Tidal Currents and Estuarine-Type Circulation in Johnstone Strait, British Columbia

Four months of current meter observations across the western basin of Johnstone Strait have been examined, with particular attention given to the mean flow and to variations at tidal frequencies. We show that the time-averaged motions are typical of a moderately stratified estuary driven by tidal mixing and nonlinear advection. Steady currents are nearly unidirectional at all depths with the net outflow in the upper layer essentially balanced by a net inflow in the lower layer to order 103 m3∙s−1. In addition, the relatively small variation in residual current speed is found to decrease with depth and to be associated mostly with the quasi-fortnightly tidal cycle. Near the surface the variance in the residual flow appears to be related to along-channel winds whose speeds and duration exceed 6 m∙s−1 and 24 h, respectively. Time-dependent motions are dominated by the tidal signal which is mixed, predominately semidiurnal. Maximum speeds of order 1 m∙s−1 are found at depth and are generally 1.5–1.7 times larger than in the upper layer. There is also a strong correlation between the tidal current speeds below 150-m depth and the local tide height lagged by 6 h. It is suggested that these large lower layer currents are associated with baroclinic motions being generated by the barotropic tide propagating over the rapidly shoaling bathymetry to the east of the observation region.

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On strongly nonlinear gravity waves in a vertically sheared atmosphere

Mathematics of Climate and Weather Forecasting ◽

10.1515/mcwf-2020-0103 ◽

2020 ◽

Vol 6 (1) ◽

pp. 63-74

Author(s):

Mark Schlutow ◽

Georg S. Voelker

Keyword(s):

Gravity Waves ◽

Lower Layer ◽

Vertical Shear ◽

Horizontal Wind ◽

Necessary Condition ◽

Mean Flow ◽

Individual Layer ◽

Strongly Nonlinear ◽

The Mean ◽

The Stability

Abstract We investigate strongly nonlinear stationary gravity waves which experience refraction due to a thin vertical shear layer of horizontal background wind. The velocity amplitude of the waves is of the same order of magnitude as the background flow and hence the self-induced mean flow alters the modulation properties to leading order. In this theoretical study, we show that the stability of such a refracted wave depends on the classical modulation stability criterion for each individual layer, above and below the shearing. Additionally, the stability is conditioned by novel instability criteria providing bounds on the mean-flow horizontal wind and the amplitude of the wave. A necessary condition for instability is that the mean-flow horizontal wind in the upper layer is stronger than the wind in the lower layer.

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Instabilities of buoyancy-driven coastal currents and their nonlinear evolution in the two-layer rotating shallow water model. Part 2. Active lower layer

Journal of Fluid Mechanics ◽

10.1017/s0022112010003903 ◽

2010 ◽

Vol 665 ◽

pp. 209-237 ◽

Cited By ~ 17

Author(s):

J. GULA ◽

V. ZEITLIN ◽

F. BOUCHUT

Keyword(s):

Shallow Water ◽

Linear Stability ◽

Nonlinear Evolution ◽

Lower Layer ◽

Short Wave ◽

Finite Volume Scheme ◽

Coastal Currents ◽

Mean Flow ◽

The Mean ◽

Rotating Shallow Water

This paper is the second part of the work on linear and nonlinear stability of buoyancy-driven coastal currents. Part 1, concerning a passive lower layer, was presented in the companion paper Gula & Zeitlin (J. Fluid Mech., vol. 659, 2010, p. 69). In this part, we use a fully baroclinic two-layer model, with active lower layer. We revisit the linear stability problem for coastal currents and study the nonlinear evolution of the instabilities with the help of high-resolution direct numerical simulations. We show how nonlinear saturation of the ageostrophic instabilities leads to reorganization of the mean flow and emergence of coherent vortices. We follow the same lines as in Part 1 and, first, perform a complete linear stability analysis of the baroclinic coastal currents for various depths and density ratios. We then study the nonlinear evolution of the unstable modes with the help of the recent efficient two-layer generalization of the one-layer well-balanced finite-volume scheme for rotating shallow water equations, which allows the treatment of outcropping and loss of hyperbolicity associated with shear, Kelvin–Helmholtz type, instabilities. The previous single-layer results are recovered in the limit of large depth ratios. For depth ratios of order one, new baroclinic long-wave instabilities come into play due to the resonances among Rossby and frontal- or coastal-trapped waves. These instabilities saturate by forming coherent baroclinic vortices, and lead to a complete reorganization of the initial current. As in Part 1, Kelvin fronts play an important role in this process. For even smaller depth ratios, short-wave shear instabilities with large growth rates rapidly develop. We show that at the nonlinear stage they produce short-wave meanders with enhanced dissipation. However, they do not change, globally, the structure of the mean flow which undergoes secondary large-scale instabilities leading to coherent vortex formation and cutoff.

