scholarly journals Bathymetric Influences on the Estuarine Equilibrium Length and Adjustment Time

2017 ◽  
Vol 47 (7) ◽  
pp. 1719-1736
Author(s):  
Shih-Nan Chen
Keyword(s):  
Numerical Solutions ◽  
Salt Content ◽  
Length Change ◽  
Adjustment Process ◽  
Adjustment Time ◽  
Variable Sensitivity ◽  
Equilibrium Length ◽  
Averaged Model ◽  
Bathymetric Changes ◽  
Sloping Bottom

AbstractLinear theories are extended to enable investigations of how exponentially convergent width and sloping bottom affect the sensitivity of estuarine equilibrium length and adjustment time. This study focuses on the response to river forcing and considers a regime dominated by gravitational circulation, but the results are generalizable. For a range of forcing and bathymetric profiles, the predicted equilibrium length and adjustment time compare favorably with numerical solutions from a width-averaged model. The main findings are that 1) convergent width and sloping bottom reduce the sensitivity of equilibrium length to river forcing. The sensitivity is governed by a dimensionless parameter that measures the degree of width and depth changes sampled by the intrusion length. Hence, the sensitivity is not a constant in a system but varies with forcing: when discharge increases, a shortened estuary experiences less bathymetric changes over its intrusion. The sensitivity therefore increases progressively toward the conventional −⅓ power law. An observational example of variable sensitivity from Delaware Bay is given. 2) Width convergence and bottom slope help accelerate the adjustment process. It is shown that the linear adjustment time is set by the ratio of salt content variations to the discharge perturbation. Hence, under the same forcing, the adjustment time is controlled by the salt content variations, which decrease monotonically with increasing convergence and slope. This means that, to achieve a given length change, a more strongly convergent and sloped system simply requires transport of less salt, thereby needing a shorter adjustment time.

scholarly journals Using an Isohaline Flux Analysis to Predict the Salt Content in an Unsteady Estuary

2017 ◽  
Vol 47 (11) ◽  
pp. 2811-2828 ◽  
Author(s):  
Matthew D. Rayson ◽  
Edward S. Gross ◽  
Robert D. Hetland ◽  
Oliver B. Fringer
Keyword(s):  
River Flow ◽  
Salt Content ◽  
Box Model ◽  
Flux Analysis ◽  
Galveston Bay ◽  
Exchange Flow ◽  
Salt Intrusion ◽  
Adjustment Time ◽  
The Mean ◽  
Salinity Difference

AbstractAn estuary is classified as unsteady when the salinity adjustment time is longer than the forcing time scale. Predicting salt content or salt intrusion length using scaling arguments based on a steady-state relationship between flow and salinity is inaccurate in these systems. In this study, a time-dependent salinity box model based on an unsteady Knudsen balance is used to demonstrate the effects of river flow, inward total exchange flow (tidal plus steady), and the salinity difference between inflow and outflow on the salt balance. A key component of the box model is a relationship that links the normalized difference between inflowing and outflowing salinity at the mouth and the mean salinity content. The normalized salinity difference is shown to be proportional to the mean salinity squared, based on theoretical arguments from the literature. The box model is validated by hindcasting 5 years of mean salinity in Galveston Bay (estimated from coarse observations) in response to highly variable river discharge. It is shown that this estuary typically has a long adjustment time relative to the forcing time scales, and, therefore, the volume-averaged salinity rarely reaches equilibrium. The box model highlights the reasons why the adjustment time in a large, partially mixed estuary like Galveston Bay is slower when the mean salt content is higher. Furthermore, it elucidates why the salt content in the estuary is more responsive to changes in river flow than in landward exchange flow at the estuary mouth, even though the latter quantity is usually several times larger.

The spin-up of fluid in a rectangular container with sloping bottom

1994 ◽  
Vol 265 ◽  
pp. 125-159 ◽  
Author(s):  
G. J. F. Van Heijst ◽  
L. R. M. Maas ◽  
C. W. M. Williams
Keyword(s):  
Bottom Topography ◽  
Fluid Motion ◽  
Adjustment Process ◽  
Ultimate State ◽  
Cyclonic Vorticity ◽  
Absolute Vorticity ◽  
Flow Cells ◽  
Dependent Part ◽  
Starting Flow ◽  
Sloping Bottom

