A Numerical Study of Stratified Tidal Rectification over Finite-Amplitude Banks. Part I: Symmetric Banks

Abstract. The 2-D version of the non-hydrostatic fully compressible model MOLOCH developed at ISAC-CNR was used in idealized set-up to study the start-up and finite amplitude evolution of symmetric instability. The unstable basic state was designed by numerical integration of the equation which defines saturated equivalent potential vorticity qe*. We present the structure and growth rates of the linear modes both for a supersaturated initial state ("super"-linear mode) and for a saturated one ("pseudo"-linear mode) and the modifications induced on the base state by their finite amplitude evolution.

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Numerical study of the stabilisation of boundary-layer disturbances by finite amplitude streaks

International Journal of Flow Control ◽

10.1260/1756-8250.2.4.259 ◽

2010 ◽

Vol 2 (4) ◽

pp. 259-288 ◽

Cited By ~ 17

Author(s):

Philipp Schlatter ◽

Enrico Deusebio ◽

Rick de Lange ◽

Luca Brandt

Keyword(s):

Boundary Layer ◽

Numerical Study ◽

Finite Amplitude

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Centrifugal Instability and Mixing in the California Undercurrent

Journal of Physical Oceanography ◽

10.1175/jpo-d-13-0269.1 ◽

2015 ◽

Vol 45 (5) ◽

pp. 1224-1241 ◽

Cited By ~ 28

Author(s):

W. K. Dewar ◽

J. C. McWilliams ◽

M. J. Molemaker

Keyword(s):

Potential Energy ◽

Numerical Study ◽

Current System ◽

Finite Amplitude ◽

Relative Vorticity ◽

Monterey Bay ◽

Diapycnal Mixing ◽

California Current System ◽

Centrifugal Instability ◽

Lee Waves

AbstractA regional numerical study of the California Current System near Monterey Bay, California, is conducted using both hydrostatic and nonhydrostatic models. Frequent sighting of strong anticyclones (Cuddies) have occurred in the area, and previous studies have identified Monterey Bay as an apparent region of strong unbalanced flow generation. Here, by means of a downscaling exercise, a domain just downstream of Point Sur is analyzed and argued to be a preferred site of diapycnal mixing. The scenario suggested by the simulations involves the generation of negative relative vorticity in a bottom boundary layer of the California Undercurrent on the continental shelf break. At Point Sur, the current separates from the coast and moves into deep waters where it rapidly develops finite-amplitude instabilities. These manifest as isopycnal overturnings, but in contrast to the normal Kelvin–Helmholtz paradigm for mixing, this study argues that the instability is primarily centrifugal. The evidence for this comes from comparisons of the model with linear results for ageostrophic instabilities. Mixing increases background potential energy. The authors argue the regional potential energy generation near Point Sur in the upper few hundred meters is comparable to that found in open-ocean regions of strong diapycnal mixing, either by abyssal tides and lee waves near topography. This study computes diapycnal fluxes and estimates turbulent diffusivities to argue mixing by centrifugal instability is characterized by diffusivities O(10−4) m2 s−1, although the potential for contamination by explicit diffusivities exists.

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A numerical study of stratified tidal rectification

Continental Shelf Research ◽

10.1016/s0278-4343(99)00057-6 ◽

2000 ◽

Vol 20 (1) ◽

pp. 37-68 ◽

Cited By ~ 4

Author(s):

Nicolas Pérenne ◽

Annick Pichon ◽

Philippe Huet

Keyword(s):

Numerical Study ◽

Tidal Rectification

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Onset of Convection in a Horizontal Porous Layer Saturated by a Power-Law Fluid

Journal of Heat Transfer ◽

10.1115/1.4006244 ◽

2012 ◽

Vol 134 (9) ◽

Cited By ~ 9

Author(s):

Z. Alloui ◽

N. Ben Khelifa ◽

H. Beji ◽

P. Vasseur

Keyword(s):

