scholarly journals Increase in the skewness of extratropical vertical velocities with climate warming: fully nonlinear simulations versus moist baroclinic instability

2017 ◽  
Vol 144 (710) ◽  
pp. 208-217 ◽  
Author(s):  
Paul A. O'Gorman ◽  
Timothy M. Merlis ◽  
Martin S. Singh
Keyword(s):  
Climate Warming ◽  
Baroclinic Instability ◽  
Fully Nonlinear ◽  
Nonlinear Simulations

scholarly journals Steep unidirectional wave groups – fully nonlinear simulations vs. experiments

2015 ◽  
Vol 2 (4) ◽  
pp. 1159-1195 ◽  
Author(s):  
L. Shemer ◽  
B. K. Ee
Keyword(s):  
Wave Breaking ◽  
Surface Elevation ◽  
Computational Results ◽  
Local Surface ◽  
Qualitative Comparison ◽  
Wave Groups ◽  
Fully Nonlinear ◽  
Nonlinear Simulations ◽  
Velocity Of Propagation ◽  
Steep Waves

Abstract. A method was developed to carry out detailed qualitative comparison of fully nonlinear computations with the measurements of unidirectional wave groups. Computational results on evolving wave groups were compared with the available experiments. The local surface elevation variation, evolution of envelope shapes, the velocity of propagation of the steepest crests in the group and their relation to the height of the crests were obtained numerically and experimentally. Conditions corresponding to incipient wave breaking were investigated in greater detail. The results shed additional light on the limits of applicability of the computational results, as well as on mechanisms leading to the breaking of steep waves.

CONVECTIVE PATTERNS IN LIQUID–VAPOR SYSTEMS WITH DIFFUSE INTERFACE

2006 ◽  
Vol 16 (09) ◽  
pp. 2705-2711 ◽  
Author(s):  
RODICA BORCIA ◽  
DOMNIC MERKT ◽  
MICHAEL BESTEHORN
Keyword(s):  
Phase Field ◽  
Compressible Fluid ◽  
Field Model ◽  
Marangoni Convection ◽  
Van Der Waals ◽  
Phase Field Model ◽  
Diffuse Interface ◽  
Fully Nonlinear ◽  
Nonlinear Simulations ◽  
Liquid Vapor

Recently, we have developed a phase field model to describe Marangoni convection with evaporation in a compressible fluid of van der Waals type away from criticality [Eur. Phys. J. B44 (2005)]. Using this model, we report now 2D fully nonlinear simulations where we emphasize the influence of evaporation on convective patterns.

scholarly journals Scales of Linear Baroclinic Instability and Macroturbulence in Dry Atmospheres

2009 ◽  
Vol 66 (6) ◽  
pp. 1821-1833 ◽  
Author(s):  
Timothy M. Merlis ◽  
Tapio Schneider
Keyword(s):  
Growth Rate ◽  
Linear Stability ◽  
General Circulation ◽  
Baroclinic Instability ◽  
Circulation Model ◽  
Length Scale ◽  
Stability Analyses ◽  
Scaling Relationship ◽  
Wide Range ◽  
Nonlinear Simulations

Abstract Linear stability analyses are performed on a wide range of mean flows simulated with a dry idealized general circulation model. The zonal length scale of the linearly most unstable waves is similar to the Rossby radius. It is also similar to the energy-containing zonal length scale in statistically steady states of corresponding nonlinear simulations. The meridional length scale of the linearly most unstable waves is generally smaller than the energy-containing meridional length scale in the corresponding nonlinear simulations. The growth rate of the most unstable waves increases with increasing Eady growth rate, but the scaling relationship is not linear in general. The available potential energy and barotropic and baroclinic kinetic energies of the linearly most unstable waves scale linearly with each other, with similar partitionings among the energy forms as in the corresponding nonlinear simulations. These results show that the mean flows in the nonlinear simulations are baroclinically unstable, yet there is no substantial inverse cascade of barotropic eddy kinetic energy from the baroclinic generation scale to larger scales, even in strongly unstable flows. Some aspects of the nonlinear simulations, such as partitionings among eddy energies, can be understood on the basis of linear stability analyses; for other aspects, such as the structure of heat and momentum fluxes, nonlinear modifications of the waves are important.

scholarly journals Fully nonlinear simulations of unidirectional extreme waves provoked by strong depth transitions: The effect of slope

2020 ◽  
Vol 5 (6) ◽  
Author(s):  
Yaokun Zheng ◽  
Zhiliang Lin ◽  
Yan Li ◽  
T. A. A. Adcock ◽  
Ye Li ◽  
...  
Keyword(s):  
Extreme Waves ◽  
Fully Nonlinear ◽  
Nonlinear Simulations

scholarly journals Evolution and Stability of Two-Dimensional Anelastic Internal Gravity Wave Packets

2018 ◽  
Vol 75 (10) ◽  
pp. 3703-3724 ◽  
Author(s):  
Alain D. Gervais ◽  
Gordon E. Swaters ◽  
Ton S. van den Bremer ◽  
Bruce R. Sutherland
Keyword(s):  
Wave Packet ◽  
Gravity Wave ◽  
Linear Theory ◽  
Nonlinear Evolution ◽  
Wave Packets ◽  
Internal Gravity Wave ◽  
Two Dimensional ◽  
Fully Nonlinear ◽  
Weakly Nonlinear ◽  
Nonlinear Simulations

