The energy flux of three-dimensional waves in the atmosphere: Exact expression for a basic model diagnosis with no equatorial gap

2021 ◽  
Author(s):  
Hidenori Aiki ◽  
Yoshiki Fukutomi ◽  
Yuki Kanno ◽  
Tomomichi Ogata ◽  
Takahiro Toyoda ◽  
...  
Keyword(s):  
Energy Flux ◽  
Water Waves ◽  
Rossby Waves ◽  
Three Dimensional ◽  
Equatorial Waves ◽  
Scalar Quantity ◽  
Basic Model ◽  
Model Diagnosis ◽  
Universal Expression ◽  
Equatorial Rossby Waves

AbstractA model diagnosis for the energy flux of off-equatorial Rossby waves in the atmosphere has previously been done using quasi-geostrophic equations and is singular at the equator. The energy flux of equatorial waves has been separately investigated in previous studies using a space-time spectral analysis or a ray theory. A recent analytical study has derived an exact universal expression for the energy flux which can indicate the direction of the group velocity for linear shallow water waves at all latitudes. This analytical result is extended in the present study to a height-dependent framework for three-dimensional waves in the atmosphere. This is achieved by investigating the classical analytical solution of both equatorial and off-equatorial waves in a Boussinesq fluid. For the horizontal component of the energy flux, the same expression has been obtained between equatorial waves and off-equatorial waves in the height-dependent framework, which is linked to a scalar quantity inverted from the isentropic perturbation of Ertel’s potential vorticity. The expression of the vertical component of the energy flux requires computation of another scalar quantity that may be obtained from the meridional integral of geopotential anomaly in a wavenumber-frequency space. The exact version of the universal expression is explored and illustrated for three-dimensional waves induced by an idealized Madden-Julian Oscillation forcing in a basic model experiment. The zonal and vertical fluxes manifest the energy transfer of both equatorial Kelvin waves and off-equatorial Rossby waves with a smooth transition at around 10°S and around 10°N. The meridional flux of wave energy represents connection between off-equatorial divergence regions and equatorial convergence regions.

scholarly journals The characteristics of the equatorial waves caused a record torrential rain event over western Sumatra

2021 ◽  
Vol 893 (1) ◽  
pp. 012015
Author(s):  
P Wu ◽  
Y Fukutomi ◽  
K Kikuchi
Keyword(s):  
Rossby Waves ◽  
Phase Speed ◽  
Kelvin Waves ◽  
Precipitation Event ◽  
Western Coast ◽  
Rain Event ◽  
Equatorial Waves ◽  
Torrential Rain ◽  
Sumatra Island ◽  
Equatorial Rossby Waves

Abstract This study examined the cause of a record torrential rain event over the western coast of Sumatra Island in March 2016. The influence of atmospheric equatorial waves (EWs) and the characteristics of the EWs were investigated. Analysis of the Japanese 55-year Reanalysis data (JRA-55) and precipitation data from the Global Precipitation Measurement (GPM) satellite showed that the event was caused by the combined effects of Kelvin waves, equatorial Rossby waves, and westward inertio-gravity (WIG) waves. An examination of the characteristics of the EWs revealed that the Kelvin waves had longitudinal scales of ~6,000 km, with a period of ~6 days and phase speed of ~12 m s-1, which was typical of the convectively coupled Kelvin waves in this region. The WIG waves had a scale of ~2,500 km, with a period of 2.5 days and a relatively fast phase speed of 12~13 m s-1. Heavy precipitation occurred when an eastward Kelvin wave from the Indian Ocean encountered a westward inertio-gravity (WIG) over Sumatra Island. It was concluded that along with the Kelvin and equatorial Rossby waves, the WIG waves might have played a major role in the formation of the extreme precipitation event.

scholarly journals Variational formulations of steady rotational equatorial waves

2020 ◽  
Vol 10 (1) ◽  
pp. 534-547
Author(s):  
Jifeng Chu ◽  
Joachim Escher
Keyword(s):  
Linear Stability ◽  
Stream Function ◽  
Water Waves ◽  
Variational Formulation ◽  
Energy Functional ◽  
Equatorial Waves ◽  
Second Variation ◽  
Governing Equations ◽  
The Second Variation ◽  
Variational Formulations

Abstract When the vorticity is monotone with depth, we present a variational formulation for steady periodic water waves of the equatorial flow in the f-plane approximation, and show that the governing equations for this motion can be obtained by studying variations of a suitable energy functional 𝓗 in terms of the stream function and the thermocline. We also compute the second variation of the constrained energy functional, which is related to the linear stability of steady water waves.