Rayleigh Number ◽

Newtonian Fluid ◽

Power Law ◽

Numerical Study ◽

Flow Characteristics ◽

Finite Amplitude ◽

Parallel Flow ◽

Governing Equations ◽

Onset Of Convection ◽

Power Law Index

This paper investigates the onset of motion, and the subsequent finite-amplitude convection, in a shallow porous cavity filled with a non-Newtonian fluid. A power-law model is used to characterize the non-Newtonian fluid behavior of the saturating fluid. Constant fluxes of heat are imposed on the horizontal walls of the layer. The governing parameters of the problem under study are the Rayleigh number R, the power-law index n, and the aspect ratio of the cavity A. An analytical solution, valid for shallow enclosures (A ≫ 1), is derived on the basis of the parallel flow approximation. In the range of the governing parameters considered in this study, a good agreement is found between the analytical predictions and the numerical results obtained by solving the full governing equations. For dilatant fluids (n > 1), it is found that the onset of motion is linearly unstable, i.e., always occurs provided that the supercritical Rayleigh number RCsup≥0. For pseudoplastic fluids (n < 1), the supercritical Rayleigh number for the onset of motion is RCsup=∞. However, it is demonstrated, on the basis of the nonlinear parallel flow theory, that the onset of motion occurs above a subcritical Rayleigh number RCsub which depends upon the power-law index n. For finite-amplitude convection, the heat and flow characteristics predicted by the analytical model are found to agree well with a numerical study of the full governing equations.

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A NUMERICAL STUDY OF NONLINEAR PROPAGATION OF DISTURBANCES IN TWO-DIMENSIONS

Journal of Computational Acoustics ◽

10.1142/s0218396x9600009x ◽

1996 ◽

Vol 04 (03) ◽

pp. 291-319 ◽

Cited By ~ 6

Author(s):

TONY W.H. SHEU ◽

C.C. FANG

Keyword(s):

Acoustic Field ◽

Numerical Study ◽

Element Model ◽

Analytic Solutions ◽

Finite Amplitude ◽

Euler System ◽

Two Dimensions ◽

Nonlinear Propagation ◽

Characteristic Model ◽

Transport Problems

In the spirit of the method of characteristics, we present in this paper a generalized Taylor-Galerkin finite element model to simulate the nonlinear propagation of finite-amplitude disturbances. In a nonlinear Euler system, the multi-dimensional formulation is constructed through the conservation variables. Noticeable is that the scheme is found to exhibit high-phase-accuracy, together with minimal numerical damping. This scheme, therefore, is best-suited to simulation of disturbances in an acoustic field. To begin with, we validate the characteristic model by simulating two transport problems amenable to analytic solutions. Motivated by the apparent success, we apply the proposed third-order accurate upwind model to investigate a truly nonlinear acoustic field. The present analysis is intended to elucidate to what extent the nondissipative, nondispersive and isotropic characteristics pertaining to three wave modes of the acoustic system are still valid.

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Analysis of the Fluid Motion Induced by a Vibrating Lamina Through Free Surface-Lattice Boltzmann Coupled Method

Volume 9: Mechanics of Solids, Structures, and Fluids ◽

10.1115/imece2018-87715 ◽

2018 ◽

Author(s):

Daniele Chiappini ◽

Giovanni Di Ilio ◽

Gino Bella

Keyword(s):

Free Surface ◽

Lattice Boltzmann ◽

Parametric Analysis ◽

Numerical Study ◽

Fluid Motion ◽

Added Mass ◽

Finite Amplitude ◽

Viscous Damping ◽

Integrated Method ◽

Hydrodynamic Function

In this work, we perform a numerical study on the flow induced by the motion of a rigid cantilever beam undergoing finite amplitude oscillations, in a viscous fluid, under a free surface. To this aim, we use a lattice Boltzmann volume of fluid (LB-VOF) integrated method, which includes the tracking of the fluid surface. The adopted approach couples the simplicity of the LB method with the possibility to track the free surface by means of a VOF strategy. Through a parametric analysis, we study the effects related to the depth of submergence, for several values of the oscillation frequency and amplitude. Results are provided in terms of a complex hydrodynamic function, whose real and imaginary parts are the added mass and the viscous damping, respectively, acting on the lamina. Validation of the results is carried out by comparing the solution, for the limit case of lamina submerged in an infinite fluid, with those from available literature studies. We find that the presence of the free surface strongly influences the flow physics around the lamina, especially at low values of the depth of submergence. In facts, when the lamina approaches to the free surface, the fluid waves, generated by the motion of the lamina, interact with the oscillating body itself, giving rise to additional effects, which we quantify in terms of added mass and viscous damping.

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