scholarly journals Lifecycle of a Submesoscale Front Birthed from a Nearshore Internal Bore

2021 ◽  
Author(s):  
Sean R. Haney ◽  
Alexandra J. Simpson ◽  
Jacqueline M. McSweeney ◽  
Amy F. Waterhouse ◽  
Merrick C. Haller ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Wave Speed ◽  
Gravity Current ◽  
Gravity Currents ◽  
Coastal Ocean ◽  
Rossby Number ◽  
Lateral Shear ◽  
Turbulent Dissipation ◽  
Shear Instabilities ◽  
Internal Bore

AbstractThe ocean is home to many different submesoscale phenomena, including internal waves, fronts, and gravity currents. Each of these processes entail complex nonlinear dynamics, even in isolation. Here we present shipboard, moored, and remote observations of a submesoscale gravity current front created by a shoaling internal tidal bore in the coastal ocean. The internal bore is observed to flatten as it shoals, leaving behind a gravity current front that propagates significantly slower than the bore. We posit that the generation and separation of the front from the bore is related to particular stratification ahead of the bore, which allows the bore to reach the maximum possible internal wave speed. After the front is calved from the bore, it is observed to propagate as a gravity current for ≈4 hours, with associated elevated turbulent dissipation rates. A strong cross-shore gradient of along-shore velocity creates enhanced vertical vorticity (Rossby number ≈ 40) that remains locked with the front. Lateral shear instabilities develop along the front and may hasten its demise.

scholarly journals Gravity currents and internal waves in a stratified fluid

2008 ◽  
Vol 616 ◽  
pp. 327-356 ◽  
Author(s):  
BRIAN L. WHITE ◽  
KARL R. HELFRICH
Keyword(s):  
Internal Waves ◽  
Wave Speed ◽  
Numerical Solutions ◽  
Gravity Current ◽  
Gravity Currents ◽  
Stratified Fluid ◽  
Front Speed ◽  
Long Wave ◽  
Conjugate State ◽  
Energy Conserving

A steady theory is presented for gravity currents propagating with constant speed into a stratified fluid with a general density profile. Solution curves for front speed versus height have an energy-conserving upper bound (the conjugate state) and a lower bound marked by the onset of upstream influence. The conjugate state is the largest-amplitude nonlinear internal wave supported by the ambient stratification, and in the limit of weak stratification approaches Benjamin's energy-conserving gravity current solution. When the front speed becomes critical with respect to linear long waves generated above the current, steady solutions cannot be calculated, implying upstream influence. For non-uniform stratification, the critical long-wave speed exceeds the ambient long-wave speed, and the critical-Froude-number condition appropriate for uniform stratification must be generalized. The theoretical results demonstrate a clear connection between internal waves and gravity currents. The steady theory is also compared with non-hydrostatic numerical solutions of the full lock release initial-value problem. Some solutions resemble classic gravity currents with no upstream disturbance, but others show long internal waves propagating ahead of the gravity current. Wave generation generally occurs when the stratification and current speed are such that the steady gravity current theory fails. Thus the steady theory is consistent with the occurrence of either wave-generating or steady gravity solutions to the dam-break problem. When the available potential energy of the dam is large enough, the numerical simulations approach the energy-conserving conjugate state. Existing laboratory experiments for intrusions and gravity currents produced by full-depth lock exchange flows over a range of stratification profiles show excellent agreement with the conjugate state solutions.

Gravity currents and related phenomena

1968 ◽  
Vol 31 (2) ◽  
pp. 209-248 ◽  
Author(s):  
T. Brooke Benjamin
Keyword(s):  
Salt Water ◽  
Gravity Current ◽  
Circular Cross Section ◽  
Gravity Currents ◽  
Head Wave ◽  
Physical Problems ◽  
Energy Conserving ◽  
Fluid Theory ◽  
Hydrodynamical Problem ◽  
Upper Boundary

This paper presents a broad investigation into the properties of steady gravity currents, in so far as they can be represented by perfect-fluid theory and simple extensions of it (like the classical theory of hydraulic jumps) that give a rudimentary account of dissipation. As usually understood, a gravity current consists of a wedge of heavy fluid (e.g. salt water, cold air) intruding into an expanse of lighter fluid (fresh water, warm air); but it is pointed out in § 1 that, if the effects of viscosity and mixing of the fluids at the interface are ignored, the hydrodynamical problem is formally the same as that for an empty cavity advancing along the upper boundary of a liquid. Being simplest in detail, the latter problem is treated as a prototype for the class of physical problems under study: most of the analysis is related to it specifically, but the results thus obtained are immediately applicable to gravity currents by scaling the gravitational constant according to a simple rule.In § 2 the possible states of steady flow in the present category between fixed horizontal boundaries are examined on the assumption that the interface becomes horizontal far downstream. A certain range of flows appears to be possible when energy is dissipated; but in the absence of dissipation only one flow is possible, in which the asymptotic level of the interface is midway between the plane boundaries. The corresponding flow in a tube of circular cross-section is found in § 3, and the theory is shown to be in excellent agreement with the results of recent experiments by Zukoski. A discussion of the effects of surface tension is included in § 3. The two-dimensional energy-conserving flow is investigated further in § 4, and finally a close approximation to the shape of the interface is obtained. In § 5 the discussion turns to the question whether flows characterized by periodic wavetrains are realizable, and it appears that none is possible without a large loss of energy occurring. In § 6 the case of infinite total depth is considered, relating to deeply submerged gravity currents. It is shown that the flow must always feature a breaking ‘head wave’, and various properties of the resulting wake are demonstrated. Reasonable agreement is established with experimental results obtained by Keulegan and others.

