scholarly journals Parameterizing non-propagating form drag over rough bathymetry

2021 ◽  
Author(s):  
Jody M. Klymak ◽  
Dhruv Balwada ◽  
Alberto Naveira Garabato ◽  
Ryan Abernathey
Keyword(s):  
Mesoscale Eddy ◽  
Low Frequency ◽  
Wave Drag ◽  
Linear Wave ◽  
Internal Motions ◽  
Quadratic Drag ◽  
Non Linear ◽  
Linear Drag ◽  
Drag Law ◽  
Work Done

AbstractSlowly-evolving stratified flow over rough topography is subject to substantial drag due to internal motions, but often numerical simulations are carried out at resolutions where this “wave” drag must be parameterized. Here we highlight the importance of internal drag from topography with scales that cannot radiate internal waves, but may be highly non-linear, and we propose a simple parameterization of this drag that has a minimum of fit parameters compared to existing schemes. The parameterization smoothly transitions from a quadratic drag law () for low- (linear wave dynamics) to a linear drag law () for high- flows (non-linear blocking and hydraulic dynamics), where N is the stratification, h is the height of the topography, and u0 is the near-bottom velocity; the parameterization does not have a dependence on Coriolis frequency. Simulations carried out in a channel with synthetic bathymetry and steady body forcing indicate that this parameterization accurately predicts drag across a broad range of forcing parameters when the effect of reduced near-bottom mixing is taken into account by reducing the effective height of the topography. The parameterization is also tested in simulations of wind-driven channel flows that generate mesoscale eddy fields, a setup where the downstream transport is sensitive to the bottom drag parameterization and its effect on the eddies. In these simulations, the parameterization replicates the effect of rough bathymetry on the eddies. If extrapolated globally, the sub-inertial topographic scales can account for 2.7 TW of work done on the low-frequency circulation, an important sink that is redistributed to mixing in the open ocean.

On Quadratic Bottom Drag, Geostrophic Turbulence, and Oceanic Mesoscale Eddies

2008 ◽  
Vol 38 (1) ◽  
pp. 84-103 ◽  
Author(s):  
Brian K. Arbic ◽  
Robert B. Scott
Keyword(s):  
Mesoscale Eddy ◽  
Wave Drag ◽  
Ocean Model ◽  
Strength Parameter ◽  
Altimeter Data ◽  
Mean Flow ◽  
Quadratic Drag ◽  
Linear Drag ◽  
Geostrophic Turbulence ◽  
Satellite Altimeter Data

Abstract Many investigators have idealized the oceanic mesoscale eddy field with numerical simulations of geostrophic turbulence forced by a horizontally homogeneous, baroclinically unstable mean flow. To date such studies have employed linear bottom Ekman friction (hereinafter, linear drag). This paper presents simulations of two-layer baroclinically unstable geostrophic turbulence damped by quadratic bottom drag, which is generally thought to be more realistic. The goals of the paper are 1) to describe the behavior of quadratically damped turbulence as drag strength changes, using previously reported behaviors of linearly damped turbulence as a point of comparison, and 2) to compare the eddy energies, baroclinicities, and horizontal scales in both quadratic and linear drag simulations with observations and to discuss the constraints these comparisons place on the form and strength of bottom drag in the ocean. In both quadratic and linear drag simulations, large barotropic eddies develop with weak damping, large equivalent barotropic eddies develop with strong damping, and the comparison in goal 2 above is closest when the nondimensional friction strength parameter is of order 1. Typical values of the quadratic drag coefficient (cd ∼ 0.0025) and of boundary layer depths (Hb ∼ 50 m) imply that the quadratic friction strength parameter cdLd/Hb, where Ld is the deformation radius, may indeed be of order 1 in the ocean. Model eddies are realistic over a wider range of friction strengths when drag is quadratic, because of a reduced sensitivity to friction strength in that case. The quadratic parameter is independent of the mean shear, in contrast to the linear parameter. Plots of eddy length scales, computed from satellite altimeter data, versus mean shear and versus rough estimates of the friction strength parameters suggest that both linear and quadratic bottom drag may be active in the ocean. Topographic wave drag contains terms that are linear in the bottom flow, thus providing some justification for the use of linear bottom drag in models.