Energetics of Barotropic and Baroclinic Tides in the Monterey Bay Area

2012 ◽  
Vol 42 (2) ◽  
pp. 272-290 ◽  
Author(s):  
Dujuan Kang ◽  
Oliver Fringer
Keyword(s):  
Energy Flux ◽  
Three Dimensional ◽  
Internal Tide ◽  
Submarine Canyon ◽  
Tidal Energy ◽  
Energy Partitioning ◽  
Navier Stokes ◽  
Monterey Bay ◽  
Topographic Features ◽  
Bay Area

Abstract A detailed energy analysis of the barotropic and baroclinic M2 tides in the Monterey Bay area is performed. The authors first derive a theoretical framework for analyzing internal tide energetics based on the complete form of the barotropic and baroclinic energy equations, which include the full nonlinear and nonhydrostatic energy flux contributions as well as an improved evaluation of the available potential energy. This approach is implemented in the Stanford Unstructured Nonhydrostatic Terrain-Following Adaptive Navier–Stokes Simulator (SUNTANS). Results from three-dimensional, high-resolution SUNTANS simulations are analyzed to estimate the tidal energy partitioning among generation, radiation, and dissipation. A 200 km × 230 km domain including all typical topographic features in this region is used to represent the Monterey Bay area. Of the 152-MW energy lost from the barotropic tide, approximately 133 MW (88%) is converted into baroclinic energy through internal tide generation, and 42% (56 MW) of this baroclinic energy radiates away into the open ocean. The tidal energy partitioning depends greatly on the topographic features. The Davidson Seamount is most efficient at baroclinic energy generation and radiation, whereas the Monterey Submarine Canyon acts as an energy sink. Energy flux contributions from nonlinear and nonhydrostatic effects are also examined. In the Monterey Bay area, the nonlinear and nonhydrostatic contributions are quite small. Moreover, the authors investigate the character of internal tide generation and find that in the Monterey Bay area the generated baroclinic tides are mainly linear and in the form of internal tidal beams. Comparison of the modeled tidal conversion to previous theoretical estimates shows that they are consistent with one another.

scholarly journals A three-dimensional model study of long-term mid-high latitude lower stratosphere ozone changes

2003 ◽  
Vol 3 (1) ◽  
pp. 1081-1107 ◽  
Author(s):  
M. P. Chipperfield
Keyword(s):  
High Latitude ◽  
Lower Stratosphere ◽  
Transport Model ◽  
Three Dimensional ◽  
Horizontal Resolution ◽  
Chemical Transport Model ◽  
Three Dimensional Model ◽  
Detailed Chemistry ◽  
Basic Model ◽  
Column Ozone

Abstract. We have used a 3D off-line chemical transport model (CTM) to study the causes of the observed changes in ozone in the mid-high latitude lower stratosphere from 1979–1998. The model was forced by European Centre for Medium Range Weather Forecasts (ECMWF) analyses and contains a detailed chemistry scheme. A series of model runs were performed at a horizontal resolution of 7.5°×7.5° and covered the domain from about 12 km to 30 km. The basic model performs well in reproducing the decadal evolution of the springtime depletion in the northern hemisphere (NH) and southern hemisphere (SH) high latitudes in the 1980s and early 1990s. After about 1994 the modelled interannual variability does not match the observations as well, which is probably due in part to changes in the operational ECMWF analyses – which places limits on using this dataset to diagnose dynamical trends. For mid-latitudes (35°–60°) the basic model reproduces the observed column ozone decreases from 1980 until the early 1990s. Model experiments show that the halogen trends appear to dominate this modelled decrease and of this around 30–50% is due to high-latitude processing on polar stratospheric clouds (PSCs). Dynamically induced ozone variations in the model correlate with observations over the timescale of a few years. Large discrepancies between the modelled and observed variations in the mid 1980s and mid 1990s can be largely resolved by assuming that the 11-year solar cycle (not explicitly included in the 3D model) causes a 2% (min-max) change in mid-latitude column ozone.

Numerical Calculation of the Wave Integrals in the Linearized Theory of Water Waves

1977 ◽  
Vol 21 (01) ◽  
pp. 1-10 ◽  
Author(s):  
Hung-Tao Shen ◽  
Cesar Farell
Keyword(s):  
Water Waves ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Three Dimensional Flow ◽  
Integral Term ◽  
Linearized Theory ◽  
Single Integral ◽  
Numerical Computing ◽  
Complex Exponential ◽  
Derivatives Of

A method for the numerical evaluation of the derivatives of the linearized velocity potential for three-dimensional flow past a unit source submerged in a uniform stream is presented together with a discussion of existing techniques. It is shown in particular that calculation of the double integral term in these functions can be efficiently accomplished in terms of a single integral with the integrand expressed in terms of the complex exponential integral, for which numerical computing techniques are available.

On the subharmonic instabilities of steady three-dimensional deep water waves

1994 ◽  
Vol 262 ◽  
pp. 265-291 ◽  
Author(s):  
Mansour Ioualalen ◽  
Christian Kharif
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Water Waves ◽  
Transverse Direction ◽  
Plane Waves ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Two Dimensional ◽  
Wave Steepness ◽  
Oblique Angle

A numerical procedure has been developed to study the linear stability of nonlinear three-dimensional progressive gravity waves on deep water. The three-dimensional patterns considered herein are short-crested waves which may be produced by two progressive plane waves propagating at an oblique angle, γ, to each other. It is shown that for moderate wave steepness the dominant resonances are sideband-type instabilities in the direction of propagation and, depending on the value of γ, also in the transverse direction. It is also shown that three-dimensional progressive gravity waves are less unstable than two-dimensional progressive gravity waves.

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