### When to avoid a static solver in oceanographic moorings

**Originally published on dsaocean.com**

It was when the traffic light turned green, and my car lurched forward from a stop when it happened. A warning light flickered on the dash, but then quickly turned off again. Fortunately for me, it wasn’t a sign of disaster with the engine – it was just a light indicating more window washer fluid was needed. But the warning light wasn’t on all the time – yet.

Now, it’s right at this stage that I turn into Mr. Scrooge with my window washer fluid. The little bit left in the tank is sloshing around, and I know if I use one tiny spritz more to clean my windshield, the light will stay on. And if the light stays on? Well, it’s another problem I need to solve on my long to-do list! So my short term solution? Never clean the windshield. It may seem counterintuitive because that’s exactly what washer fluid is supposed to be for – cleaning my windshield. But instead, I completely avoid it.

Likewise, there’s some things I also completely avoid in mooring analysis. In particular, when we’re looking for a static mooring profile, it may seem counterintuitive to avoid using a static solver. But there’s good reason to avoid them in some circumstances. In this article, we’re going to focus on when to avoid using a static solver and what to do instead.

### A static solver can mean many different things depending on the problem you’re trying to solve

In the case of mooring analysis, one problem we’re trying to solve is to find the static deflection of a mooring system to steady loads. Most often, these steady loads are from effects like ocean currents and wind. In the case of mooring design, this is what we mean by a static solver.

### A static solver is a great tool to have

Ideally, they work quickly to give you a solution that shows what the mooring deflection looks like to specific steady loads. These static solvers compute the tensions in the mooring lines, too. This feedback is really helpful in the early stages of the mooring system’s design, so you can narrow down the materials and concepts to find something workable.

Often, you may need to screen mooring designs to make sure the deflection isn’t too high and check the lines are strong enough to handle the loads. But timelines are often tight in these projects. So getting to the next step in mooring design in short order is crucial.

### Finding a static mooring deflection may sound like a straightforward problem

But it can be tricky depending on the complexity of the mooring system. Because of this complexity, there’s no single static solver algorithm that’s useful for all mooring systems. Ultimately though, there’s a common idea behind these static solvers. The idea is that they look for a mooring configuration in which the external forces, such as those from ocean currents and wind, are in balance with the internal forces, such as the mooring tensions.

As a static solver goes through a solution process, it can make large jumps to test what the mooring profile looks like. These jumps aren’t random. But they certainly do depend on how the forces are balanced between the environmental effects and the mooring loads. These jumps are a static solver’s greatest advantage: when they work well, they jump instantly to the right solution! But then sometimes they also struggle. When they struggle, it looks like they jump around and around a potential solution, but never quite land on one. Or, in some circumstances, there just may not be any solution at all.

### It’s when static solvers struggle that they lose their advantage of speed

Suddenly, the static solver process is churning away, but just not getting anywhere. It can take a long time to process, whirring away on calculations, and never end up with anything useful. We call this a failure to converge to a solution. Suddenly, the trusty tool that quickly got you to the next step has betrayed you!

### Now what do you do?

One alternative is dynamic relaxation. Dynamic relaxation is a very simple and direct approach, and there’s only a few steps. First, you start with a basic crude guess for the mooring system layout. This crude guess might look like diagonal straight lines from the anchor to the fairlead. Next, you simply run a dynamic analysis solver to let the system respond dynamically to steady forces from ocean currents and winds. The mooring system “relaxes” and deflects naturally to its steady state configuration.

The advantage here is that it’s a typically very robust approach: there’s no guessing about mooring profiles – it evolves a realistic deflection of the mooring over time and eventually to a steady state profile.

### Why don’t we use dynamic relaxation all the time?

It all has to do with time. Unfortunately, dynamic relaxation can be quite slow! The longer the mooring lines and the deeper the water, and the lower the forces involved, the longer it takes to relax and settle to a steady state profile. A full ocean depth mooring might take over 24 hours to compute a steady state profile by dynamic relaxation – but only a few minutes for a static solver. So when do you want to use dynamic relaxation?

### It’s hard to know when to use dynamic relaxation ahead of time

But there are a few guidelines you can keep in mind. Generally, what you need to keep your eyes peeled for are strong forces or abrupt changes in the environmental effects. This might look like a very severe shear profile in the ocean current, or perhaps an abruptly varying sea bottom. But one of the most common effects you’ll see is the effect of shallow water. In shallow water, small changes in mooring deflection can mean big changes in forces acting on the mooring – from buoyancy if the lines come out of the water, or ground contact if they touch the seabed.

This is where those jumps that static solvers make in guessing the mooring profile can run into problems. It can take a long time to settle and often you may find it fails to converge to a solution. But the good news is that dynamic relaxation can really shine in shallow water conditions. After all, often, mooring lines are shorter in shallow water. It doesn’t take much time for a mooring to deflect a short distance and reach a steady state.

### Wait a minute. What do you mean by shallow water?

It’s one of those grey areas. There isn’t an exact answer. But fortunately, it’s often easy to try both techniques in parallel – static solver and dynamic relaxation – so really it’s up to you to learn what works. I think you will find that there is a range where one works better, and a range where they both work OK, too.

### No really, can you give me a specific water depth?

Ok. Fine. For oceanographic moorings, I would suggest definitely trying dynamic relaxation if your mooring is in less than 100m of water depth. But again, it’s ultimately up to you to judge what works best for your specific problem.

### Let’s look at an example

The CURBY (CURents BuoY) is a shallow water mooring deployed in the Delaware River. It’s certainly shallow at just over 10m depth. But the currents can rip through there fairly quick. The mooring is a simple design with a surface buoy and a few different sizes of chain along the span. In this example, the ProteusDS static solver struggles to find a solution in certain environmental conditions. But the shallow water is so short, that a dynamic relaxation finds a solution in only about 20 seconds of simulation in a strong current.

### It’s time for a summary

We covered a fair bit on static mooring solutions, so now it’s time to review. There are many different techniques that may be used in static solver algorithms. It’s common for them to use an iterative approach that jumps to a solution, continually seeking a balance of internal tensions with external environmental loads from ocean currents and winds. But sometimes they just don’t work. When they don’t work, either they take way too long or fail entirely to reach a solution. You may find this when there are big discontinuities in the environment, like a very strong current shear, or a shallow water depth. In these cases, you may consider dynamic relaxation as an alternative.

Dynamic relaxation is a process that uses a dynamic solver that lets the system evolve through time from the effects of constant loads. While it’s often much slower than static solvers, in shallow water conditions, it should be plenty speedy – and at least there are no problems like failing to converge. Think about using dynamic relaxation in 100m water depth or less – but always be sure to judge for yourself what works best.

You may not be as annoyed as me when the window washer fluid light goes on. Of course, it seems counter intuitive to avoid using the window washer in your car. In a similar way, avoiding static solvers in mooring design may seem counter intuitive. But fortunately, there are only a few circumstances in which you need to use a workaround.

### Next step

Check out this video tutorial that shows an example of what it looks like to skip the static mooring analysis process in ProteusDS for a shallow water mooring here.

### Thanks to NOAA CO-OPS

Thanks to Laura Fiorentino from NOAA CO-OPS for sharing technical pointers and data for the CURBY mooring for the example.