The spin-up from rest of a homogeneous free-surface fluid contained in a rectangular tank with an inclined bottom has been studied in the laboratory. As in the case of a tank without bottom topography, it is found that in the spin-up process leading to the ultimate state of rigid-body rotation a number of stages can be distinguished, these being (i) the starting flow, characterized by zero absolute vorticity, (ii) the viscous generation of cyclonic vorticity at the lateral tank walls, leading to flow separation, and (iii) the formation of cyclonic and anticyclonic flow cells, which show a complicated interaction. When the topography steepness is small, these cells become organized in a regular array similar to what is observed in the non-sloping bottom case. For steeper topography, however, no organization into a regular cellular pattern is observed, and the relative fluid motion remains unsteady and irregular until eventually it has decayed owing to the spin-ip/spin-down mechanism provided by the Ekman layer at the tank bottom. During the first stage of the adjustment process the starting flow takes on the appearance of a large anticyclonic cell that fills the fluid domain entirely. Depending on the ratio of the horizontal and vertical lengthscales of the tank this cell is either symmetric or asymmetric, with a higher density of streamlines in the deeper part of the tank. The coupled vorticity equation, governing the depth-independent part of the starting flow, and the potential equation describing its depth-dependent part have been solved analytically, and the comparison between these results and observational data is generally good.

Transient response of a compressible fluid in a rapidly rotating circular pipe

2001 ◽  
Vol 427 ◽  
pp. 275-297 ◽  
Author(s):  
JUN SANG PARK ◽  
JAE MIN HYUN
Keyword(s):  
Angular Momentum ◽  
Analytical Solutions ◽  
Compressible Fluid ◽  
Numerical Solutions ◽  
Fluid Motion ◽  
Temperature Fields ◽  
Adjustment Process ◽  
Formal Stability ◽  
Entire Flow ◽  
Heavy Gas

The transient adjustment process of a compressible fluid in a rapidly rotating pipe is studied. The system Ekman number E is small, and the assumptions of small Mach number and the heavy-gas limit (γ = 1.0) are invoked. Fluid motion is generated by imposing a step-change perturbation in the temperature at the pipe wall Tw. Comprehensive analytical solutions are obtained by deploying the matched asymptotic technique with proper timescales O(E−1/2) and O(E−1). These analytical solutions are shown to be consistent with corresponding full numerical solutions. The detailed profiles of major variables are delineated, and evolution of velocity and temperature fields is portrayed. At moderate times, the entire flow field can be divided into two regions. In the inner inviscid region, thermo-acoustic compression takes place, and the process is isothermal–isentropic with the angular momentum being conserved. In the outer viscous region, diffusion of angular momentum occurs. The principal dynamic mechanisms are discussed, and physical rationalizations are offered. The essential differences between the responses of a compressible and an incompressible fluid are highlighted.The issue of stability of the analytically obtained flow is addressed by undertaking a formal stability analysis. It is illustrated that, within the range of parameters of present concern, the flow is stable when ε ∼ O(E).

Laboratory experiments and a non-harmonic theory for topographic Rossby waves over a linearly sloping bottom on the f-plane

2010 ◽  
Vol 645 ◽  
pp. 479-496 ◽  
Author(s):  
YAIR COHEN ◽  
NATHAN PALDOR ◽  
JOËL SOMMERIA
Keyword(s):  
Eigenvalue Problem ◽  
Laboratory Experiments ◽  
Numerical Solutions ◽  
Order Approximation ◽  
Low Frequency ◽  
Phase Speed ◽  
Wave Trapping ◽  
The Cross ◽  
The Waves ◽  
Sloping Bottom

Low-frequency waves that develop in a shallow layer of fluid, contained in a channel with linearly slopping bottom and rotating with uniform angular speed are investigated theoretically and experimentally. Exact numerical solutions of the eigenvalue problem, obtained from the linearized shallow water equations on the f-plane, show that the waves are trapped near the channel's shallow wall and propagate along it with the shallow side on their right in the Northern hemisphere. The phase speed of the waves is slower compared with that of the harmonic theory in which bottom slope is treated inconsistently. A first-order approximation of the cross-channel dependence of the coefficient in the eigenvalue equation yields an approximation of the cross-channel velocity eigenfunction as an Airy function, which, for sufficiently wide channels, yields an explicit expression for the wave's dispersion relation. The analytic solutions of the eigenvalue problem agree with the numerical solutions in both the wave trapping and the reduced phase speed. For narrow channels, our theory yields an estimate of the channel width below which the harmonic theory provides a more accurate approximation. Laboratory experiments were conducted on a 13 m diameter turntable at LEGI-Coriolis (France) into which a linearly sloping bottom of 10 % incline was installed. A wavemaker generated waves of known frequency at one end of the turntable and the wavenumbers of these waves were measured at the opposite end using a particle imaging velocimetry technique. The experimental results regarding the phase speed and the radial structure of the amplitude are in very good agreement with our theoretical non-harmonic predictions, which support the present modification of the harmonic theory in wide channels.