Measurements of Form and Frictional Drags over a Rough Topographic Bank

2014 ◽  
Vol 44 (9) ◽  
pp. 2409-2432 ◽  
Author(s):  
H. W. Wijesekera ◽  
E. Jarosz ◽  
W. J. Teague ◽  
D. W. Wang ◽  
D. B. Fribance ◽  
...  
Keyword(s):  
Drag Coefficient ◽  
Low Frequency ◽  
Multiple Time ◽  
Linear Wave ◽  
Frictional Drag ◽  
Form Drag ◽  
Quadratic Drag ◽  
Roughness Elements ◽  
Roughness Lengths ◽  
Surface Generate

Abstract Pressure differences across topography generate a form drag that opposes the flow in the water column, and viscous and pressure forces acting on roughness elements of the topographic surface generate a frictional drag on the bottom. Form drag and bottom roughness lengths were estimated over the East Flower Garden Bank (EFGB) in the Gulf of Mexico by combining an array of bottom pressure measurements and profiles of velocity and turbulent kinetic dissipation rates. The EFGB is a coral bank about 6 km wide and 10 km long located at the shelf edge that rises from 100-m water depth to about 18 m below the sea surface. The average frictional drag coefficient over the entire bank was estimated as 0.006 using roughness lengths that ranged from 0.001 cm for relatively smooth portions of the bank to 1–10 cm for very rough portions over the corals. The measured form drag over the bank showed multiple time-scale variability. Diurnal tides and low-frequency motions with periods ranging from 4 to 17 days generated form drags of about 2000 N m−1 with average drag coefficients ranging between 0.03 and 0.22, which are a factor of 5–35 times larger than the average frictional drag coefficient. Both linear wave and quadratic drag laws have similarities with the observed form drag. The form drag is an important flow retardation mechanism even in the presence of the large frictional drag associated with coral reefs and requires parameterization.

Generation of surf beat by non-linear wave interactions

1971 ◽  
Vol 49 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Brent Gallagher
Keyword(s):  
Gravity Waves ◽  
Numerical Evaluation ◽  
Low Frequency ◽  
Linear Wave ◽  
Transfer Energy ◽  
Wave Interactions ◽  
Frequency Spectra ◽  
Non Linear ◽  
Linear Interactions ◽  
Low Frequency Waves

Non-linear interactions among wind-generated gravity waves transfer energy to low frequency waves in a coastal zone. A transfer function is derived for a straight coastline of constant bottom slope. This model is applied to three actual cases, and numerical evaluation of the energy transfer produces low frequency spectra which are compared with observations.

scholarly journals The Control of Surface Friction on the Scales of Baroclinic Eddies in a Homogeneous Quasigeostrophic Two-Layer Model

2019 ◽  
Vol 76 (6) ◽  
pp. 1627-1643 ◽  
Author(s):  
Chiung-Yin Chang ◽  
Isaac M. Held
Keyword(s):  
Lower Layer ◽  
Homogeneous Model ◽  
Surface Friction ◽  
Inverse Cascade ◽  
Inverse Energy Cascade ◽  
Quadratic Drag ◽  
Ideal System ◽  
Linear Drag ◽  
Quasigeostrophic Model ◽  
Drag Law