Numerical simulations of lock-exchange compositional gravity current

2009 ◽  
Vol 635 ◽  
pp. 361-388 ◽  
Author(s):  
SENG KEAT OOI ◽  
GEORGE CONSTANTINESCU ◽  
LARRY WEBER
Keyword(s):  
High Resolution ◽  
Dissipation Rate ◽  
Friction Velocity ◽  
Gravity Current ◽  
Gravity Currents ◽  
Inviscid Limit ◽  
Grashof Number ◽  
Front Speed ◽  
Initial Volume ◽  
Bed Friction

Compositional gravity current flows produced by the instantaneous release of a finite-volume, heavier lock fluid in a rectangular horizontal plane channel are investigated using large eddy simulation. The first part of the paper focuses on the evolution of Boussinesq lock-exchange gravity currents with a large initial volume of the release during the slumping phase in which the front of the gravity current propagates with constant speed. High-resolution simulations are conducted for Grashof numbers $\sqrt {Gr}$ = 3150 (LGR simulation) and $\sqrt {Gr}$ = 126000 (HGR simulation). The Grashof number is defined with the channel depth h and the buoyancy velocity ub = $\sqrt {g'h}$ (g′ is the reduced gravity). In the HGR simulation the flow is turbulent in the regions behind the two fronts. Compared to the LGR simulation, the interfacial billows lose their coherence much more rapidly (over less than 2.5h behind the front), which results in a much faster decay of the large-scale content and turbulence intensity in the trailing regions of the flow. A slightly tilted, stably stratified interface layer develops away from the two fronts. The concentration profiles across this layer can be approximated by a hyperbolic tangent function. In the HGR simulation the energy budget shows that for t > 18h/ub the flow reaches a regime in which the total dissipation rate and the rates of change of the total potential and kinetic energies are constant in time. The second part of the paper focuses on the study of the transition of Boussinesq gravity currents with a small initial volume of the release to the buoyancy–inertia self-similar phase. When the existence of the back wall is communicated to the front, the front speed starts to decrease, and the current transitions to the buoyancy–inertia phase. Three high-resolution simulations are performed at Grashof numbers between $\sqrt {Gr}$ = 3 × 104 and $\sqrt {Gr}$ = 9 × 104. Additionally, a calculation at a much higher Grashof number ($\sqrt {Gr}$ = 106) is performed to understand the behaviour of a bottom-propagating current closer to the inviscid limit. The three-dimensional simulations correctly predict a front speed decrease proportional to t−α (the time t is measured from the release time) over the buoyancy–inertia phase, with the constant α approaching the theoretical value of 1/3 as the current approaches the inviscid limit. At Grashof numbers for which $\sqrt {Gr}$ > 3 × 104, the intensity of the turbulence in the near-wall region behind the front is large enough to induce the formation of a region containing streaks of low and high streamwise velocities. The streaks are present well into the buoyancy–inertia phase before the speed of the front decays below values at which the streaks can be sustained. The formation of the velocity streaks induces a streaky distribution of the bed friction velocity in the region immediately behind the front. This distribution becomes finer as the Grashof number increases. For simulations in which the only difference was the value of the Grashof number ($\sqrt {Gr}$ = 4.7 × 104 versus $\sqrt {Gr}$ = 106), analysis of the non-dimensional bed friction velocity distributions shows that the capacity of the gravity current to entrain sediment from the bed increases with the Grashof number. Past the later stages of the transition to the buoyancy–inertia phase, the temporal variations of the potential energy, the kinetic energy and the integral of the total dissipation rate are logarithmic.

scholarly journals Entrainment in Shallow Rotating Gravity Currents: A Modeling Study

