Steady Wind Forcing Research Articles

Numerical investigation on hopf bifurcation problem for nonlinear dynamics of a towed vessel in calm water and waves

In this study, the Hopf bifurcation problem with regard to the nonlinear dynamics of a towed vessel was numerically investigated. A time-domain simulation method based on three degrees-of-freedom maneuvering equations of motion was applied to study the nonlinear dynamic responses of a towed vessel in calm water, wind and waves. In the towing operation, it is assumed that a vessel is passively towed by a tug via a towline with a constant towing speed following a straight line. In the case of wind or wave conditions, the steady wind or wave drift forces are considered as additional external force components. The hydrodynamic forces acting on the towed vessel are modeled as a modular-type hull force model, and the towline force is simply modeled as a linear spring. First, for the validation, the motion trajectories of the towed vessel were compared between the experimental data and numerical simulation results under the calm water condition. Discussions are provided on the effect of skegs on the dynamics of the towed vessel and related Hopf bifurcation according to the skeg size. Next, the wind speed was changed, and the resulting limit cycles were studied. It can be observed that the Hopf bifurcation can be delayed according to the wind speed and direction. Finally, the dynamic characteristics of the towed vessel in regular waves were investigated via numerical simulations. The stability of the towed vessel with no skegs increases owing to the mean wave drift forces for both the model test and numerical simulation. The effects of the wave height and period on the Hopf bifurcation were studied based on numerical simulations. It was found that the occurrence of Hopf bifurcation for nonlinear dynamics of a towed vessel is sensitive to the conditions of wave height and period.

Spatially evolving regular water wave under the action of steady wind forcing

The spectra plotted in this work demonstrate suppression of random wind-generated waves by a deterministic long wavemaker-generated wave in a moderately sized wind-wave facility. Experiments performed for a wide range of experimental conditions show that the effect of a regular wave on the local wind-wave field excited by steady wind remains essential as long as the local dominant frequency of random wind waves remains below that of the regular waves.

Effects of Adding Forced Near-Inertial Motion to a Wind-Driven Channel Flow

AbstractAn eddy-resolving primitive equation ocean model is used to examine energy transfers between frequency bands. Steady wind forcing is used to drive a geostrophic channel to which high-frequency winds are added. This excites near-inertial motion, which exerts a Reynolds stress on the slowly varying flow and acts to transfer kinetic energy between low and high frequencies. These transfers extract balanced energy primarily from the mesoscale. A frequency analysis of the transfers shows the bulk of the energy to be extracted from an intermediate range of frequencies that are large relative to the dominant kinetic energy–containing frequencies and small relative to the spectral gap separating high- and low-frequency bands. This phenomenon is robust and is found in systems spanning two orders of magnitude of kinetic energy. Direct calculation of potential energy transfers proved more difficult but nonetheless shows a similar low-to-high frequency transfer. For the parameter range considered, the ratio of potential-to-kinetic energy transfers is slightly larger than unity, and as such is consistent with balanced energy being extracted from horizontal scales that are somewhat larger than the relevant deformation radius.

Equatorial Deep Jets and Their Influence on the Mean Equatorial Circulation in an Idealized Ocean Model Forced by Intraseasonal Momentum Flux Convergence

AbstractEquatorial deep jets (EDJ) are vertically stacked, downward propagating zonal currents that alternate in direction with depth. In the tropical Atlantic, they have been shown to influence both surface conditions and tracer variability. Despite their importance, the EDJ are absent in most ocean models. Here we show that EDJ can be generated in an idealized ocean model when the model is driven only by the convergence of the meridional flux of intraseasonal zonal momentum diagnosed from a companion model run driven by steady wind forcing, corroborating the recent theory that intraseasonal momentum flux convergence maintains the EDJ. Additionally, the EDJ in our model nonlinearly generate mean zonal currents at intermediate depths that show similarities in structure to the observed circulation in the deep equatorial Atlantic, indicating their importance for simulating the tropical ocean mean state.

