Evaluation of an autoregressive spectral estimation technique for determining horizontal wave-number content in shallow water

2002 ◽  
Vol 111 (5) ◽  
pp. 2388
Author(s):  
Kyle M. Becker ◽  
George V. Frisk
Keyword(s):  
Shallow Water ◽  
Spectral Estimation ◽  
Wave Number ◽  
Estimation Technique ◽  
Horizontal Wave

PARAMETER SENSITIVITIES IN TWO-LAYER ISOSPEED MODELS OF SHALLOW WATER CHANNELS

1993 ◽  
Vol 01 (04) ◽  
pp. 469-486 ◽  
Author(s):  
R. J. CEDERBERG ◽  
W. L. SIEGMANN ◽  
M. J. JACOBSON ◽  
W. M. CAREY
Keyword(s):  
Shallow Water ◽  
Low Frequency ◽  
Propagation Model ◽  
Wave Number ◽  
Parameter Uncertainties ◽  
Rates Of Change ◽  
Wave Numbers ◽  
Analytic Expressions ◽  
Horizontal Wave ◽  
Order Of Magnitude

Sensitivities of relative intensity, interference wavelength, and horizontal wave number predictions to input parameters in two-layer isospeed models of shallow-water, low-frequency (less than 100 Hz) acoustic propagation problems are examined. The investigation is directed toward environmental parameter values corresponding generally to those near the site of a recent New Jersey shelf experiment. Typical parameter uncertainties in the environment of the experiment site are used to determine effects of parameter sensitivities on the accuracy of propagation model predictions. Also, analytic expressions for rates of change of wave numbers with respect to parameters are used to compute wave number and interference wavelength changes caused by parameter variations corresponding to the uncertainties. It is found that channel depth variations cause the largest change in intensity, while water sound speed variations have the greatest effect on wave numbers. Variabilities of the parameter sensitivities in regions about the base parameter sets are also examined, with the rates of change generally staying of the same order of magnitude throughout the regions considered. However, wave numbers which are close to cutoff can produce rates of change which vary by as much as three orders of magnitude.

Gravitational instability of a viscous fluid in a magnetic field

1965 ◽  
Vol 22 (3) ◽  
pp. 579-586 ◽  
Author(s):  
Chia-Shun Yih
Keyword(s):  
Magnetic Field ◽  
Viscous Fluid ◽  
Hartmann Number ◽  
Gravitational Instability ◽  
Unstable Mode ◽  
Stability Boundary ◽  
Wave Number ◽  
Symmetric Mode ◽  
Critical Stability ◽  
Horizontal Wave

The instability of a viscous fluid between two infinite vertical plates and heated from below in the presence of a magnetic field perpendicular to the plates is investigated, and the most critical stability boundary in the space of the Rayleigh number R, Hartmann number M, and the horizontal wave number a is determined. It is found that the most unstable mode is a symmetric mode with zero wave-number, and that for any M the fluid is unstable for any non-zero R, however small.

scholarly journals Propagation properties of Rossby waves for latitudinal β-plane variations of <I>f</I> and zonal variations of the shallow water speed

2012 ◽  
Vol 30 (5) ◽  
pp. 849-855 ◽  
Author(s):  
C. T. Duba ◽  
J. F. McKenzie
Keyword(s):  
Shallow Water ◽  
Group Velocity ◽  
Rossby Wave ◽  
Rossby Waves ◽  
Low Frequency ◽  
Wave Number ◽  
Coriolis Parameter ◽  
Propagation Properties ◽  
Wave Normal ◽  
Water Speed

Abstract. Using the shallow water equations for a rotating layer of fluid, the wave and dispersion equations for Rossby waves are developed for the cases of both the standard β-plane approximation for the latitudinal variation of the Coriolis parameter f and a zonal variation of the shallow water speed. It is well known that the wave normal diagram for the standard (mid-latitude) Rossby wave on a β-plane is a circle in wave number (ky,kx) space, whose centre is displaced −β/2 ω units along the negative kx axis, and whose radius is less than this displacement, which means that phase propagation is entirely westward. This form of anisotropy (arising from the latitudinal y variation of f), combined with the highly dispersive nature of the wave, gives rise to a group velocity diagram which permits eastward as well as westward propagation. It is shown that the group velocity diagram is an ellipse, whose centre is displaced westward, and whose major and minor axes give the maximum westward, eastward and northward (southward) group speeds as functions of the frequency and a parameter m which measures the ratio of the low frequency-long wavelength Rossby wave speed to the shallow water speed. We believe these properties of group velocity diagram have not been elucidated in this way before. We present a similar derivation of the wave normal diagram and its associated group velocity curve for the case of a zonal (x) variation of the shallow water speed, which may arise when the depth of an ocean varies zonally from a continental shelf.

Excitation of internal waves in a stably-stratified atmosphere with considerable wind-shear

1968 ◽  
Vol 32 (1) ◽  
pp. 145-171 ◽  
Author(s):  
A. A. Townsend
Keyword(s):  
Boundary Layer ◽  
Internal Waves ◽  
Wind Shear ◽  
Wave Packets ◽  
Normal Modes ◽  
Wave Number ◽  
Spectral Energy ◽  
Air Turbulence ◽  
Wave Numbers ◽  
Horizontal Wave

The rate of generation of internal waves by a thin turbulent boundary layer was calculated in a previous paper for a stably-stratified atmosphere with no significant wind-shear outside the boundary layer by considering the excitation of normal modes of wave propagation. By using the concept of wave-packets propagating upwards from the boundary layer, the effects of wind-shear can be included. Conditions for the validity of the approximation are given. In general, the spectral distribution of wave-energy at a particular height takes large values in two bands of horizontal wave-number, one band deriving from wave-packets undergoing internal reflexion near that height and the other from wave-packets of very small local frequency that accumulate there. The ‘reflexion’ wave-numbers are dominant if the wind increases with height and the ‘accumulation’ wave-numbers if the wind initially decreases with height. The spectral energy distributions and intensities of the wave-motion are discussed in more detail for an atmosphere of uniform stability and unidirectional wind-shear. The accumulation process may lead to instability or overturning of the waves, and estimates are made of the probable scale and intensity of the ‘clear-air’ turbulence produced. An interesting point is that the rate of energy loss from the boundary layer by radiation of internal waves turns out to be comparable with the rate of production in the outer nine-tenths of the layer, both for atmospheric boundary layers and for the surface layer of the ocean. It seems likely that radiation limits the layer thickness to some extent.

scholarly journals Nonlinear hydromagnetic convection in a moderate prandtl number fluid

1981 ◽  
Vol 23 (3) ◽  
pp. 321-338 ◽  
Author(s):  
N. Riahi
Keyword(s):  
Prandtl Number ◽  
Lorentz Force ◽  
Strong Field ◽  
Inertial Force ◽  
Weak Field ◽  
Wave Number ◽  
Boundary Layer Method ◽  
Horizontal Wave ◽  
Moderate Field ◽  
Moderate Prandtl Number Fluid

Nonlinear hydromagnetic connection is investigated using the modal equations for cellular convection. The boundary layer method is used assuming large Rayleigh number R, moderate Prandtl number σ and for different ranges of the Chandrasekhar number Q. The heat flux F is determined for the value of the horizontal wave number which maximizes F. For a weak field, the inertial force dominates over the Lorentz force. F is independent of Q, but it increases with R and σ. For a moderate field, the Lorentz force is significant. F increases with R and σ and decreases as Q increases. For a strong field, the Lorentz force dominates over the inertial force. F is independent of σ, but it increases with R and decreases as Q increases.

Sign in / Sign up

Export Citation Format

Share Document