Abstract In idealized models of the extratropical troposphere, both β and surface friction can control the equilibrated scales of baroclinic eddies by stopping the inverse cascade. A scaling theory on how surface friction alone sets these scales was proposed by Held in 1999 in the case of a quadratic drag law. However, the theory breaks down when friction is modeled by linear damping, and there are other reasons to suspect that it is oversimplified. An ideal system to test the theory is the homogeneous two-layer quasigeostrophic model in the β = 0 limit with quadratic damping. This study investigates some numerical simulations of the model to analyze two causes of the theory’s breakdown. They are 1) the asymmetry between two layers due to confinement of friction to the lower layer and 2) deviation from a spectrally local inverse energy cascade due to the spread of wavenumbers over which energy is input into the barotropic mode. The former is studied by comparing the simulations with drag appearing asymmetrically or symmetrically between the two layers. The latter is addressed with a heuristic modification of the theory. A regime where eddies equilibrate without an inverse cascade is also examined. A comparison is then made between quadratic and linear drag simulations. The connection to a competing theory based on the dynamics of equivalent barotropic vortices with thermal signatures is further discussed. Finally, we present an example of an inhomogeneous statistically steady state to argue that the diffusivity obtained from the homogeneous model has relevance to more realistic configurations.

Measurement of Tidal Form Drag Using Seafloor Pressure Sensors

2013 ◽  
Vol 43 (6) ◽  
pp. 1150-1172 ◽  
Author(s):  
Sally J. Warner ◽  
Parker MacCready ◽  
James N. Moum ◽  
Jonathan D. Nash
Keyword(s):  
Bluff Body ◽  
Unit Length ◽  
Puget Sound ◽  
Pressure Sensors ◽  
Wave Drag ◽  
Linear Wave ◽  
Bottom Pressure ◽  
Form Drag ◽  
Seafloor Pressure ◽  
Drag Law

Abstract As currents flow over rough topography, the pressure difference between the up- and downstream sides results in form drag—a force that opposes the flow. Measuring form drag is valuable because it can be used to estimate the loss of energy from currents as they interact with topography. An array of bottom pressure sensors was used to measure the tidal form drag on a sloping ridge in 200 m of water that forms a 1-km headland at the surface in Puget Sound, Washington. The form drag per unit length of the ridge reached 1 × 104 N m−1 during peak flood tides. The tidally averaged power removed from the tidal currents by form drag was 0.2 W m−2, which is 30 times larger than power losses to friction. Form drag is best parameterized by a linear wave drag law as opposed to a bluff body drag law because the flow is stratified and both internal waves and eddies are generated on the sloping topography. Maximum turbulent kinetic energy dissipation rates of 5 × 10−5 W kg−1 were measured with a microstructure profiler and are estimated to account for 25%–50% of energy lost from the tides. This study is among the first to measure form drag directly using bottom pressure sensors. The measurement and analysis techniques presented here are suitable for periodically reversing flows because they require the removal of a time-mean signal. The advantage of this technique is that it delivers a continuous record of form drag and is much less ship intensive compared to previous methods for estimation of the bottom pressure field.

Non-Linear Wave Forces Acting on a Body of Arbitrary Shape Slowly Oscillating in Waves

2005 ◽  
Author(s):  
Yasunori Nihei ◽  
Takeshi Kinoshita ◽  
Weiguang Bao
Keyword(s):  
Low Frequency ◽  
The Body ◽  
Coordinate Frame ◽  
Wave Forces ◽  
Linear Wave ◽  
Wave Loads ◽  
Low Frequency Oscillation ◽  
Wave Drift ◽  
Non Linear ◽  
Low Frequency Motion

In the present study, non-linear wave loads such as the wave drift force, wave drift damping and wave drift added mass, acting on a moored body is evaluated based on the potential theory. The body is oscillating at a low frequency under the non-linear excitation of waves. The problem of interaction between the low-frequency oscillation of the body and ambient wave fields is considered. A moving coordinate frame following the low frequency motion is adopted. Two small parameters, which measure the wave slope and the frequency of slow oscillations (compared with the wave frequency) respectively, are used in the perturbation analysis. So obtained boundary value problems for each order of potentials are solved by means of the hybrid method. The fluid domain is divided into two regions by an virtual circular cylinder surrounding the body. Different approaches, i.e. boundary element method and eigen-function expansion, are applied to these two regions. Calculated nonlinear wave loads are compared to the semi-analytical results to validate the present method.