IL-1β decreases the elastic modulus of human tenocytes

2006 ◽  
Vol 101 (1) ◽  
pp. 189-195 ◽  
Author(s):  
Jie Qi ◽  
Ann Marie Fox ◽  
Leonidas G. Alexopoulos ◽  
Liqun Chi ◽  
Donald Bynum ◽  
...  
Keyword(s):  
Extracellular Matrix ◽  
Young’S Modulus ◽  
Mechanical Loading ◽  
Actin Filaments ◽  
Young's Modulus ◽  
Length Change ◽  
Cellular Responses ◽  
Cell Stiffness ◽  
Mechanical Stimuli ◽  
Equilibrium Length

Cellular responses to mechanical stimuli are regulated by interactions with the extracellular matrix, which, in turn, are strongly influenced by the degree of cell stiffness (Young's modulus). It was hypothesized that a more elastic cell could better withstand the rigors of remodeling and mechanical loading. It was further hypothesized that interleukin-1β (IL-1β) would modulate intracellular cytoskeleton polymerization and regulate cell stiffness. The purpose of this study was to investigate the utility of IL-1β to alter the Young's modulus of human tenocytes. Young's modulus is the ratio of the stress to the strain, E = stress/strain = (F/ A)/(Δ L/ L0), where L0 is the equilibrium length, Δ L is the length change under the applied stress, F is the force applied, and A is the area over which the force is applied. Human tenocytes were incubated with 100 pM recombinant human IL-1β for 5 days. The Young's modulus was reduced by 27–63%. Actin filaments were disrupted in >75% of IL-1β-treated cells, resulting in a stellate shape. In contrast, immunostaining of α-tubulin showed increased intensity in IL-1β-treated tenocytes. Human tenocytes in IL-1β-treated bioartificial tendons were more tolerant to mechanical loading than were untreated counterparts. These results indicate that IL-1β reduced the Young's modulus of human tenocytes by disrupting the cytoskeleton and/or downregulating the expression of actin and upregulating the expression of tubulins. The reduction in cell modulus may help cells to survive excessive mechanical loading that may occur in damaged or healing tendons.

scholarly journals Cusp-like free-surface flows due to a submerged source or sink in the presence of a flat or sloping bottom

1985 ◽  
Vol 26 (4) ◽  
pp. 470-486 ◽  
Author(s):  
G. C. Hocking
Keyword(s):  
Free Surface ◽  
Line Source ◽  
Numerical Solutions ◽  
Free Surface Flows ◽  
Surface Flows ◽  
Sloping Bottom

AbstractSolutions are found to several problems involving a line source or sink beneath a cusped free surface, over several different impermeable bases. These are compared with known exact and numerical solutions, and with other work, both theoretical and experimental, on similar problems.

scholarly journals Some New Aspects of the Joint Effect of Rotation and Topography on Internal Solitary Waves

2019 ◽  
Vol 49 (6) ◽  
pp. 1639-1649 ◽  
Author(s):  
Lev A. Ostrovsky ◽  
Karl R. Helfrich
Keyword(s):  
Solitary Wave ◽  
Variable Coefficient ◽  
Asymptotic Theory ◽  
Numerical Solutions ◽  
Lower Layer ◽  
Joint Effect ◽  
Layer Depth ◽  
Adiabatic Evolution ◽  
Qualitative And Quantitative ◽  
Sloping Bottom

AbstractUsing a recently developed asymptotic theory of internal solitary wave propagation over a sloping bottom in a rotating ocean, some new qualitative and quantitative features of this process are analyzed for internal waves in a two-layer ocean. The interplay between different singularities—terminal damping due to radiation and disappearing quadratic nonlinearity, and reaching an “internal beach” (e.g., zero lower-layer depth)—is discussed. Examples of the adiabatic evolution of a single solitary wave over a uniformly sloping bottom under realistic conditions are considered in more detail and compared with numerical solutions of the variable-coefficient, rotation-modified Korteweg–de Vries (rKdV) equation.

