are generally observed when the local Richardson number at the JAW inlet exceeds the threshold for instability.
more »
« less
- Award ID(s):
- 1830056
- PAR ID:
- 10641522
- Publisher / Repository:
- Spinger
- Date Published:
- Journal Name:
- Experiments in Fluids
- Volume:
- 66
- Issue:
- 3
- ISSN:
- 0723-4864
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
We consider high-order strongly nonlinear long wave models expanded in a single small parameter measuring the ratio of the water depth to the characteristic wavelength. By examining its dispersion relation, the high-order system for the bottom velocity is found stable to all disturbances at any order of approximation. On the other hand, systems for other velocities can be unstable and even ill-posed, as signified by the unbounded maximum growth. Under the steady assumption, a new third-order solitary wave solution of the Euler equations is obtained using the high-order strongly nonlinear system and is expanded in an amplitude parameter, which is different from that used in weakly nonlinear theory. The third-order solution is shown to well describe various physical quantities induced by a finite-amplitude solitary wave, including the wave profile, horizontal velocity profile, particle velocity at the crest and bottom pressure. For numerical computations, the first- and second-order strongly nonlinear systems for the bottom velocity are considered. It is shown that finite difference schemes are unstable due to truncation errors introduced in approximating high-order spatial derivatives and, therefore, a more accurate spatial discretization scheme is necessary. Using a pseudo-spectral method based on finite Fourier series combined with an iterative scheme for the inversion of a non-local operator, the strongly nonlinear systems are solved numerically for the propagation of a single solitary wave and the head-on collision of two counter-propagating solitary waves of finite amplitudes, and the results are compared with previous laboratory measurements.more » « less
-
We consider a strongly nonlinear long wave model for large amplitude internal waves in a three-layer flow between two rigid boundaries. The model extends the two-layer Miyata–Choi–Camassa (MCC) model (Miyata, Proceedings of the IUTAM Symposium on Nonlinear Water Waves , eds. H. Horikawa & H. Maruo, 1988, pp. 399–406; Choi & Camassa, J. Fluid Mech. , vol. 396, 1999, pp. 1–36) and is able to describe the propagation of long internal waves of both the first and second baroclinic modes. Solitary-wave solutions of the model are shown to be governed by a Hamiltonian system with two degrees of freedom. Emphasis is given to the solitary waves of the second baroclinic mode (mode 2) and their strongly nonlinear characteristics that fail to be captured by weakly nonlinear models. In certain asymptotic limits relevant to oceanic applications and previous laboratory experiments, it is shown that large amplitude mode-2 waves with single-hump profiles can be described by the solitary-wave solutions of the MCC model, originally developed for mode-1 waves in a two-layer system. In other cases, however, e.g. when the density stratification is weak and the density transition layer is thin, the richness of the dynamical system with two degrees of freedom becomes apparent and new classes of mode-2 solitary-wave solutions of large amplitudes, characterized by multi-humped wave profiles, can be found. In contrast with the classical solitary-wave solutions described by the MCC equation, such multi-humped solutions cannot exist for a continuum set of wave speeds for a given layer configuration. Our analytical predictions based on asymptotic theory are then corroborated by a numerical study of the original Hamiltonian system.more » « less
-
Empirical models have been previously developed using the large dataset of satellite observations to obtain the global distributions of total electron density and whistler-mode wave power, which are important in modeling radiation belt dynamics. In this paper, we apply the empirical models to construct the total electron density and the wave amplitudes of chorus and hiss, and compare them with the observations along Van Allen Probes orbits to evaluate the model performance. The empirical models are constructed using the Hp30 and SME (or SML) indices. The total electron density model provides an overall high correlation coefficient with observations, while large deviations are found in the dynamic regions near the plasmapause or in the plumes. The chorus wave model generally agrees with observations when the plasma trough region is correctly modeled and for modest wave amplitudes of 10–100 pT. The model overestimates the wave amplitude when the chorus is not observed or weak, and underestimates the wave amplitude when a large-amplitude chorus is observed. Similarly, the hiss wave model has good performance inside the plasmasphere when modest wave amplitudes are observed. However, when the modeled plasmapause location does not agree with the observation, the model misidentifies the chorus and hiss waves compared to observations, and large modeling errors occur. In addition, strong (>200 pT) hiss waves are observed in the plumes, which are difficult to capture using the empirical model due to their transient nature and relatively poor sampling statistics. We also evaluate four metrics for different empirical models parameterized by different indices. Among the tested models, the empirical model considering a plasmapause and controlled by Hp* (the maximum Hp30 during the previous 24 h) and SME* (the maximum SME during the previous 3 h) or Hp* and SML has the best performance with low errors and high correlation coefficients. Our study indicates that the empirical models are applicable for predicting density and whistler-mode waves with modest power, but large errors could occur, especially near the highly-dynamic plasmapause or in the plumes.more » « less
-
A strongly nonlinear long-wave approximation is adopted to obtain a high-order model for large-amplitude long internal waves in a two-layer system by assuming the water depth is much smaller than the typical wavelength. When truncated at the first order, the model can be reduced to the regularized strongly nonlinear model of Choiet al.(J. Fluid Mech., vol. 629, 2009, pp. 73–85), which lessens the Kelvin–Helmholtz instability excited by the tangential velocity jump across the interface in the inviscid Miyata–Choi–Camassa (MCC) equations. Using the second-order model, the next-order correction to the internal solitary wave solution of the MCC equations is found and its validity is examined with the Euler solution in terms of the wave profile, the effective wavelength and the velocity profile. It is shown that the correction greatly improves the comparison with the Euler solution for the whole range of wave amplitudes and no further correction is necessary for practical applications. Based on a local stability analysis, the region of stability for the second-order long-wave model is identified in the physical parameter space so that the efficient numerical scheme developed for the first-order model can be used for the second-order model.more » « less