2010 ◽  
Vol 40 (8) ◽  
pp. 1819-1834 ◽  
Author(s):  
Lars Umlauf ◽  
Lars Arneborg ◽  
Richard Hofmeister ◽  
Hans Burchard
Keyword(s):  
Froude Number ◽  
Gravity Current ◽  
Vertical Mixing ◽  
Spatial Separation ◽  
Gravity Currents ◽  
Transverse Jet ◽  
Entrainment Process ◽  
Set Up ◽  
Rotation Set ◽  
Bulk Parameters

Abstract The physics of shallow gravity currents passing through a rotating channel at subcritical Froude number is investigated here with a series of idealized numerical experiments. It is found that the combined effects of friction and rotation set up a complex transverse circulation that has some crucial implications for the entrainment process. A key component of this secondary circulation is a geostrophically balanced transverse jet in the interface that laterally drains fluid from the interface. This effect is shown to result in a strong cross-channel asymmetry and a spatial separation of the entrainment process: drained interfacial fluid is partly replaced by entrained ambient fluid on the deep side of the gravity current, whereas the downward mixing of buoyant fluid occurs on the shallow side. These results, closely corresponding to recent measurements in a shallow, channelized gravity current in the western Baltic Sea, illustrate that the description of entrainment as a strictly vertical mixing process with the help of local bulk parameters like the Froude number is not generally applicable in rotating gravity currents.

scholarly journals Axisymmetric viscous gravity currents flowing over a porous medium

2009 ◽  
Vol 622 ◽  
pp. 135-144 ◽  
Author(s):  
MELISSA J. SPANNUTH ◽  
JEROME A. NEUFELD ◽  
J. S. WETTLAUFER ◽  
M. GRAE WORSTER
Keyword(s):  
Porous Medium ◽  
Steady State ◽  
Gravity Current ◽  
Gravity Currents ◽  
Constant Input ◽  
Radial Extent ◽  
Vertically Aligned ◽  
Analytical Expressions ◽  
Permeability Structure ◽  
Good Agreement

We study the axisymmetric propagation of a viscous gravity current over a deep porous medium into which it also drains. A model for the propagation and drainage of the current is developed and solved numerically in the case of constant input from a point source. In this case, a steady state is possible in which drainage balances the input, and we present analytical expressions for the resulting steady profile and radial extent. We demonstrate good agreement between our experiments, which use a bed of vertically aligned tubes as the porous medium, and the theoretically predicted evolution and steady state. However, analogous experiments using glass beads as the porous medium exhibit a variety of unexpected behaviours, including overshoot of the steady-state radius and subsequent retreat, thus highlighting the importance of the porous medium geometry and permeability structure in these systems.

Modelling of an Internal Wave Gravity Current Using Eulers Equations

2002 ◽  
Author(s):  
Deborah J. Wood
Keyword(s):  
Internal Wave ◽  
Wave Speed ◽  
Gravity Current ◽  
Laboratory Scale ◽  
Navier Stokes ◽  
Linear Wave ◽  
Field Observations ◽  
Medium Density ◽  
Sloping Bottom

In nature where thermoclines exist an internal wave may form, and if a sloping bottom is also present then a gravity current may occur. In this study we use a Navier-Stokes solver to solve Eulers equations to simulate the generation and evolution of such a wave. The thermoclines used in this study are similar to those seen in nature except scaled down to the laboratory scale used by some ongoing experiments. We find that the Navier-Stokes solver generates and evolves a wave similar to experimental observations. The head of the gravity current is dominated by medium density fluid with the thermocline thickness growing and becoming thickest at the centre of the head. Maximum velocities of approximately 0.5 of the linear wave speed are found which are similar to experimental and field observations.

The Prediction of Velocity and Temperature Profiles in Gravity Currents for Use in Chilled Water Storage Tanks

1994 ◽  
Vol 116 (1) ◽  
pp. 83-90 ◽  
Author(s):  
J. T. Nakos
Keyword(s):  
Storage Tank ◽  
Gravity Current ◽  
Water Storage ◽  
Gravity Currents ◽  
The Body ◽  
Temperature Profiles ◽  
Singular Perturbation Method ◽  
Efficient Manner ◽  
Water Storage Tank ◽  
Chilled Water

It has been demonstrated that one way of producing thin thermoclines (temperature gradients) in a chilled water storage tank is by introducing the water horizontally in the form of a gravity current. A gravity current is a fluid intrusion into a body of stagnant fluid at a different density. The incoming fluid is introduced at the bottom of the body of fluid if it is more dense; it is introduced at the top if it is less dense. In the application considered here, chilled water is to be stored in an efficient manner under the original body of warmer water. Vertical profiles of velocity and temperature in transient, two-dimensional, laminar, thermally driven, constant inflow gravity currents are studied. This provides a basis for understanding the initial stages of the formation of a thermocline in a chilled water storage tank. Two laminar flow formulations were developed to predict velocity and temperature profiles in the inertia-buoyancy regime. One formulation uses a strictly numerical approach, while the other uses a singular perturbation method to analyze the flow. Experimental temperature profiles are compared with the results from both formulations, and show good agreement.