The weakly nonlinear evolution, stability, and overturning of horizontally and vertically localized internal gravity wave packets is examined for a nonrotating, anelastic atmosphere that is stationary in the absence of waves. The weakly nonlinear evolution is examined through the derivation of their wave-induced mean flow, which is used to formulate a nonlinear Schrödinger equation. The induced flow is manifest as a long, hydrostatic, bow wake-like disturbance, whose flow direction transitions from positive on the leading flank of the wave packet to negative on the trailing flank of the wave packet. As such, two-dimensional wave packets are always modulationally unstable. This instability results in enhanced amplitude growth confined to either the leading or trailing flank. Hence, when combined with anelastic growth predicted by linear theory, we anticipate two-dimensional waves will overturn either somewhat below or just above the heights predicted by linear theory. Numerical solutions of the Schrödinger equation are compared with the results of fully nonlinear simulations to establish the validity of the weakly nonlinear theory. Actual wave overturning heights are determined quantitatively from a range of fully nonlinear simulations.

scholarly journals Steep unidirectional wave groups – fully nonlinear simulations vs. experiments

2015 ◽  
Vol 22 (6) ◽  
pp. 737-747 ◽  
Author(s):  
L. Shemer ◽  
B. K. Ee
Keyword(s):  
Wave Breaking ◽  
Initial Conditions ◽  
Crucial Importance ◽  
Local Surface ◽  
Exact Matching ◽  
Wave Groups ◽  
Fully Nonlinear ◽  
Nonlinear Simulations ◽  
Velocity Of Propagation ◽  
Steep Waves

Abstract. A detailed quantitative comparison of fully nonlinear computations with the measurements of unidirectional wave groups is presented. Computational results on evolving wave groups were compared with previous available experiments. The local surface elevation variation, the evolution of envelope shapes, the velocity of propagation of the steepest crests in the group and their relation to the height of the crests were obtained numerically and experimentally. Conditions corresponding to incipient wave breaking were investigated in greater detail. The results shed additional light on mechanisms leading to the breaking of steep waves, as well as on the crucial importance of exact matching between initial conditions in computations and experiments.

Steep Unidirectional Wave Groups: Fully Nonlinear Simulations vs Experiments

2015 ◽  
Author(s):  
Lev Shemer ◽  
Bernard K. Ee
Keyword(s):  
Surface Elevation ◽  
Computational Results ◽  
Local Surface ◽  
Qualitative Comparison ◽  
Wave Groups ◽  
Fully Nonlinear ◽  
Nonlinear Simulations ◽  
Velocity Of Propagation ◽  
Steep Waves

A method was developed to carry out detailed qualitative comparison of fully nonlinear computations with the measurements of unidirectional wave groups. Computational results on evolving wave groups were compared with the available experiments. The local surface elevation variation, evolution of envelope shapes, the velocity of propagation of the steepest crests in the group and their relation to the height of the crests were obtained numerically and experimentally. The results shed additional light on the mechanisms leading to the breaking of steep waves.

scholarly journals Statistical state dynamics of vertically sheared horizontal flows in two-dimensional stratified turbulence

2018 ◽  
Vol 854 ◽  
pp. 544-590 ◽  
Author(s):  
Joseph G. Fitzgerald ◽  
Brian F. Farrell
Keyword(s):  
Large Scale ◽  
Second Order ◽  
Two Dimensional ◽  
Stratified Turbulence ◽  
Stochastic Excitation ◽  
Mean Flow ◽  
Fully Nonlinear ◽  
Statistical State ◽  
Horizontal Flows ◽  
Nonlinear Simulations

Simulations of strongly stratified turbulence often exhibit coherent large-scale structures called vertically sheared horizontal flows (VSHFs). VSHFs emerge in both two-dimensional (2D) and three-dimensional (3D) stratified turbulence with similar vertical structure. The mechanism responsible for VSHF formation is not fully understood. In this work, the formation and equilibration of VSHFs in a 2D Boussinesq model of stratified turbulence is studied using statistical state dynamics (SSD). In SSD, equations of motion are expressed directly in the statistical variables of the turbulent state. Restriction to 2D turbulence facilitates application of an analytically and computationally attractive implementation of SSD referred to as S3T, in which the SSD is expressed by coupling the equation for the horizontal mean structure with the equation for the ensemble mean perturbation covariance. This second-order SSD produces accurate statistics, through second order, when compared with fully nonlinear simulations. In particular, S3T captures the spontaneous emergence of the VSHF and associated density layers seen in simulations of turbulence maintained by homogeneous large-scale stochastic excitation. An advantage of the S3T system is that the VSHF formation mechanism, which is wave–mean flow interaction between the emergent VSHF and the stochastically excited large-scale gravity waves, is analytically understood in the S3T system. Comparison with fully nonlinear simulations verifies that S3T solutions accurately predict the scale selection, dependence on stochastic excitation strength, and nonlinear equilibrium structure of the VSHF. These results constitute a theory for VSHF formation applicable to interpreting simulations and observations of geophysical examples of turbulent jets such as the ocean’s equatorial deep jets.

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