Time-varying storm surges on Lorentz\u2019s Wadden Sea networks

We present an idealized network model for storm surges in the Wadden Sea, specifically including a time-dependent wind forcing (wind speed and direction). This extends the classical work by H.A. Lorentz who only considered the equilibrium response to a steady wind forcing. The solutions obtained in the frequency domain for the linearized shallow-water equations in a channel are combined in an algebraic system for the network. The velocity scale that is used for the linearized friction coefficient is determined iteratively. The hindcast of the storm surge of 5 December 2013 produces credible time-varying results. The effects of storm and basin parameters on the peak surge elevation are the subject of a sensitivity analysis. The formulation in the frequency domain reveals which modes in the external forcing lead to the largest surge response at coastal stations. There appears to be a minimum storm duration, of about 3–4 h, that is required for a surge to attain its maximum elevation. The influence of the water levels at the North Sea inlets on the Wadden Sea surges decreases towards the shore. In contrast, the wind shearing generates its largest response near the shore, where the fetch length is at its maximum.

South China Sea Wave Characteristics under Combined Wind Forcing of Typhoon and Winter Monsoon

Since monsoon winds prevail in South China Sea (SCS), SCS is unique for investigating wave characteristics during a typhoon’s passage in conjunction with steady monsoon wind forcing. This study investigated SCS wave characteristics using Wave Watch III, the third-generation wave model with winter typhoon forcing. The model was forced by a high resolution wind field from NASA’s Cross Calibrated Multi Platform (CCMP) ocean surface winds combined with the tropical cyclone wind model. The Wave Watch III model was evaluated using Jason-2 altimetry observations during the period of Typhoon Durian (2006).

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing.

This manuscript describes an experimental procedure that allows obtaining diverse quantitative information on temporal and spatial evolution of water waves excited by time-dependent and steady wind forcing. Capacitance-type wave gauge and Laser Slope Gauge (LSG) are used to measure instantaneous water surface elevation and two components of the instantaneous surface slope at a number of locations along the test section of a wind-wave facility. The computer-controlled blower provides airflow over the water in the tank whose rate can vary in time. In the present experiments, the wind speed in the test section initially increases quickly from rest to the set value. It is then kept constant for the prescribed duration; finally, the airflow is shut down. At the beginning of each experimental run, the water surface is calm and there is no wind. Operation of the blower is initiated simultaneously with the acquisition of data provided by all sensors by a computer; data acquisition continues until the waves in the tank fully decay. Multiple independent runs performed under identical forcing conditions allow determining statistically reliable ensemble-averaged characteristic parameters that quantitatively describe wind-waves' variation in time for the initial development stage as a function of fetch. The procedure also allows characterizing the spatial evolution of the wave field under steady wind forcing, as well as decay of waves in time, once the wind is shut down, as a function of fetch.

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing

Effective Fetch and Duration of Tropical Cyclone Wind Fields Estimated from Simultaneous Wind and Wave Measurements: Surface Wave and Air–Sea Exchange Computation

AbstractSimultaneous wind and wave measurements have been obtained inside tropical cyclones in several hurricane hunter missions. Analyses of these datasets show that the surface wave development inside hurricanes follows essentially the same duration- and fetch-limited growth functions established in steady wind forcing conditions. This paper explores the application of several parameterization functions of wind-wave systems to quantify the energy and momentum exchanges inside hurricanes from an initially limited input of the environmental parameters, such as the wind field alone. A critical prerequisite to applying the wind-wave growth functions is the knowledge of fetch and duration for the hurricane wind field. Four sets of simultaneous wind and wave measurements from hurricane hunter missions are analyzed to derive a fetch and duration scaling model. Time series of 2D hurricane wind fields can then be used to investigate the detailed spatial distribution and temporal evolution of the sea state parameters and the associated air–sea energy and momentum exchanges following the hurricane development.

Azimuthal and Radial Variation of Wind-Generated Surface Waves inside Tropical Cyclones

