Trapped waves on the mid-latitude β-plane

Author(s):  
Nathan Paldor ◽  
Andrey Sigalov
Keyword(s):  
2018 ◽  
Vol 167 ◽  
pp. 14-31 ◽  
Author(s):  
Yang Ding ◽  
Xianwen Bao ◽  
Zhigang Yao ◽  
Dehai Song ◽  
Jun Song ◽  
...  

2006 ◽  
Vol 63 (2) ◽  
pp. 617-633 ◽  
Author(s):  
Qingfang Jiang ◽  
James D. Doyle ◽  
Ronald B. Smith

Abstract The absorption of trapped lee waves by the atmospheric boundary layer (BL) is investigated based on numerical simulations and theoretical formulations. It is demonstrated that the amplitude of trapped waves decays exponentially with downstream distance due to BL absorption. The decay coefficient, α, defined as the inverse of the e-folding decay distance, is found to be sensitive to both surface momentum and heat fluxes. Specifically, α is larger over a rougher surface, associated with a more turbulent BL. On the other hand, the value of α decreases with increasing surface heating and increases with increasing surface cooling, implying that a stable nocturnal BL is more efficient in absorbing trapped waves than a typically deeper and more turbulent convective BL. A stagnant layer could effectively absorb trapped waves and increase α. Over the range of parameters examined, the absorption coefficient shows little sensitivity to wave amplitude. A relationship is derived to relate the surface reflection factor and the wave decay coefficient. Corresponding to wave absorption, there are positive momentum and negative energy fluxes across the boundary layer top, indicating that an absorbing BL serves as a momentum source and energy sink to trapped waves. Wave reflection by a shallow viscous layer with a linear shear is examined using linear theory, and its implication on BL wave absorption is discussed.


2004 ◽  
Vol 31 (12) ◽  
pp. n/a-n/a ◽  
Author(s):  
Yong-Gang Li ◽  
John E. Vidale ◽  
Elizabeth S. Cochran

1969 ◽  
Vol 38 (2) ◽  
pp. 365-374 ◽  
Author(s):  
Joseph B. Keller ◽  
Van C. Mow

An asymptotic solution is obtained to the problem of internal wave propagation in a horizontally stratified inhomogeneous fluid of non-uniform depth. It also applies to fluids which are not stratified, but in which the constant density surfaces have small slopes. The solution is valid when the wavelength is small compared to all horizontal scale lengths, such as the radius of curvature of a wavefront, the scale length of the bottom surface variations and the scale length of the horizontal density variations. The theory underlying the solution involves rays, a phase function satisfying the eiconal equation, and amplitude functions satisfying transport equations. All these equations are solved in terms of the rays and of the solution of the internal wave problem for a horizontally stratified fluid of constant depth. The theory is thus very similar to geometrical optics and its extensions. It can be used to treat problems of propagation, reflexion from vertical cliffs or from shorelines, refraction, determination of the frequencies and wave patterns of trapped waves, etc. For fluid of constant density, it reduces to the theory of Keller (1958). The theory is applied to waves in a fluid with an exponential density distribution on a uniformly sloping beach. The predicted wavelength is shown to agree well with the experimental result of Wunsch (1969). It is also applied to determine edge waves near a shoreline and trapped waves in a channel.


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