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Overtransmission of Rossby Waves at a Lower-Layer Critical Latitude in the Two-Layer Model

Journal of the Atmospheric Sciences ◽

10.1175/jas-d-19-0055.1 ◽

2020 ◽

Vol 77 (3) ◽

pp. 859-870 ◽

Cited By ~ 1

Author(s):

Matthew T. Gliatto ◽

Isaac M. Held

Keyword(s):

Rossby Waves ◽

Lower Layer ◽

Scattering Problem ◽

Lower Troposphere ◽

Vertical Shear ◽

Mean Flow ◽

External Mode ◽

The Mean ◽

Critical Latitude ◽

Pv Gradient

Abstract Rossby waves, propagating from the midlatitudes toward the tropics, are typically absorbed by critical latitudes (CLs) in the upper troposphere. However, these waves typically encounter CLs in the lower troposphere first. We study a two-layer linear scattering problem to examine the effects of lower CLs on these waves. We begin with a review of the simpler barotropic case to orient the reader. We then progress to the baroclinic case using a two-layer quasigeostrophic model in which there is vertical shear in the mean flow on which the waves propagate, and in which the incident wave is assumed to be an external-mode Rossby wave. We use linearized equations and add small damping to remove the critical-latitude singularities. We consider cases in which either there is only one CL, in the lower layer, or there are CLs in both layers, with the lower-layer CL encountered first. If there is only a CL in the lower layer, the wave’s response depends on the sign of the mean potential vorticity gradient at this lower-layer CL: if the PV gradient is positive, then the CL partially absorbs the wave, as in the barotropic case, while for a negative PV gradient, the CL is a wave emitter, and can potentially produce overreflection and/or overtransmission. Our numerical results indicate that overtransmission is by far the dominant response in these cases. When an upper-layer absorbing CL is encountered, following the lower-layer encounter, one can still see the signature of overtransmission at the lower-layer CL.

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Eddy fluxes and topography in stratified quasi-geostrophic models

Journal of Fluid Mechanics ◽

10.1017/s0022112098003656 ◽

1999 ◽

Vol 380 ◽

pp. 59-80 ◽

Cited By ~ 12

Author(s):

WILLIAM J. MERRYFIELD ◽

GREG HOLLOWAY

Keyword(s):

Layer Thickness ◽

Stream Function ◽

Potential Vorticity ◽

Lower Layer ◽

Stratified Flow ◽

Mean Flow ◽

Random Forcing ◽

Flow Over Topography ◽

Eddy Fluxes ◽

The Mean

Turbulent stratified flow over topography is studied using layered quasi-geostrophic models. Mean flows develop under random forcing, with lower-layer mean stream-function positively correlated with topography. When friction is sufficiently small, upper-layer mean flow is weaker than, but otherwise resembles, lower-layer mean flow. When lower-layer friction is larger, upper-layer mean flow reverses and can exceed lower-layer mean flow in strength. The mean interface between layers is domed over topographic elevations. Eddy fluxes of potential vorticity and layer thickness act in the sense of driving the flow toward higher entropy. Such behaviour contradicts usual eddy parameterizations, to which modifications are suggested.