AbstractFor wind-generated waves, the wind-wave triplets (reference wind speed, significant wave height, and spectral peak wave period) are intimately connected through the fetch- or duration-limited wave growth functions. The full set of the triplets can be obtained knowing only one of the three, together with the input of fetch (duration) information using the pair of fetch-limited (duration limited) wave growth functions. The air–sea energy and momentum exchanges are functions of the wind-wave triplets, and they can be quantified with the wind-wave growth functions. Previous studies have shown that the wave development inside hurricanes follows essentially the same growth functions established for steady wind forcing conditions. This paper presents the analysis of wind-wave triplets collected inside Hurricane Bonnie 1998 at category 2 stage along 10 transects radiating from the hurricane center. A fetch model is formulated for any location inside the hurricane. Applying the fetch model to the 2D hurricane wind field, the detailed spatial distribution of the wave field and the associated energy and momentum exchanges inside the hurricane are investigated. For the case studied, the energy and momentum exchanges display two local maxima resulting from different weightings of wave age and wind speed. Referenced to the hurricane heading, the exchanges on the right half plane of the hurricane are much stronger than those on the left half plane. Integrated over the hurricane coverage area, the right-to-left ratio is about 3:1 for both energy and momentum exchanges. Computed exchange rates with and without considering wave properties differ significantly.

Pathways and mechanisms of offshore water intrusions on the Espírito Santo Basin shelf (18°S–22°S, Brazil)

AbstractThe pathways and physical mechanisms associated with intrusions of cold, nutrient‐rich South Atlantic Central Water (SACW) on the continental shelf of the Espírito Santo Basin (ESB), off southeast Brazil (18°S–22°S), are investigated. To this end, a set of process‐oriented, Primitive‐Equation (PE) numerical models are used, together with an independent and more complete PE model, available observations and simple theoretical ideas. SACW enters the model ESB shelf mostly through two preferential pathways along the Tubarão Bight (TB, 19.5°S–22°S). These pathways are found to be locations where an equatorward along‐isobath pressure gradient force (PGFy*) of m s−2) develops in response to steady wind forcing. This equatorward PGFy* is essentially in geostrophic balance, inducing onshore flow across the shelf edge, and most of the shelf proper. The Brazil Current (BC) imparts an additional periodic (in the along‐shelf direction) PGFy* on the shelf. The intrinsic pycnocline uplifting effect of the BC in making colder water available at the shelf edge is quantified. The BC also induces local intrusions by inertially overshooting the shelf edge, consistent with estimated Rossby numbers of 0.3–0.5. In addition, the planetary β‐effect is related to a background equatorward PGFy*. A modified Arrested Topographic Wave model is shown to be a plausible rationalization for the shelf‐wide spreading of the pressure field imparted by the BC at the shelf edge. The deep‐ocean processes examined here are found to enhance the onshore transport of SACW, while wind forcing is found to dominate it at leading order.

Influence of the equatorial deep jets on the north equatorial countercurrent

An ocean circulation model is run using two different idealized equatorial basin configurations under steady wind forcing. Both model versions produce bands of vertically alternating zonal flow at depth, similar to observed Equatorial Deep Jets (EDJs) and with a time scale corresponding to that of the gravest equatorial basin mode for the dominant baroclinic vertical normal mode. Both model runs show evidence for enhanced variability in the surface signature of the North Equatorial Counter Current (NECC) with the same time scale. We also find the same link between the observed NECC and the EDJs in the Atlantic by comparing the signature of the EDJ in moored zonal velocity data at 23° W on the equator with the signature of the NECC in geostrophic velocities from altimeter data. We argue that the presence of a peak in variability in the NECC associated with the EDJ basin mode period is evidence that the influenceatthis time scale is upward, from the EDJ to the NECC.

Effects of unsteady mountain‐gap winds on eddies in the Red Sea

AbstractAtmosphere and ocean simulations capture the Tokar mountain‐gap wind jet and associated eddy dipole in the Red Sea. Results suggest that, once generated by a wind event, the anticyclonic eddy is further intensified through the summer by subsequent events. An asymmetry in magnitude of the two eddies is observed with the anticyclonic eddy attaining greater magnitude. A series of simulations with idealized wind forcing show that this asymmetry is not present under steady wind forcing. This effect depends on the intermittency of the wind forcing and the presence of a background northerly wind field.