New Methods to Solve High Order Potential Used in Calculating Non-Linear Wave Loads

2006 ◽  
Author(s):  
Yasunori Nihei ◽  
Weiguang Bao ◽  
Takeshi Kinoshita
Keyword(s):  
Perturbation Expansion ◽  
Low Frequency ◽  
The Body ◽  
Body Motion ◽  
Moving Frame ◽  
Linear Wave ◽  
Wave Loads ◽  
Wave Drift ◽  
Non Linear ◽  
Low Frequency Motion

In the present study, non-linear wave loads such as the wave-drift force, wave-drift damping and wave-drift added mass, acting on the body is considered based on the potential theory. To investigate non-linear wave loads, consistent perturbation expansion by means of two small parameters, i.e. the incident wave slope and the low frequency body motion, is performed on a moving frame (body-fixed) coordinate system. To avoid complicated free surface integrals as much as possible, new approach for the higher order potential in the interaction problem of low frequency motion and waves is suggested in the present work. Instead of integrals, derivative operators are defined to obtain special solutions efficiently.

scholarly journals Coordination of multiple appendages in drag-based swimming

2010 ◽  
Vol 7 (52) ◽  
pp. 1545-1557 ◽  
Author(s):  
Silas Alben ◽  
Kevin Spears ◽  
Stephen Garth ◽  
David Murphy ◽  
Jeannette Yen
Keyword(s):  
Fixed Time ◽  
Power Stroke ◽  
Long Distance ◽  
Velocity Amplitude ◽  
Quadratic Drag ◽  
Locomotory Performance ◽  
Recovery Stroke ◽  
Drag Law ◽  
Work Done ◽  
Average Body

Krill are aquatic crustaceans that engage in long distance migrations, either vertically in the water column or horizontally for 10 km (over 200 000 body lengths) per day. Hence efficient locomotory performance is crucial for their survival. We study the swimming kinematics of krill using a combination of experiment and analysis. We quantify the propulsor kinematics for tethered and freely swimming krill in experiments, and find kinematics that are very nearly metachronal. We then formulate a drag coefficient model which compares metachronal, synchronous and intermediate motions for a freely swimming body with two legs. With fixed leg velocity amplitude, metachronal kinematics give the highest average body speed for both linear and quadratic drag laws. The same result holds for five legs with the quadratic drag law. When metachronal kinematics is perturbed towards synchronous kinematics, an analysis shows that the velocity increase on the power stroke is outweighed by the velocity decrease on the recovery stroke. With fixed time-averaged work done by the legs, metachronal kinematics again gives the highest average body speed, although the advantage over synchronous kinematics is reduced.

scholarly journals Non-linear Terahertz driving of plasma waves in layered cuprates

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Francesco Gabriele ◽  
Mattia Udina ◽  
Lara Benfatto
Keyword(s):  
Low Frequency ◽  
Plasma Waves ◽  
Meissner Effect ◽  
High Energy ◽  
Plasma Mode ◽  
Light Pulses ◽  
High Frequency Plasma ◽  
Non Linear ◽  
Out Of Plane ◽  
Layered Cuprates

AbstractThe hallmark of superconductivity is the rigidity of the quantum-mechanical phase of electrons, responsible for superfluid behavior and Meissner effect. The strength of the phase stiffness is set by the Josephson coupling, which is strongly anisotropic in layered cuprates. So far, THz light pulses have been used to achieve non-linear control of the out-of-plane Josephson plasma mode, whose frequency lies in the THz range. However, the high-energy in-plane plasma mode has been considered insensitive to THz pumping. Here, we show that THz driving of both low-frequency and high-frequency plasma waves is possible via a general two-plasmon excitation mechanism. The anisotropy of the Josephson couplings leads to markedly different thermal effects for the out-of-plane and in-plane response, linking in both cases the emergence of non-linear photonics across Tc to the superfluid stiffness. Our results show that THz light pulses represent a preferential knob to selectively drive phase excitations in unconventional superconductors.

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