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Monthly-mean residual flows through the Dover Strait, 1949–1972

Journal of the Marine Biological Association of the United Kingdom ◽

10.1017/s0025315400056897 ◽

1978 ◽

Vol 58 (4) ◽

pp. 965-973 ◽

Cited By ~ 32

Author(s):

D. Prandle

Keyword(s):

Time Series ◽

North Sea ◽

Marine Biology ◽

Small Variation ◽

Mean Value ◽

Residual Flow ◽

Mean Flow ◽

The North ◽

The North Sea ◽

The Mean

An estimate is made of the mean value of residual flow through the Dover Strait for each month over the 24–year period from 1949 to 1972. The estimates are based on results from a modelling investigation by Prandle (1978) where it was shown that the residual flow consists of three components, (a) a tidal residual, (b), a wind-driven residual and (c) a flow due to a long-term gradient in mean sea level. The components (a) and (c) are assumed to be constant and the value of (b) is deduced using wind data recorded by Dutch Light Vessels located in the southern North Sea.The mean flow over the whole period amounts to 155 × 103 m3 s–1 into the North Sea with a maximum value of 364 x 103 m3 s–1 and a minimum of – 15 × 103 m3 s–1 (out of the North Sea). One notable feature of the complete time series is the surprisingly small variation in the annual mean flows; perhaps this stability in the annual flow is of significance to the marine biology of the area.The validity of the computed time series is established by reference to comparable data including a 9–year record, from cross-channel submarine cables, of the potential induced by the flow of water through the Earth's magnetic field. Additional comparisons are also made with the results of a previous study of daily-mean flows.

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Impact of the dense water flow over the sloping bottom on the open-sea circulation: Laboratory experiments and the Ionian Sea (Mediterranean) example

10.5194/os-2020-122 ◽

2021 ◽

Author(s):

Miroslav Gačić ◽

Laura Ursella ◽

Vedrana Kovačević ◽

Milena Menna ◽

Vlado Malačič ◽

...

Keyword(s):

Kinetic Energy ◽

Laboratory Experiments ◽

Lower Layer ◽

Water Injection ◽

Ionian Sea ◽

Mean Flow ◽

Flat Bottom ◽

Dense Water ◽

Open Sea ◽

The Mean

Abstract. The North Ionian Gyre (NIG) displays prominent inversions on decadal scales. We investigate the role of internal forcing, induced by changes of the horizontal pressure gradient due to the varying density of the Adriatic Deep Water (AdDW), that spreads into the deep layers of the Northern Ionian Sea. In turn, the AdDW density fluctuates according to the circulation of the NIG through a feedback mechanism named Bimodal Oscillating System. We set up laboratory experiments with a two-layer ambient fluid in a circular rotating tank, where densities of 1000/1015 kg m−3 characterise the upper/lower layer, respectively. From the potential vorticity evolution during the dense water outflow from a marginal sea, we analyse the response of the open-sea circulation to the along-slope dense water flow. In addition, we show some features of the cyclonic/anticyclonic eddies that form in the upper layer over the slope area. We illustrate the outcome of the experiments of varying density and varying discharge rates associated with the dense water injection. When the density is high, 1020 kg m−3, and the discharge is large, the kinetic energy of the mean flow is stronger than the eddy kinetic energy. On the other hand, when the density is smaller, 1010 kg m−3, and the discharge is reduced, vortices are more energetic than the mean flow, that is, the eddy kinetic energy is larger than the kinetic energy of the mean flow. In general, over the slope, following the onset of the dense water injection, the cyclonic vorticity associated with a current shear develops in the upper layer. The vorticity behaves in a two-layer fashion, thus becoming anticyclonic in the lower layer of the slope area. Concurrently, over the deep flat-bottom portion of the basin, a large-scale anticyclonic gyre forms in the upper layer extending partly toward a sloping rim. Density record shows the rise of the pycnocline due to the dense water sinking toward the flat-bottom portion of the tank. We show that the rate of increase of the anticyclonic potential vorticity is proportional to the rate of the rise of the interface, namely, to the rate of decrease of the upper layer thickness (i.e., the upper layer squeezing). The comparison of laboratory experiments with the Ionian Sea is made for a situation when the sudden switch from the cyclonic to the anticyclonic basin-wide circulation took place following the extremely dense Adriatic water overflow after the harsh winter in 2012. We show how similar are the temporal evolution and the vertical structure in both laboratory and oceanic conditions. The demonstrated similarity further supports the assertion that the wind-stress curl over the Ionian Sea is not of paramount importance in generating basin-wide circulation inversions, as compared to the internal forcing.