A global perspective on Langmuir turbulence in the ocean surface boundary layer

The turbulent mixing in thin ocean surface boundary layers (OSBL), which occupy the upper 100 m or so of the ocean, control the exchange of heat and trace gases between the atmosphere and ocean. Here we show that current parameterizations of this turbulent mixing lead to systematic and substantial errors in the depth of the OSBL in global climate models, which then leads to biases in sea surface temperature. One reason, we argue, is that current parameterizations are missing key surface‐wave processes that force Langmuir turbulence that deepens the OSBL more rapidly than steady wind forcing. Scaling arguments are presented to identify two dimensionless parameters that measure the importance of wave forcing against wind forcing, and against buoyancy forcing. A global perspective on the occurrence of wave‐forced turbulence is developed using re‐analysis data to compute these parameters globally. The diagnostic study developed here suggests that turbulent energy available for mixing the OSBL is under‐estimated without forcing by surface waves. Wave‐forcing and hence Langmuir turbulence could be important over wide areas of the ocean and in all seasons in the Southern Ocean. We conclude that surface‐wave‐forced Langmuir turbulence is an important process in the OSBL that requires parameterization.

Observations of Wind Wave Development in Mixed Seas and Unsteady Wind Forcing*

Abstract Theoretical study and experimental verification of wind wave generation and evolution focus generally on ideal conditions of steady state and quiescent initial background, of which the ideal fetch-limited wind wave growth is an important benchmark. In nature, unsteady winds and swell presence are more common. Here, the observations of wind wave development in mixed seas under unsteady and quasi-steady wind forcing are presented. With reference to the ideal fetch-limited growth functions established under steady wind forcing in the absence of swell, the analysis shows that the wind-steadiness factor impacts wave growth. The wind wave variance in mixed sea is enhanced in both accelerating and decelerating phases of an unsteady wind event, with a larger enhancement in the accelerating phase than in the decelerating phase. Spatial and temporal wind wave measurements under similar environmental conditions are also compared; the quantifiable differences in the wave development are attributable to the wind-steadiness factor. Coupled with the empirical observation that the average wind stress is decreased in mixed sea, these results suggest that wind wave generation and development are more efficient in mixed sea than in wind sea. Possible causes include (i) oscillatory modulation of surface roughness increases air–sea exchanges, (ii) background surface motion reduces energy waste for cold start of wind wave generation from a quiescent state, and (iii) breaking of short waves redistributes wind input and allows more of the available wind power to be directed to the longer waves for their continuous growth.

A PROBABILISTIC MODEL FOR THE DETERMINATION OF HYDRAULIC BOUNDARY CONDITIONS IN A DYNAMIC COASTAL SYSTEM

In 2011 new Hydraulic Boundary Conditions must be established for the statutory assessment of flood protection in the Wadden Sea area, which is a complex tidal system in the northern part of the Netherlands. The aim is to base these normative wave conditions on the wave simulation model SWAN and the probabilistic method Hydra-K, to be consistent with other systems as the Holland Coast and the Zeeland Delta. Assumptions made for the latter water systems, like steady state wind forcing, uniform water levels and neglect of currents, are not valid in the tidal basin of the Wadden Sea. A schematic temporal variation of both wind direction and wind speed is applied to define wind fields that drive the hydrodynamic computations. Both wind fields and resulting water level and current fields form the input of SWAN computations for a large number of combinations of basic wind speed and wind direction, offshore surge level and phase difference between tide and maximum wind speed. The result is a large database of SWAN results that is used as a look-up table in Hydra-K to transform the offshore statistics to the load on the primary sea defenses. In general the more advanced method leads to wave heights that are up to 10% lower and wave periods that are 10-20% smaller than those obtained with the method that is presently applied for the Holland Coast and the Zeeland Delta. These differences can be ascribed to the inclusion of currents and positive shoreward tilt in water level. The inclusion of relevant physics in the hydrodynamic computations increases the accuracy of the resulting HBC. Therefore, the more advanced method will be applied to determine the HBC for 2011.