scholarly journals Numerical Study of the Elastic Pendulum on the Rotating Earth

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Aleš Stanovnik ◽  
Borut Jurcic-Zlobec
Keyword(s):  
Numerical Solutions ◽  
Numerical Study ◽  
Nonlinear Differential Equations ◽  
String Length ◽  
Foucault Pendulum ◽  
First Case ◽  
Equilibrium Length ◽  
Local Observer ◽  
Oscillation Plane ◽  
Elastic Pendulum

The elastic pendulum is a simple physical system represented by nonlinear differential equations. Analytical solutions for the bob trajectories on the rotating earth may be obtained in two limiting cases: for the ideally elastic pendulum with zero unstressed string length and for the Foucault pendulum with an inextensible string. The precession period of the oscillation plane, as seen by the local observer on the rotating earth, is 24 hours in the first case and has a well-known latitude dependence in the second case. In the present work, we have obtained numerical solutions of the nonlinear equations for different string elasticities in order to study the transition from one precession period to the other. It is found that the transition is abrupt and that it occurs for a quite small perturbation of the ideally elastic pendulum, that is, for the unstressed string length equal to about 10−4 of the equilibrium length due to the weight of the bob.

scholarly journals Interaction of near-inertial waves with an anticyclonic vortex

2021 ◽  
Author(s):  
Hossein A. Kafiabad ◽  
Jacques Vanneste ◽  
William R. Young
Keyword(s):  
Numerical Solutions ◽  
Energy Levels ◽  
Three Dimensional ◽  
Boussinesq Equations ◽  
Kinetic Energy Density ◽  
Nonlinear Feedback ◽  
Inertial Waves ◽  
Energy Signature ◽  
Averaged Model ◽  
The Waves

AbstractAnticyclonic vortices focus and trap near-inertial waves so that near-inertial energy levels are elevated within the vortex core. Some aspects of this process, including the nonlinear modification of the vortex by the wave, are explained by the existence of trapped near-inertial eigenmodes. These vortex eigenmodes are easily excited by an initialwave with horizontal scale much larger than that of the vortex radius. We study this process using a wave-averaged model of near-inertial dynamics and compare its theoretical predictions with numerical solutions of the three-dimensional Boussinesq equations. In the linear approximation, the model predicts the eigenmode frequencies and spatial structures, and a near-inertial wave energy signature that is characterized by an approximately time-periodic, azimuthally invariant pattern. The wave-averaged model represents the nonlinear feedback of the waves on the vortex via a wave-induced contribution to the potential vorticity that is proportional to the Laplacian of the kinetic energy density of the waves. When this is taken into account, the modal frequency is predicted to increase linearly with the energy of the initial excitation. Both linear and nonlinear predictions agree convincingly with the Boussinesq results.

Transient Buoyant Convection of a Contained Fluid Driven by the Changes in the Boundary Temperatures

1985 ◽  
Vol 52 (1) ◽  
pp. 193-198 ◽  
Author(s):  
J. M. Hyun
Keyword(s):  
Time Scale ◽  
Numerical Solutions ◽  
Temperature Fields ◽  
Adjustment Process ◽  
Final State ◽  
Vertical Coordinate ◽  
Buoyant Convection ◽  
Contour Maps ◽  
Boussinesq Fluid ◽  
The Impact

Finite-difference numerical solutions are obtained for transient buoyant convection at high Rayleigh numbers of a Boussinesq fluid in a closed cylinder. We consider the linear motions that occur due to a small change in the boundary temperature profiles linear in the vertical coordinate. Previous theoretical studies showed that the meridional circulation, driven by the sidewall boundary layer pumping, brings about the final state on a time scale th = Ra1/4 N−1, where N is the Brunt-Va¨isa¨la¨ frequency. By choosing th as the time scale of interest, the theory filters out the internal-gravity oscillations of time scale N−1. New details on the radial and vertical structures of the flow and temperature fields are presented. The impact of the internal-gravity oscillations on the temperature field is shown to be minor. However, the evolution of the velocities is highly oscillatory in time due to the dominant presence of the internal-gravity oscillations. Numerically calculated contour maps of the temperature and stream function are constructed, which illustrate the effect of Ra on the flow patterns and on the temperature adjustment process.

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