Propagation of viscous currents on a porous substrate with finite capillary entry pressure

2016 ◽  
Vol 801 ◽  
pp. 65-90 ◽  
Author(s):  
Roiy Sayag ◽  
Jerome A. Neufeld
Keyword(s):  
Laboratory Experiments ◽  
Gravity Current ◽  
Fluid Pressure ◽  
Analytical Techniques ◽  
Gravity Currents ◽  
Porous Substrate ◽  
Entry Pressure ◽  
Self Similar ◽  
Capillary Entry Pressure ◽  
Theoretical Results

We study the propagation of viscous gravity currents over a thin porous substrate with finite capillary entry pressure. Near the origin, where the current is deep, propagation of the current coincides with leakage through the substrate. Near the nose of the current, where the current is thin and the fluid pressure is below the capillary entry pressure, drainage is absent. Consequently the flow can be characterised by the evolution of drainage and fluid fronts. We analyse this flow using numerical and analytical techniques combined with laboratory-scale experiments. At early times, we find that the position of both fronts evolve as $t^{1/2}$, similar to an axisymmetric gravity current on an impermeable substrate. At later times, the growing effect of drainage inhibits spreading, causing the drainage front to logarithmically approach a steady position. In contrast, the asymptotic propagation of the fluid front is quasi-self-similar, having identical structure to the solution of gravity currents on an impermeable substrate, only with slowly varying fluid flux. We benchmark these theoretical results with laboratory experiments that are consistent with our modelling assumption, but that also highlight the detailed dynamics of drainage inhibited by finite capillary pressure.

Converging gravity currents over a permeable substrate

2015 ◽  
Vol 778 ◽  
pp. 669-690 ◽  
Author(s):  
Zhong Zheng ◽  
Sangwoo Shin ◽  
Howard A. Stone
Keyword(s):  
Power Law ◽  
Gravity Current ◽  
Gravity Currents ◽  
Numerical Predictions ◽  
Front Position ◽  
Dependent Position ◽  
Self Similar ◽  
Vertical Leakage ◽  
Similar Solutions ◽  
Lock Gate

We study the propagation of viscous gravity currents along a thin permeable substrate where slow vertical drainage is allowed from the boundary. In particular, we report the effect of this vertical fluid drainage on the second-kind self-similar solutions for the shape of the fluid–fluid interface in three contexts: (i) viscous axisymmetric gravity currents converging towards the centre of a cylindrical container; (ii) viscous gravity currents moving towards the origin in a horizontal Hele-Shaw channel with a power-law varying gap thickness in the horizontal direction; and (iii) viscous gravity currents propagating towards the origin of a porous medium with horizontal permeability and porosity gradients in power-law forms. For each of these cases with vertical leakage, we identify a regime diagram that characterizes whether the front reaches the origin or not; in particular, when the front does not reach the origin, we calculate the final location of the front. We have also conducted laboratory experiments with a cylindrical lock gate to generate a converging viscous gravity current where vertical fluid drainage is allowed from various perforated horizontal substrates. The time-dependent position of the propagating front is captured from the experiments, and the front position is found to agree well with the theoretical and numerical predictions when surface tension effects can be neglected.

Front dynamics and entrainment of finite circular gravity currents on an unbounded uniform slope

2016 ◽  
Vol 801 ◽  
pp. 322-352 ◽  
Author(s):  
N. Zgheib ◽  
A. Ooi ◽  
S. Balachandar
Keyword(s):  
Froude Number ◽  
Temporal Evolution ◽  
Gravity Current ◽  
Gravity Currents ◽  
Front Velocity ◽  
Acceleration Phase ◽  
Simple Method ◽  
Entrainment Coefficient ◽  
Converging Flow ◽  
Front Dynamics

We report on the dynamics of circular finite-release Boussinesq gravity currents on a uniform slope. The study comprises a series of highly resolved direct numerical simulations for a range of slope angles between $5^{\circ }$ and $20^{\circ }$. The simulations were fixed at Reynolds number $Re=5000$ for all slopes considered. The temporal evolution of the front is compared to available experimental data. One of the interesting aspects of this study is the detection of a converging flow towards the centre of the gravity current. This converging flow is a result of the finite volume of the release coupled with the presence of a sloping boundary, which results in a second acceleration phase in the front velocity of the current. The details of the dynamics of this second acceleration and the redistribution of material in the current leading to its development will be discussed. These finite-release currents are invariably dominated by the head where most of the mixing and ambient entrainment occurs. We propose a simple method for defining the head of the current from which we extract various properties including the front Froude number and entrainment coefficient. The Froude number is seen to increase with steeper slopes, whereas the entrainment coefficient is observed to be weakly dependent on the bottom slope.

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