A Nonlinear Theory of the Kuroshio Extension Bimodality

Abstract The Kuroshio Extension (KE) flow in the North Pacific Ocean displays a very distinctive decadal variability of bimodal character involving two completely different states (a large-meander “elongated” state and a small-meander “contracted” state) connected by very asymmetric temporal transitions. Although such a flow has been widely studied by means of a suite of mathematical models and by using several observational platforms, a satisfactory theoretical framework answering quite elementary questions is still lacking, the main question being whether such variability is induced by a time-varying wind forcing or, rather, by intrinsic oceanic mechanisms. In this context, the chaotic relaxation oscillation produced by a process-oriented model of the KE low-frequency variability, with steady climatological wind forcing, was recently recognized to be in substantial agreement with altimeter data. Here those model results are further compared with a comprehensive altimeter dataset. The positive result of such a comparison allows the conclusion that a minimal model for the KE bimodality has been identified and that, consequently, nonlinear intrinsic oceanic mechanisms are likely to be the main cause of the observed variability. By applying the methods of nonlinear dynamical systems theory, relevant dynamical features of the modeled flow are then explained, such as the origin of the relaxation oscillation as a consequence of a homoclinic bifurcation, the spatiotemporal character of the bimodal behavior, and the degree of predictability of the flow in the different stages of the oscillation (evaluated through a field of finite-time Lyapunov exponents and the corresponding Lagrangian time series).

The role of numerical implementation on open boundary behaviour in limited area ocean models

Applying open boundary conditions to the primitive equations in regional ocean domains presents many challenges. The response of the model domain interior may be sensitive to the choice of open boundary condition (OBC), and the performance of the OBC itself may be dependent on the method of its implementation, the physics of the problem under investigation and the type of model used. There have been many assessments of OBCs in the literature, but little dedicated assessment of model performance with respect to the implementation method of the open boundary has been provided. This study assesses open boundary performance in terms of the cell location where normal velocity is implemented for a variety of test cases. Specifically, a ‘normal velocity outside elevation’ node location (NVOE) was assessed, where normal velocity occupies the out-most boundary cell face, and a ‘normal velocity inside elevation’ node location (NVIE) where normal velocity occupies the cell face interior to the boundary cell centre. These implementations were evaluated for steady wind forcing, barotropic relaxation, forced waves of tidal period and a travelling storm on a simple test domain. Results show that different implementations of the same boundary condition result in different model behaviour. Both the open boundary condition and its implementation should be chosen so as be compatible with the dominant physics of the problem at hand.

Numerical prediction of MODUs drift during Hurricane Katrina

Severe hurricanes, such as Katrina, broke the mooring lines of a number of mobile offshore drilling units (MODU) deployed in the Gulf of Mexico and some of those MODUs went adrift. A drifting MODU may damage other critical elements of the offshore oil and gas infrastructure by colliding with floating or fixed production systems and transportation hubs, or by rupturing pipelines owing to their dragging anchors over the seabed. To avoid or mitigate the damage caused by a drifting MODU, it is desirable to understand the mechanics of the drift of a MODU under the impact of severe wind, wave and current and have the capability of predicting the trajectory of the drift. To explore the feasibility and accuracy of predicting the trajectory of a drifting MODU based on hindcast met-ocean conditions and limited knowledge of the condition of the drifting MODU, this study employed a simplified equation describing only the horizontal (surge, sway and yaw) motions of a MODU under the impact of steady wind, current and wave forces. The simplified hydrodynamic model neglects the first- and second-order oscillatory wave forces, unsteady wind forces (owing to wind gustiness), wave drift damping, and the effects of the body oscillation on the steady wind and current forces. It was assumed that the net effects of the oscillatory forces on the steady motion are insignificant. To verify the accuracy and feasibility of our simplified approach, the predicted drifting trajectories of two MODUs were compared with the corresponding measurements recorded by the global positioning system (GPS).

South China Sea wave characteristics during typhoon Muifa passage in winter 2004

The responses to tropical cyclones of ocean wave characteristics in deep water of the western Atlantic Ocean have been investigated extensively, but not the regional seas in the western Pacific such as the South China Sea (SCS), due to a lack of observational and modeling studies there. Since monsoon winds prevail in the SCS but not in the western Atlantic Ocean, the SCS is unique for investigating wave characteristics during a typhoon’s passage in conjunction with steady monsoon wind forcing. To do so, the Wavewatch-III (WW3) is used to study the response of the SCS to Typhoon Muifa (2004), which passed over not only deep water but also the shallow shelf of the SCS. The WW3 model is forced by the NASA QuikSCAT winds and tropical cyclone wind profile model during Typhoon Muifa’s passage from 0000UTC 16 on November to 1200UTC on 25 November 2004. The results reveal the unique features of the SCS wave characteristics in response to Muifa, such as non-decaying, monsoon-generated swell throughout the typhoon period and strong topographic effects on the directional wave spectrum.