Stability of Finite-Amplitude Baroclinic Waves in a Two-Layer Channel Flow

Yoshizaki, Masanori

doi:10.2151/jmsj1965.60.2_620

Cited by 7 publications

(3 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Pedlosky first established the quasi-geostrophic vorticity conservation equation in two-layer fluid motion and discussed the influence of physical factors, such as the β effect and baroclinic instability on wave propagation [13]. Based on the study of Pedlosky, Steinsaltz continued to consider the influence of topography on wave height [14,15].…”

Section: Introductionmentioning

confidence: 99%

Barotropic-Baroclinic Coherent-Structure Rossby Waves in Two-Layer Cylindrical Fluids

Xu,

Fang,

Geng

et al. 2023

Axioms

View full text Add to dashboard Cite

In this paper, the propagation of Rossby waves under barotropic-baroclinic interaction in polar co-ordinates is studied. By starting from the two-layer quasi-geotropic potential vorticity equation (of equal depth) with the β effect, the coupled KdV equations describing barotropic-baroclinic waves are derived using multi-scale analysis and the perturbation expansion method. Furthermore, in order to more accurately describe the propagation characteristics of barotropic-baroclinic waves, fifth-order coupled KdV-mKdV equations were obtained for the first time. On this basis, the Lie symmetry and conservation laws of the fifth-order coupled KdV-mKdV equations are analyzed in terms of their properties. Then, the elliptic function expansion method is applied to find the soliton solutions of the fifth-order coupled KdV-mKdV equations. Based on the solutions, we further simulate the evolution of Rossby wave amplitudes and investigate the influence of the high-order terms—time and wave number—on the propagation of barotropic waves and baroclinic waves. The results show that the appearance of the higher-order effect makes the amplitude of the wave lower, the width of the wave larger, and the whole wave flatter, which is obviously closer to actual Rossby wave propagation. The time and wave number will also influence wave amplitude and wave width.

show abstract

Section: Introductionmentioning

confidence: 99%

Barotropic-Baroclinic Coherent-Structure Rossby Waves in Two-Layer Cylindrical Fluids

Xu,

Fang,

Geng

et al. 2023

Axioms

View full text Add to dashboard Cite

show abstract

“…Thus, the preferred wavenumber does not seem to be determined by the wavenumber of the most unstable wave. Rather it is related to the wavenumbers of stable finite-amplitude waves as shown for baroclinic instability by Yoshizaki (1982b).…”

Section: Introductionmentioning

confidence: 99%

“…He considered the stability with respect to its side-band modes. Stuart and DiPrima (1978) Niino (1982a) or Yoshizaki (1982a)). Although *,* and * are generally complex numbers, the stability of the steady wave with respect to side-band modes had been studied only for real values of *,* and * (Kogelman and DiPrima, 1973) or for *=0 and pure imaginary values of * and * (Benjamin and Feir, 1967) until Stuart and DiPrima (1978) extended the analysis to complex values of * and *.…”

Section: Introductionmentioning

confidence: 99%

A Note on the Stability of a Finite-amplitude Wave Solution of the Generalized Landau Equation

Niino¹

1982

Journal of the Meteorological Society of Japan

View full text Add to dashboard Cite

show abstract

A linear stability theory of double-diffusive horizontal intrusions in a temperature–salinity front

Niino

1986

J. Fluid Mech.

View full text Add to dashboard Cite

The stability of a temperature–salinity front of finite width in which the density is exactly compensated for in the horizontal direction is studied by means of a linear theory. It is assumed that salt fingers are responsible for vertical transports of salinity and heat. The front is found to be always unstable even if viscosity is present. Horizontal intrusions are generated as a result of the instability, and cold/fresh water sinks while hot/salty water rises.The stability of the front is described by three dimensionless parameters: a frontal stability parameter G = [g(1 − γ)βΔS]6/κe2a2N10, a stratification parameter $\mu = g(1-\gamma)\beta\overline{S}_z/N^2$ and a Schmidt number ε = ν/κe, where g is the acceleration due to gravity, β the salinity contraction coefficient, ΔS half of the salinity difference across the front, γ the density-flux ratio of temperature to salt due to salt fingers, N the Brunt–Väisälä frequency corresponding to the basic density stratification, a the half-width of the front, $\overline{S}_z$ the vertical gradient of the basic salinity, κe the eddy diffusivity of salt due to salt fingers, and ν is either molecular or eddy kinematic viscosity. When ε is not zero it is found that a modified frontal stability parameter R defined by R = G/ε plays an important role in determining the stability for a fixed value of μ. In particular, when ε is larger than 10, the stability is almost completely determined by R if μ is specified.The dependence of the vertical scale h of the fastest-growing mode on external parameters varies according to the value of R for a given value of μ. When R is less than 40(1 + μ)5.4 (for ε = 10−3-103) h becomes independent of R and ε and is given by h = 2.2d/(1 + μ), where d = g(1 − γ)βΔS/N2 is the scale suggested by Ruddick & Turner (1979) who performed an experiment on horizontal intrusions across a narrow front. When R > 2 × 1055 (1 + μ)4.9, on the other hand, h becomes proportional to dR−1/4, the scale suggested by Toole & Georgi (1978), who considered the stability of a temperature–salinity front of infinite width. The constant of the proportionality is a weak function of ε and varies from 2π[(2 + μ)/4(1 + μ)2]−¼ to 2π[2(1 + μ + (1 + μ)½)]½ as ε goes from zero to infinity. Thus a front can be said to be narrow if R < 40(1 + μ)5.4 and wide if R > 2 × 105(1 + μ)4.9.The results of the theory explain those of Ruddick & Turner's experiment (1979) reasonably well.

show abstract

Stability of Finite-Amplitude Baroclinic Waves in a Two-Layer Channel Flow

Cited by 7 publications

References 27 publications

Barotropic-Baroclinic Coherent-Structure Rossby Waves in Two-Layer Cylindrical Fluids

Barotropic-Baroclinic Coherent-Structure Rossby Waves in Two-Layer Cylindrical Fluids

A Note on the Stability of a Finite-amplitude Wave Solution of the Generalized Landau Equation

A linear stability theory of double-diffusive horizontal intrusions in a temperature–salinity front

Contact Info

Product

Resources

About