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Eddy forcing of the mean flow in the Southern Ocean

Journal of Geophysical Research Atmospheres ◽

10.1029/1999jc900332 ◽

2001 ◽

Vol 106 (C2) ◽

pp. 2713-2722 ◽

Cited By ~ 3

Author(s):

Chris W. Hughes

Keyword(s):

Southern Ocean ◽

Mean Flow ◽

The Mean

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Simple explicit model of liquid mean flow in region above axial impeller

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19852396 ◽

1985 ◽

Vol 50 (11) ◽

pp. 2396-2410

Author(s):

Miloslav Hošťálek ◽

Ivan Fořt

Keyword(s):

Vortex Flow ◽

Flow Model ◽

Quantitative Agreement ◽

Mean Flow ◽

Flat Bottom ◽

Proposed Model ◽

Minimum Number ◽

The Mean ◽

Model Equations ◽

Radial Circulation

The study describes a method of modelling axial-radial circulation in a tank with an axial impeller and radial baffles. The proposed model is based on the analytical solution of the equation for vortex transport in the mean flow of turbulent liquid. The obtained vortex flow model is tested by the results of experiments carried out in a tank of diameter 1 m and with the bottom in the shape of truncated cone as well as by the data published for the vessel of diameter 0.29 m with flat bottom. Though the model equations are expressed in a simple form, good qualitative and even quantitative agreement of the model with reality is stated. Apart from its simplicity, the model has other advantages: minimum number of experimental data necessary for the completion of boundary conditions and integral nature of these data.

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Technical note: Inherent benchmark or not? Comparing Nash–Sutcliffe and Kling–Gupta efficiency scores

Hydrology and Earth System Sciences ◽

10.5194/hess-23-4323-2019 ◽

2019 ◽

Vol 23 (10) ◽

pp. 4323-4331 ◽

Cited By ~ 60

Author(s):

Wouter J. M. Knoben ◽

Jim E. Freer ◽

Ross A. Woods

Keyword(s):

Time Series ◽

Coefficient Of Variation ◽

Ad Hoc ◽

Model Performance ◽

Technical Note ◽

Mean Flow ◽

Model Adequacy ◽

Robust Model ◽

The Mean ◽

Adequacy Assessment

Abstract. A traditional metric used in hydrology to summarize model performance is the Nash–Sutcliffe efficiency (NSE). Increasingly an alternative metric, the Kling–Gupta efficiency (KGE), is used instead. When NSE is used, NSE = 0 corresponds to using the mean flow as a benchmark predictor. The same reasoning is applied in various studies that use KGE as a metric: negative KGE values are viewed as bad model performance, and only positive values are seen as good model performance. Here we show that using the mean flow as a predictor does not result in KGE = 0, but instead KGE =1-√2≈-0.41. Thus, KGE values greater than −0.41 indicate that a model improves upon the mean flow benchmark – even if the model's KGE value is negative. NSE and KGE values cannot be directly compared, because their relationship is non-unique and depends in part on the coefficient of variation of the observed time series. Therefore, modellers who use the KGE metric should not let their understanding of NSE values guide them in interpreting KGE values and instead develop new understanding based on the constitutive parts of the KGE metric and the explicit use of benchmark values to compare KGE scores against. More generally, a strong case can be made for moving away from ad hoc use of aggregated efficiency metrics and towards a framework based on purpose-dependent evaluation metrics and benchmarks that allows for more robust model adequacy assessment.

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